The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

Maxis-A rezoning and remapping code in two dimensional cylindrical geometry

NASA Astrophysics Data System (ADS)

Lin, Zhiwei; Jiang, Shaoen; Zhang, Lu; Kuang, Longyu; Li, Hang

2018-06-01

This paper presents the new version of our code Maxis (Lin et al., 2011). Maxis is a local rezoning and remapping code in two dimensional cylindrical geometry, which can be employed to address the grid distortion problem of unstructured meshes. The new version of Maxis is mostly programmed in the C language which considerably improves its computational efficiency with respect to the former Matlab version. A new algorithm for determining the intersection of two arbitrary convex polygons is also incorporated into the new version. Some additional linking functions are further provided in the new version for the purpose of combining Maxis and MULTI2D.

A computational method for sharp interface advection.

PubMed

Roenby, Johan; Bredmose, Henrik; Jasak, Hrvoje

2016-11-01

We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists of two parts. First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step. Second, from the reconstructed surface, we model the motion of the face-interface intersection line for a general polygonal face to obtain the time evolution within a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total volume of fluid transported across the face. The method was tested on simple two-dimensional and three-dimensional interface advection problems on both structured and unstructured meshes. The results are very satisfactory in terms of volume conservation, boundedness, surface sharpness and efficiency. The isoAdvector method was implemented as an OpenFOAM ® extension and is published as open source.

Perceptually stable regions for arbitrary polygons.

PubMed

Rocha, J

2003-01-01

Zou and Yan have recently developed a skeletonization algorithm of digital shapes based on a regularity/singularity analysis; they use the polygon whose vertices are the boundary pixels of the image to compute a constrained Delaunay triangulation (CDT) in order to find local symmetries and stable regions. Their method has produced good results but it is slow since its complexity depends on the number of contour pixels. This paper presents an extension of their technique to handle arbitrary polygons, not only polygons of short edges. Consequently, not only can we achieve results as good as theirs for digital images, but we can also compute skeletons of polygons of any number of edges. Since we can handle polygonal approximations of figures, the skeletons are more resilient to noise and faster to process.

A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of themore » method with respect to the plate thickness.« less

A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-10-04

We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of themore » method with respect to the plate thickness.« less

Numerical calculation of listener-specific head-related transfer functions and sound localization: Microphone model and mesh discretization

PubMed Central

Ziegelwanger, Harald; Majdak, Piotr; Kreuzer, Wolfgang

2015-01-01

Head-related transfer functions (HRTFs) can be numerically calculated by applying the boundary element method on the geometry of a listener’s head and pinnae. The calculation results are defined by geometrical, numerical, and acoustical parameters like the microphone used in acoustic measurements. The scope of this study was to estimate requirements on the size and position of the microphone model and on the discretization of the boundary geometry as triangular polygon mesh for accurate sound localization. The evaluation involved the analysis of localization errors predicted by a sagittal-plane localization model, the comparison of equivalent head radii estimated by a time-of-arrival model, and the analysis of actual localization errors obtained in a sound-localization experiment. While the average edge length (AEL) of the mesh had a negligible effect on localization performance in the lateral dimension, the localization performance in sagittal planes, however, degraded for larger AELs with the geometrical error as dominant factor. A microphone position at an arbitrary position at the entrance of the ear canal, a microphone size of 1 mm radius, and a mesh with 1 mm AEL yielded a localization performance similar to or better than observed with acoustically measured HRTFs. PMID:26233020

A computational method for sharp interface advection

PubMed Central

Bredmose, Henrik; Jasak, Hrvoje

2016-01-01

We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists of two parts. First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step. Second, from the reconstructed surface, we model the motion of the face–interface intersection line for a general polygonal face to obtain the time evolution within a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total volume of fluid transported across the face. The method was tested on simple two-dimensional and three-dimensional interface advection problems on both structured and unstructured meshes. The results are very satisfactory in terms of volume conservation, boundedness, surface sharpness and efficiency. The isoAdvector method was implemented as an OpenFOAM® extension and is published as open source. PMID:28018619

Progressive simplification and transmission of building polygons based on triangle meshes

NASA Astrophysics Data System (ADS)

Li, Hongsheng; Wang, Yingjie; Guo, Qingsheng; Han, Jiafu

2010-11-01

Digital earth is a virtual representation of our planet and a data integration platform which aims at harnessing multisource, multi-resolution, multi-format spatial data. This paper introduces a research framework integrating progressive cartographic generalization and transmission of vector data. The progressive cartographic generalization provides multiple resolution data from coarse to fine as key scales and increments between them which is not available in traditional generalization framework. Based on the progressive simplification algorithm, the building polygons are triangulated into meshes and encoded according to the simplification sequence of two basic operations, edge collapse and vertex split. The map data at key scales and encoded increments between them are stored in a multi-resolution file. As the client submits requests to the server, the coarsest map is transmitted first and then the increments. After data decoding and mesh refinement the building polygons with more details will be visualized. Progressive generalization and transmission of building polygons is demonstrated in the paper.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duchaineau, M.; Wolinsky, M.; Sigeti, D.E.

Real-time terrain rendering for interactive visualization remains a demanding task. We present a novel algorithm with several advantages over previous methods: our method is unusually stingy with polygons yet achieves real-time performance and is scalable to arbitrary regions and resolutions. The method provides a continuous terrain mesh of specified triangle count having provably minimum error in restricted but reasonably general classes of permissible meshes and error metrics. Our method provides an elegant solution to guaranteeing certain elusive types of consistency in scenes produced by multiple scene generators which share a common finest-resolution database but which otherwise operate entirely independently. Thismore » consistency is achieved by exploiting the freedom of choice of error metric allowed by the algorithm to provide, for example, multiple exact lines-of-sight in real-time. Our methods rely on an off-line pre-processing phase to construct a multi-scale data structure consisting of triangular terrain approximations enhanced ({open_quotes}thickened{close_quotes}) with world-space error information. In real time, this error data is efficiently transformed into screen-space where it is used to guide a greedy top-down triangle subdivision algorithm which produces the desired minimal error continuous terrain mesh. Our algorithm has been implemented and it operates at real-time rates.« less

Using the Schur Complement to Reduce Runtime in KULL's Magnetic Diffusion Package

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brunner, T A; Kolev, T V

2010-12-15

Recently a Resistive Magnetohydrodynamics (MHD) package has been added to the KULL code. In order to be compatible with the underlying hydrodynamics algorithm, a new sub-zonal magnetics discretization was developed that supports arbitrary polygonal and polyhedral zones. This flexibility comes at the cost of many more unknowns per zone - approximately ten times more for a hexahedral mesh. We can eliminate some (or all, depending on the dimensionality) of the extra unknowns from the global matrix during assembly by using a Schur complement approach. This trades expensive global work for cache-friendly local work, while still allowing solution for the fullmore » system. Significant improvements in the solution time are observed for several test problems.« less

Using a two-step matrix solution to reduce the run time in KULL's magnetic diffusion package

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brunner, T A; Kolev, T V

2010-12-17

Recently a Resistive Magnetohydrodynamics (MHD) package has been added to the KULL code. In order to be compatible with the underlying hydrodynamics algorithm, a new sub-zonal magnetics discretization was developed that supports arbitrary polygonal and polyhedral zones. This flexibility comes at the cost of many more unknowns per zone - approximately ten times more for a hexahedral mesh. We can eliminate some (or all, depending on the dimensionality) of the extra unknowns from the global matrix during assembly by using a Schur complement approach. This trades expensive global work for cache-friendly local work, while still allowing solution for the fullmore » system. Significant improvements in the solution time are observed for several test problems.« less

Improved full analytical polygon-based method using Fourier analysis of the three-dimensional affine transformation.

PubMed

Pan, Yijie; Wang, Yongtian; Liu, Juan; Li, Xin; Jia, Jia

2014-03-01

Previous research [Appl. Opt.52, A290 (2013)] has revealed that Fourier analysis of three-dimensional affine transformation theory can be used to improve the computation speed of the traditional polygon-based method. In this paper, we continue our research and propose an improved full analytical polygon-based method developed upon this theory. Vertex vectors of primitive and arbitrary triangles and the pseudo-inverse matrix were used to obtain an affine transformation matrix representing the spatial relationship between the two triangles. With this relationship and the primitive spectrum, we analytically obtained the spectrum of the arbitrary triangle. This algorithm discards low-level angular dependent computations. In order to add diffusive reflection to each arbitrary surface, we also propose a whole matrix computation approach that takes advantage of the affine transformation matrix and uses matrix multiplication to calculate shifting parameters of similar sub-polygons. The proposed method improves hologram computation speed for the conventional full analytical approach. Optical experimental results are demonstrated which prove that the proposed method can effectively reconstruct three-dimensional scenes.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2014-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES

PubMed Central

GILLETTE, ANDREW; RAND, ALEXANDER; BAJAJ, CHANDRAJIT

2016-01-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties. PMID:28077939

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES.

PubMed

Gillette, Andrew; Rand, Alexander; Bajaj, Chandrajit

2016-10-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

PubMed Central

RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

2013-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called ‘serendipity’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

Generating Inviscid and Viscous Fluid-Flow Simulations over an Aircraft Surface Using a Fluid-Flow Mesh

NASA Technical Reports Server (NTRS)

Rodriguez, David L. (Inventor); Sturdza, Peter (Inventor)

2013-01-01

Fluid-flow simulation over a computer-generated aircraft surface is generated using inviscid and viscous simulations. A fluid-flow mesh of fluid cells is obtained. At least one inviscid fluid property for the fluid cells is determined using an inviscid fluid simulation that does not simulate fluid viscous effects. A set of intersecting fluid cells that intersects the aircraft surface are identified. One surface mesh polygon of the surface mesh is identified for each intersecting fluid cell. A boundary-layer prediction point for each identified surface mesh polygon is determined. At least one boundary-layer fluid property for each boundary-layer prediction point is determined using the at least one inviscid fluid property of the corresponding intersecting fluid cell and a boundary-layer simulation that simulates fluid viscous effects. At least one updated fluid property for at least one fluid cell is determined using the at least one boundary-layer fluid property and the inviscid fluid simulation.

Optical touch sensing: practical bounds for design and performance

NASA Astrophysics Data System (ADS)

Bläßle, Alexander; Janbek, Bebart; Liu, Lifeng; Nakamura, Kanna; Nolan, Kimberly; Paraschiv, Victor

2013-02-01

Touch sensitive screens are used in many applications ranging in size from smartphones and tablets to display walls and collaborative surfaces. In this study, we consider optical touch sensing, a technology best suited for large-scale touch surfaces. Optical touch sensing utilizes cameras and light sources placed along the edge of the display. Within this framework, we first find a sufficient number of cameras necessary for identifying a convex polygon touching the screen, using a continuous light source on the boundary of a circular domain. We then find the number of cameras necessary to distinguish between two circular objects in a circular or rectangular domain. Finally, we use Matlab to simulate the polygonal mesh formed from distributing cameras and light sources on a circular domain. Using this, we compute the number of polygons in the mesh and the maximum polygon area to give us information about the accuracy of the configuration. We close with summary and conclusions, and pointers to possible future research directions.

Evaluation and correction of laser-scanned point clouds

NASA Astrophysics Data System (ADS)

Teutsch, Christian; Isenberg, Tobias; Trostmann, Erik; Weber, Michael; Berndt, Dirk; Strothotte, Thomas

2005-01-01

The digitalization of real-world objects is of great importance in various application domains. E.g. in industrial processes quality assurance is very important. Geometric properties of workpieces have to be measured. Traditionally, this is done with gauges which is somewhat subjective and time-consuming. We developed a robust optical laser scanner for the digitalization of arbitrary objects, primary, industrial workpieces. As measuring principle we use triangulation with structured lighting and a multi-axis locomotor system. Measurements on the generated data leads to incorrect results if the contained error is too high. Therefore, processes for geometric inspection under non-laboratory conditions are needed that are robust in permanent use and provide high accuracy as well as high operation speed. The many existing methods for polygonal mesh optimization produce very esthetic 3D models but often require user interaction and are limited in processing speed and/or accuracy. Furthermore, operations on optimized meshes consider the entire model and pay only little attention to individual measurements. However, many measurements contribute to parts or single scans with possibly strong differences between neighboring scans being lost during mesh construction. Also, most algorithms consider unsorted point clouds although the scanned data is structured through device properties and measuring principles. We use this underlying structure to achieve high processing speeds and extract intrinsic system parameters and use them for fast pre-processing.

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

PubMed Central

Lee, Y.-G.; Zou, W.-N.; Pan, E.

2015-01-01

This paper presents a closed-form solution for the arbitrary polygonal inclusion problem with polynomial eigenstrains of arbitrary order in an anisotropic magneto-electro-elastic full plane. The additional displacements or eigendisplacements, instead of the eigenstrains, are assumed to be a polynomial with general terms of order M+N. By virtue of the extended Stroh formulism, the induced fields are expressed in terms of a group of basic functions which involve boundary integrals of the inclusion domain. For the special case of polygonal inclusions, the boundary integrals are carried out explicitly, and their averages over the inclusion are also obtained. The induced fields under quadratic eigenstrains are mostly analysed in terms of figures and tables, as well as those under the linear and cubic eigenstrains. The connection between the present solution and the solution via the Green's function method is established and numerically verified. The singularity at the vertices of the arbitrary polygon is further analysed via the basic functions. The general solution and the numerical results for the constant, linear, quadratic and cubic eigenstrains presented in this paper enable us to investigate the features of the inclusion and inhomogeneity problem concerning polynomial eigenstrains in semiconductors and advanced composites, while the results can further serve as benchmarks for future analyses of Eshelby's inclusion problem. PMID:26345141

Simulation of a Single-Element Lean-Direct Injection Combustor Using Arbitrary Polyhedral Mesh

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2012-01-01

This paper summarizes procedures of generating the arbitrary polyhedral mesh as well as presents sample results from its application to the numerical solution of a single-element LDI combustor using a preliminary version of the new OpenNCC.

Impact of MPEG-4 3D mesh coding on watermarking algorithms for polygonal 3D meshes

NASA Astrophysics Data System (ADS)

Funk, Wolfgang

2004-06-01

The MPEG-4 multimedia standard addresses the scene-based composition of audiovisual objects. Natural and synthetic multimedia content can be mixed and transmitted over narrow and broadband communication channels. Synthetic natural hybrid coding (SNHC) within MPEG-4 provides tools for 3D mesh coding (3DMC). We investigate the robustness of two different 3D watermarking algorithms for polygonal meshes with respect to 3DMC. The first algorithm is a blind detection scheme designed for labelling applications that require high bandwidth and low robustness. The second algorithm is a robust non-blind one-bit watermarking scheme intended for copyright protection applications. Both algorithms have been proposed by Benedens. We expect 3DMC to have an impact on the watermarked 3D meshes, as the algorithms used for our simulations work on vertex coordinates to encode the watermark. We use the 3DMC implementation provided with the MPEG-4 reference software and the Princeton Shape Benchmark model database for our simulations. The watermarked models are sent through the 3DMC encoder and decoder, and the watermark decoding process is performed. For each algorithm under consideration we examine the detection properties as a function of the quantization of the vertex coordinates.

Numerical analysis method for linear induction machines.

NASA Technical Reports Server (NTRS)

Elliott, D. G.

1972-01-01

A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.

Modeling the spatio-temporal variability in subsurface thermal regimes across a low-relief polygonal tundra landscape: Modeling Archive

DOE Data Explorer

Kumar, Jitendra; Collier, Nathan; Bisht, Gautam; Mills, Richard T.; Thornton, Peter E.; Iversen, Colleen M.; Romanovsky, Vladimir

2016-01-27

This Modeling Archive is in support of an NGEE Arctic discussion paper under review and available at http://www.the-cryosphere-discuss.net/tc-2016-29/. Vast carbon stocks stored in permafrost soils of Arctic tundra are under risk of release to atmosphere under warming climate. Ice--wedge polygons in the low-gradient polygonal tundra create a complex mosaic of microtopographic features. The microtopography plays a critical role in regulating the fine scale variability in thermal and hydrological regimes in the polygonal tundra landscape underlain by continuous permafrost. Modeling of thermal regimes of this sensitive ecosystem is essential for understanding the landscape behaviour under current as well as changing climate. We present here an end-to-end effort for high resolution numerical modeling of thermal hydrology at real-world field sites, utilizing the best available data to characterize and parameterize the models. We develop approaches to model the thermal hydrology of polygonal tundra and apply them at four study sites at Barrow, Alaska spanning across low to transitional to high-centered polygon and representative of broad polygonal tundra landscape. A multi--phase subsurface thermal hydrology model (PFLOTRAN) was developed and applied to study the thermal regimes at four sites. Using high resolution LiDAR DEM, microtopographic features of the landscape were characterized and represented in the high resolution model mesh. Best available soil data from field observations and literature was utilized to represent the complex hetogeneous subsurface in the numerical model. This data collection provides the complete set of input files, forcing data sets and computational meshes for simulations using PFLOTRAN for four sites at Barrow Environmental Observatory. It also document the complete computational workflow for this modeling study to allow verification, reproducibility and follow up studies.

Conservative DEC Discretization of Incompressible Navier-Stokes Equations on Arbitrary Surface Simplicial Meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh; Hirani, Anil; Samtaney, Ravi

2017-11-01

A conservative discretization of incompressible Navier-Stokes equations over surfaces is developed using discrete exterior calculus (DEC). The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of signed diagonal Hodge star operators, while using the circumcentric dual defined on arbitrary meshes, is shown to produce correct solutions even when many non-Delaunay triangles pairs exist. This allows the DEC discretization to admit arbitrary surface simplicial meshes, in contrast to the previously held notion that DEC was limited only to Delaunay meshes. The discretization scheme is presented along with several numerical test cases demonstrating its numerical convergence and conservation properties. Recent developments regarding the extension to conservative higher order methods are also presented. KAUST Baseline Research Funds of R. Samtaney.

Hierarchical image feature extraction by an irregular pyramid of polygonal partitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skurikhin, Alexei N

2008-01-01

We present an algorithmic framework for hierarchical image segmentation and feature extraction. We build a successive fine-to-coarse hierarchy of irregular polygonal partitions of the original image. This multiscale hierarchy forms the basis for object-oriented image analysis. The framework incorporates the Gestalt principles of visual perception, such as proximity and closure, and exploits spectral and textural similarities of polygonal partitions, while iteratively grouping them until dissimilarity criteria are exceeded. Seed polygons are built upon a triangular mesh composed of irregular sized triangles, whose spatial arrangement is adapted to the image content. This is achieved by building the triangular mesh on themore » top of detected spectral discontinuities (such as edges), which form a network of constraints for the Delaunay triangulation. The image is then represented as a spatial network in the form of a graph with vertices corresponding to the polygonal partitions and edges reflecting their relations. The iterative agglomeration of partitions into object-oriented segments is formulated as Minimum Spanning Tree (MST) construction. An important characteristic of the approach is that the agglomeration of polygonal partitions is constrained by the detected edges; thus the shapes of agglomerated partitions are more likely to correspond to the outlines of real-world objects. The constructed partitions and their spatial relations are characterized using spectral, textural and structural features based on proximity graphs. The framework allows searching for object-oriented features of interest across multiple levels of details of the built hierarchy and can be generalized to the multi-criteria MST to account for multiple criteria important for an application.« less

Fast and Exact Fiber Surfaces for Tetrahedral Meshes.

PubMed

Klacansky, Pavol; Tierny, Julien; Carr, Hamish; Zhao Geng

2017-07-01

Isosurfaces are fundamental geometrical objects for the analysis and visualization of volumetric scalar fields. Recent work has generalized them to bivariate volumetric fields with fiber surfaces, the pre-image of polygons in range space. However, the existing algorithm for their computation is approximate, and is limited to closed polygons. Moreover, its runtime performance does not allow instantaneous updates of the fiber surfaces upon user edits of the polygons. Overall, these limitations prevent a reliable and interactive exploration of the space of fiber surfaces. This paper introduces the first algorithm for the exact computation of fiber surfaces in tetrahedral meshes. It assumes no restriction on the topology of the input polygon, handles degenerate cases and better captures sharp features induced by polygon bends. The algorithm also allows visualization of individual fibers on the output surface, better illustrating their relationship with data features in range space. To enable truly interactive exploration sessions, we further improve the runtime performance of this algorithm. In particular, we show that it is trivially parallelizable and that it scales nearly linearly with the number of cores. Further, we study acceleration data-structures both in geometrical domain and range space and we show how to generalize interval trees used in isosurface extraction to fiber surface extraction. Experiments demonstrate the superiority of our algorithm over previous work, both in terms of accuracy and running time, with up to two orders of magnitude speedups. This improvement enables interactive edits of range polygons with instantaneous updates of the fiber surface for exploration purpose. A VTK-based reference implementation is provided as additional material to reproduce our results.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavel Kus; Pavel Solin; David Andrs

2014-11-01

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.

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

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

1997-01-01

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

Final Report of the Project "From the finite element method to the virtual element method"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Manzini, Gianmarco; Gyrya, Vitaliy

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for themore » numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.« less

An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems

NASA Astrophysics Data System (ADS)

Teng, Z. H.; Sun, F.; Wu, S. C.; Zhang, Z. B.; Chen, T.; Liao, D. M.

2018-02-01

By introducing the shape functions of virtual node polygonal (VP) elements into the standard extended finite element method (XFEM), a conforming elemental mesh can be created for the cracking process. Moreover, an adaptively refined meshing with the quadtree structure only at a growing crack tip is proposed without inserting hanging nodes into the transition region. A novel dynamic crack growth method termed as VP-XFEM is thus formulated in the framework of fracture mechanics. To verify the newly proposed VP-XFEM, both quasi-static and dynamic cracked problems are investigated in terms of computational accuracy, convergence, and efficiency. The research results show that the present VP-XFEM can achieve good agreement in stress intensity factor and crack growth path with the exact solutions or experiments. Furthermore, better accuracy, convergence, and efficiency of different models can be acquired, in contrast to standard XFEM and mesh-free methods. Therefore, VP-XFEM provides a suitable alternative to XFEM for engineering applications.

An Edge-Based Method for the Incompressible Navier-Stokes Equations on Polygonal Meshes

NASA Astrophysics Data System (ADS)

Wright, Jeffrey A.; Smith, Richard W.

2001-05-01

A pressure-based method is presented for discretizing the unsteady incompressible Navier-Stokes equations using hybrid unstructured meshes. The edge-based data structure and assembly procedure adopted lead naturally to a strictly conservative discretization, which is valid for meshes composed of n-sided polygons. Particular attention is given to the construction of a pressure-velocity coupling procedure which is supported by edge data, resulting in a relatively simple numerical method that is consistent with the boundary and initial conditions required by the incompressible Navier-Stokes equations. Edge formulas are presented for assembling the momentum equations, which are based on an upwind-biased linear reconstruction of the velocity field. Similar formulas are presented for assembling the pressure equation. The method is demonstrated to be second-order accurate in space and time for two Navier-Stokes problems admitting an exact solution. Results for several other well-known problems are also presented, including lid-driven cavity flow, impulsively started cylinder flow, and unsteady vortex shedding from a circular cylinder. Although the method is by construction minimalist, it is shown to be accurate and robust for the problems considered.

A Subgrid Approach for Modeling Microtopography Effects on Overland Flow: Application to Polygonal Tundra: Modeling Archive

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahmad Jan; Ethan Coon; Scott Painter

This Modeling Archive is in support of an NGEE Arctic manuscript under review. A new subgrid model was implemented in the Advanced Terrestrial Simulator (ATS) to capture micro-topography effects on surface flow. A comparison of the fine-scale simulations on seven individual ice-wedge polygons and a cluster of polygons was made between the results of the subgrid model and no-subgrid model. Our finding confirms that the effects of small-scale spatial heterogeneities can be captured in the coarsened models. The dataset contains meshes, inputfiles, subgrid parameters used in the simulations. Python scripts for post-processing and files for geometric analyses are also included.

Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem

NASA Astrophysics Data System (ADS)

Artioli, E.; Beirão da Veiga, L.; Lovadina, C.; Sacco, E.

2017-10-01

The present paper is the second part of a twofold work, whose first part is reported in Artioli et al. (Comput Mech, 2017. doi: 10.1007/s00466-017-1404-5), concerning a newly developed Virtual element method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoelastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method framework.

Evolution in time of an N-atom system. II. Calculation of the eigenstates

NASA Astrophysics Data System (ADS)

Rudolph, Terry; Yavin, Itay; Freedhoff, Helen

2004-01-01

We calculate the energy eigenvalues and eigenstates corresponding to coherent single and multiple excitations of a number of different arrays of N identical two-level atoms (TLA’s) or qubits, including polygons, “diamond” structures, polygon multilayers, icosahedra, and dodecahedra. We assume only that the coupling occurs via an exchange interaction which depends on the separation between the atoms. We include the interactions between all pairs of atoms, and our results are valid for arbitrary separations relative to the radiation wavelength.

TAS: A Transonic Aircraft/Store flow field prediction code

NASA Technical Reports Server (NTRS)

Thompson, D. S.

1983-01-01

A numerical procedure has been developed that has the capability to predict the transonic flow field around an aircraft with an arbitrarily located, separated store. The TAS code, the product of a joint General Dynamics/NASA ARC/AFWAL research and development program, will serve as the basis for a comprehensive predictive method for aircraft with arbitrary store loadings. This report described the numerical procedures employed to simulate the flow field around a configuration of this type. The validity of TAS code predictions is established by comparison with existing experimental data. In addition, future areas of development of the code are outlined. A brief description of code utilization is also given in the Appendix. The aircraft/store configuration is simulated using a mesh embedding approach. The computational domain is discretized by three meshes: (1) a planform-oriented wing/body fine mesh, (2) a cylindrical store mesh, and (3) a global Cartesian crude mesh. This embedded mesh scheme enables simulation of stores with fins of arbitrary angular orientation.

Multi-Resolution Unstructured Grid-Generation for Geophysical Applications on the Sphere

NASA Technical Reports Server (NTRS)

Engwirda, Darren

2015-01-01

An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kikinzon, Evgeny; Kuznetsov, Yuri; Lipnikov, Konstatin

In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

DOE PAGES

Kikinzon, Evgeny; Kuznetsov, Yuri; Lipnikov, Konstatin; ...

2017-07-08

In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.

Pizza again? On the division of polygons into sections with a common origin

NASA Astrophysics Data System (ADS)

Sinitsky, Ilya; Stupel, Moshe; Sinitsky, Marina

2018-02-01

The paper explores the division of a polygon into equal-area pieces using line segments originating at a common point. The mathematical background of the proposed method is very simple and belongs to secondary school geometry. Simple examples dividing a square into two, four or eight congruent pieces provide a starting point to discovering how to divide a regular polygon into any number of equal-area pieces using line segments originating from the centre. Moreover, it turns out that there are infinite ways to do the division. Discovering the basic invariant involved allows application of the same procedure to divide any tangential polygon, as after suitable adjustment, it can be used also for rectangles and parallelograms. Further generalization offers many additional solutions of the problem, and some of them are presented for the case of an arbitrary triangle and a square. Links to dynamic demonstrations in GeoGebra serve to illustrate the main results.

Imaging, Virtual Planning, Design, and Production of Patient-Specific Implants and Clinical Validation in Craniomaxillofacial Surgery

PubMed Central

Dérand, Per; Rännar, Lars-Erik; Hirsch, Jan-M

2012-01-01

The purpose of this article was to describe the workflow from imaging, via virtual design, to manufacturing of patient-specific titanium reconstruction plates, cutting guide and mesh, and its utility in connection with surgical treatment of acquired bone defects in the mandible using additive manufacturing by electron beam melting (EBM). Based on computed tomography scans, polygon skulls were created. Following that virtual treatment plans entailing free microvascular transfer of fibula flaps using patient-specific reconstruction plates, mesh, and cutting guides were designed. The design was based on the specification of a Compact UniLOCK 2.4 Large (Synthes®, Switzerland). The obtained polygon plates were bent virtually round the reconstructed mandibles. Next, the resections of the mandibles were planned virtually. A cutting guide was outlined to facilitate resection, as well as plates and titanium mesh for insertion of bone or bone substitutes. Polygon plates and meshes were converted to stereolithography format and used in the software Magics for preparation of input files for the successive step, additive manufacturing. EBM was used to manufacture the customized implants in a biocompatible titanium grade, Ti6Al4V ELI. The implants and the cutting guide were cleaned and sterilized, then transferred to the operating theater, and applied during surgery. Commercially available software programs are sufficient in order to virtually plan for production of patient-specific implants. Furthermore, EBM-produced implants are fully usable under clinical conditions in reconstruction of acquired defects in the mandible. A good compliance between the treatment plan and the fit was demonstrated during operation. Within the constraints of this article, the authors describe a workflow for production of patient-specific implants, using EBM manufacturing. Titanium cutting guides, reconstruction plates for fixation of microvascular transfer of osteomyocutaneous bone grafts, and mesh to replace resected bone that can function as a carrier for bone or bone substitutes were designed and tested during reconstructive maxillofacial surgery. A clinically fit, well within the requirements for what is needed and obtained using traditional free hand bending of commercially available devices, or even higher precision, was demonstrated in ablative surgery in four patients. PMID:23997858

Imaging, virtual planning, design, and production of patient-specific implants and clinical validation in craniomaxillofacial surgery.

PubMed

Dérand, Per; Rännar, Lars-Erik; Hirsch, Jan-M

2012-09-01

The purpose of this article was to describe the workflow from imaging, via virtual design, to manufacturing of patient-specific titanium reconstruction plates, cutting guide and mesh, and its utility in connection with surgical treatment of acquired bone defects in the mandible using additive manufacturing by electron beam melting (EBM). Based on computed tomography scans, polygon skulls were created. Following that virtual treatment plans entailing free microvascular transfer of fibula flaps using patient-specific reconstruction plates, mesh, and cutting guides were designed. The design was based on the specification of a Compact UniLOCK 2.4 Large (Synthes(®), Switzerland). The obtained polygon plates were bent virtually round the reconstructed mandibles. Next, the resections of the mandibles were planned virtually. A cutting guide was outlined to facilitate resection, as well as plates and titanium mesh for insertion of bone or bone substitutes. Polygon plates and meshes were converted to stereolithography format and used in the software Magics for preparation of input files for the successive step, additive manufacturing. EBM was used to manufacture the customized implants in a biocompatible titanium grade, Ti6Al4V ELI. The implants and the cutting guide were cleaned and sterilized, then transferred to the operating theater, and applied during surgery. Commercially available software programs are sufficient in order to virtually plan for production of patient-specific implants. Furthermore, EBM-produced implants are fully usable under clinical conditions in reconstruction of acquired defects in the mandible. A good compliance between the treatment plan and the fit was demonstrated during operation. Within the constraints of this article, the authors describe a workflow for production of patient-specific implants, using EBM manufacturing. Titanium cutting guides, reconstruction plates for fixation of microvascular transfer of osteomyocutaneous bone grafts, and mesh to replace resected bone that can function as a carrier for bone or bone substitutes were designed and tested during reconstructive maxillofacial surgery. A clinically fit, well within the requirements for what is needed and obtained using traditional free hand bending of commercially available devices, or even higher precision, was demonstrated in ablative surgery in four patients.

Study of the counting efficiency of a WBC setup by using a computational 3D human body library in sitting position based on polygonal mesh surfaces.

PubMed

Fonseca, T C Ferreira; Bogaerts, R; Lebacq, A L; Mihailescu, C L; Vanhavere, F

2014-04-01

A realistic computational 3D human body library, called MaMP and FeMP (Male and Female Mesh Phantoms), based on polygonal mesh surface geometry, has been created to be used for numerical calibration of the whole body counter (WBC) system of the nuclear power plant (NPP) in Doel, Belgium. The main objective was to create flexible computational models varying in gender, body height, and mass for studying the morphology-induced variation of the detector counting efficiency (CE) and reducing the measurement uncertainties. First, the counting room and an HPGe detector were modeled using MCNPX (Monte Carlo radiation transport code). The validation of the model was carried out for different sample-detector geometries with point sources and a physical phantom. Second, CE values were calculated for a total of 36 different mesh phantoms in a seated position using the validated Monte Carlo model. This paper reports on the validation process of the in vivo whole body system and the CE calculated for different body heights and weights. The results reveal that the CE is strongly dependent on the individual body shape, size, and gender and may vary by a factor of 1.5 to 3 depending on the morphology aspects of the individual to be measured.

Program Enhances Drawings Of Three-Dimensional Objects

NASA Technical Reports Server (NTRS)

Hedgley, David R., Jr.

1992-01-01

SILHOUETTE is program for line drawings rendering any subset of polygons as silhouette. Program is improvement on, and replacement for, HIDDEN LINE COMPUTER CODE (ARC-11446). Offers combinations of silhouette and nonsilhouette specifications for arbitrary solid. Written in FORTRAN 77.

2D automatic body-fitted structured mesh generation using advancing extraction method

NASA Astrophysics Data System (ADS)

Zhang, Yaoxin; Jia, Yafei

2018-01-01

This paper presents an automatic mesh generation algorithm for body-fitted structured meshes in Computational Fluids Dynamics (CFD) analysis using the Advancing Extraction Method (AEM). The method is applicable to two-dimensional domains with complex geometries, which have the hierarchical tree-like topography with extrusion-like structures (i.e., branches or tributaries) and intrusion-like structures (i.e., peninsula or dikes). With the AEM, the hierarchical levels of sub-domains can be identified, and the block boundary of each sub-domain in convex polygon shape in each level can be extracted in an advancing scheme. In this paper, several examples were used to illustrate the effectiveness and applicability of the proposed algorithm for automatic structured mesh generation, and the implementation of the method.

Fitting C 2 Continuous Parametric Surfaces to Frontiers Delimiting Physiologic Structures

PubMed Central

Bayer, Jason D.

2014-01-01

We present a technique to fit C 2 continuous parametric surfaces to scattered geometric data points forming frontiers delimiting physiologic structures in segmented images. Such mathematical representation is interesting because it facilitates a large number of operations in modeling. While the fitting of C 2 continuous parametric curves to scattered geometric data points is quite trivial, the fitting of C 2 continuous parametric surfaces is not. The difficulty comes from the fact that each scattered data point should be assigned a unique parametric coordinate, and the fit is quite sensitive to their distribution on the parametric plane. We present a new approach where a polygonal (quadrilateral or triangular) surface is extracted from the segmented image. This surface is subsequently projected onto a parametric plane in a manner to ensure a one-to-one mapping. The resulting polygonal mesh is then regularized for area and edge length. Finally, from this point, surface fitting is relatively trivial. The novelty of our approach lies in the regularization of the polygonal mesh. Process performance is assessed with the reconstruction of a geometric model of mouse heart ventricles from a computerized tomography scan. Our results show an excellent reproduction of the geometric data with surfaces that are C 2 continuous. PMID:24782911

Predicting mesh density for adaptive modelling of the global atmosphere.

PubMed

Weller, Hilary

2009-11-28

The shallow water equations are solved using a mesh of polygons on the sphere, which adapts infrequently to the predicted future solution. Infrequent mesh adaptation reduces the cost of adaptation and load-balancing and will thus allow for more accurate mapping on adaptation. We simulate the growth of a barotropically unstable jet adapting the mesh every 12 h. Using an adaptation criterion based largely on the gradient of the vorticity leads to a mesh with around 20 per cent of the cells of a uniform mesh that gives equivalent results. This is a similar proportion to previous studies of the same test case with mesh adaptation every 1-20 min. The prediction of the mesh density involves solving the shallow water equations on a coarse mesh in advance of the locally refined mesh in order to estimate where features requiring higher resolution will grow, decay or move to. The adaptation criterion consists of two parts: that resolved on the coarse mesh, and that which is not resolved and so is passively advected on the coarse mesh. This combination leads to a balance between resolving features controlled by the large-scale dynamics and maintaining fine-scale features.

Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dolbow, John; Zhang, Ziyu; Spencer, Benjamin

Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside ofmore » the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.« less

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

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

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.

Weighted straight skeletons in the plane☆

PubMed Central

Biedl, Therese; Held, Martin; Huber, Stefan; Kaaser, Dominik; Palfrader, Peter

2015-01-01

We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights. PMID:25648398

A hybrid computational model to explore the topological characteristics of epithelial tissues.

PubMed

González-Valverde, Ismael; García-Aznar, José Manuel

2017-11-01

Epithelial tissues show a particular topology where cells resemble a polygon-like shape, but some biological processes can alter this tissue topology. During cell proliferation, mitotic cell dilation deforms the tissue and modifies the tissue topology. Additionally, cells are reorganized in the epithelial layer and these rearrangements also alter the polygon distribution. We present here a computer-based hybrid framework focused on the simulation of epithelial layer dynamics that combines discrete and continuum numerical models. In this framework, we consider topological and mechanical aspects of the epithelial tissue. Individual cells in the tissue are simulated by an off-lattice agent-based model, which keeps the information of each cell. In addition, we model the cell-cell interaction forces and the cell cycle. Otherwise, we simulate the passive mechanical behaviour of the cell monolayer using a material that approximates the mechanical properties of the cell. This continuum approach is solved by the finite element method, which uses a dynamic mesh generated by the triangulation of cell polygons. Forces generated by cell-cell interaction in the agent-based model are also applied on the finite element mesh. Cell movement in the agent-based model is driven by the displacements obtained from the deformed finite element mesh of the continuum mechanical approach. We successfully compare the results of our simulations with some experiments about the topology of proliferating epithelial tissues in Drosophila. Our framework is able to model the emergent behaviour of the cell monolayer that is due to local cell-cell interactions, which have a direct influence on the dynamics of the epithelial tissue. Copyright © 2017 John Wiley & Sons, Ltd.

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.

New approaches to virtual environment surgery

NASA Technical Reports Server (NTRS)

Ross, M. D.; Twombly, A.; Lee, A. W.; Cheng, R.; Senger, S.

1999-01-01

This research focused on two main problems: 1) low cost, high fidelity stereoscopic imaging of complex tissues and organs; and 2) virtual cutting of tissue. A further objective was to develop these images and virtual tissue cutting methods for use in a telemedicine project that would connect remote sites using the Next Generation Internet. For goal one we used a CT scan of a human heart, a desktop PC with an OpenGL graphics accelerator card, and LCD stereoscopic glasses. Use of multiresolution meshes ranging from approximately 1,000,000 to 20,000 polygons speeded interactive rendering rates enormously while retaining general topography of the dataset. For goal two, we used a CT scan of an infant skull with premature closure of the right coronal suture, a Silicon Graphics Onyx workstation, a Fakespace Immersive WorkBench and CrystalEyes LCD glasses. The high fidelity mesh of the skull was reduced from one million to 50,000 polygons. The cut path was automatically calculated as the shortest distance along the mesh between a small number of hand selected vertices. The region outlined by the cut path was then separated from the skull and translated/rotated to assume a new position. The results indicate that widespread high fidelity imaging in virtual environment is possible using ordinary PC capabilities if appropriate mesh reduction methods are employed. The software cutting tool is applicable to heart and other organs for surgery planning, for training surgeons in a virtual environment, and for telemedicine purposes.

Automatic pre-processing for an object-oriented distributed hydrological model using GRASS-GIS

NASA Astrophysics Data System (ADS)

Sanzana, P.; Jankowfsky, S.; Branger, F.; Braud, I.; Vargas, X.; Hitschfeld, N.

2012-04-01

Landscapes are very heterogeneous, which impact the hydrological processes occurring in the catchments, especially in the modeling of peri-urban catchments. The Hydrological Response Units (HRUs), resulting from the intersection of different maps, such as land use, soil types and geology, and flow networks, allow the representation of these elements in an explicit way, preserving natural and artificial contours of the different layers. These HRUs are used as model mesh in some distributed object-oriented hydrological models, allowing the application of a topological oriented approach. The connectivity between polygons and polylines provides a detailed representation of the water balance and overland flow in these distributed hydrological models, based on irregular hydro-landscape units. When computing fluxes between these HRUs, the geometrical parameters, such as the distance between the centroid of gravity of the HRUs and the river network, and the length of the perimeter, can impact the realism of the calculated overland, sub-surface and groundwater fluxes. Therefore, it is necessary to process the original model mesh in order to avoid these numerical problems. We present an automatic pre-processing implemented in the open source GRASS-GIS software, for which several Python scripts or some algorithms already available were used, such as the Triangle software. First, some scripts were developed to improve the topology of the various elements, such as snapping of the river network to the closest contours. When data are derived with remote sensing, such as vegetation areas, their perimeter has lots of right angles that were smoothed. Second, the algorithms more particularly address bad-shaped elements of the model mesh such as polygons with narrow shapes, marked irregular contours and/or the centroid outside of the polygons. To identify these elements we used shape descriptors. The convexity index was considered the best descriptor to identify them with a threshold of 0.75. Segmentation procedures were implemented and applied with criteria of homogeneous slope, convexity of the elements and maximum area of the HRUs. These tasks were implemented using a triangulation approach, applying the Triangle software, in order to dissolve the polygons according to the convexity index criteria. The automatic pre-processing was applied to two peri-urban French catchment, the Mercier and Chaudanne catchments, with 7.3 km2 and 4.1 km2 respectively. We show that the optimized mesh allows a substantial improvement of the overland flow pathways, because the segmentation procedure gives a more realistic representation of the drainage network. KEYWORDS: GRASS-GIS, Hydrological Response Units, Automatic processing, Peri-urban catchments, Geometrical Algorithms

Explicitly represented polygon wall boundary model for the explicit MPS method

NASA Astrophysics Data System (ADS)

Mitsume, Naoto; Yoshimura, Shinobu; Murotani, Kohei; Yamada, Tomonori

2015-05-01

This study presents an accurate and robust boundary model, the explicitly represented polygon (ERP) wall boundary model, to treat arbitrarily shaped wall boundaries in the explicit moving particle simulation (E-MPS) method, which is a mesh-free particle method for strong form partial differential equations. The ERP model expresses wall boundaries as polygons, which are explicitly represented without using the distance function. These are derived so that for viscous fluids, and with less computational cost, they satisfy the Neumann boundary condition for the pressure and the slip/no-slip condition on the wall surface. The proposed model is verified and validated by comparing computed results with the theoretical solution, results obtained by other models, and experimental results. Two simulations with complex boundary movements are conducted to demonstrate the applicability of the E-MPS method to the ERP model.

Unstructured Polyhedral Mesh Thermal Radiation Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

How Misapplication of the Hydrologic Unit Framework Diminishes the Meaning of Watersheds

EPA Science Inventory

Hydrologic units provide a convenient nationwide set of geographic polygons based on an arbitrary subdivision of the drainage of land surface areas at several hierarchical levels. Half or more of these units, however, are not true watersheds as the official name of the framework,...

Computational Systems for Multidisciplinary Applications

NASA Technical Reports Server (NTRS)

Soni, Bharat; Haupt, Tomasz; Koomullil, Roy; Luke, Edward; Thompson, David

2002-01-01

In this paper, we briefly describe our efforts to develop complex simulation systems. We focus first on four key infrastructure items: enterprise computational services, simulation synthesis, geometry modeling and mesh generation, and a fluid flow solver for arbitrary meshes. We conclude by presenting three diverse applications developed using these technologies.

Implementing a Loosely Coupled Fluid Structure Interaction Finite Element Model in PHASTA

NASA Astrophysics Data System (ADS)

Pope, David

Fluid Structure Interaction problems are an important multi-physics phenomenon in the design of aerospace vehicles and other engineering applications. A variety of computational fluid dynamics solvers capable of resolving the fluid dynamics exist. PHASTA is one such computational fluid dynamics solver. Enhancing the capability of PHASTA to resolve Fluid-Structure Interaction first requires implementing a structural dynamics solver. The implementation also requires a correction of the mesh used to solve the fluid equations to account for the deformation of the structure. This results in mesh motion and causes the need for an Arbitrary Lagrangian-Eulerian modification to the fluid dynamics equations currently implemented in PHASTA. With the implementation of both structural dynamics physics, mesh correction, and the Arbitrary Lagrangian-Eulerian modification of the fluid dynamics equations, PHASTA is made capable of solving Fluid-Structure Interaction problems.

A Novel Polygonal Finite Element Method: Virtual Node Method

NASA Astrophysics Data System (ADS)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

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

Generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains

PubMed Central

Vasconcelos, Giovani L.

2014-01-01

A generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains is obtained by making a combined use of two preimage domains, namely, a rectilinear slit domain and a bounded circular domain. The conformal mapping from the circular domain to the polygonal region is written as an indefinite integral whose integrand consists of a product of powers of the Schottky-Klein prime functions, which is the same irrespective of the preimage slit domain, and a prefactor function that depends on the choice of the rectilinear slit domain. A detailed derivation of the mapping formula is given for the case where the preimage slit domain is the upper half-plane with radial slits. Representation formulae for other canonical slit domains are also obtained but they are more cumbersome in that the prefactor function contains arbitrary parameters in the interior of the circular domain. PMID:24910523

Generalization of the Schwarz-Christoffel mapping to multiply connected polygonal domains.

PubMed

Vasconcelos, Giovani L

2014-06-08

A generalization of the Schwarz-Christoffel mapping to multiply connected polygonal domains is obtained by making a combined use of two preimage domains, namely, a rectilinear slit domain and a bounded circular domain. The conformal mapping from the circular domain to the polygonal region is written as an indefinite integral whose integrand consists of a product of powers of the Schottky-Klein prime functions, which is the same irrespective of the preimage slit domain, and a prefactor function that depends on the choice of the rectilinear slit domain. A detailed derivation of the mapping formula is given for the case where the preimage slit domain is the upper half-plane with radial slits. Representation formulae for other canonical slit domains are also obtained but they are more cumbersome in that the prefactor function contains arbitrary parameters in the interior of the circular domain.

Fast incorporation of optical flow into active polygons.

PubMed

Unal, Gozde; Krim, Hamid; Yezzi, Anthony

2005-06-01

In this paper, we first reconsider, in a different light, the addition of a prediction step to active contour-based visual tracking using an optical flow and clarify the local computation of the latter along the boundaries of continuous active contours with appropriate regularizers. We subsequently detail our contribution of computing an optical flow-based prediction step directly from the parameters of an active polygon, and of exploiting it in object tracking. This is in contrast to an explicitly separate computation of the optical flow and its ad hoc application. It also provides an inherent regularization effect resulting from integrating measurements along polygon edges. As a result, we completely avoid the need of adding ad hoc regularizing terms to the optical flow computations, and the inevitably arbitrary associated weighting parameters. This direct integration of optical flow into the active polygon framework distinguishes this technique from most previous contour-based approaches, where regularization terms are theoretically, as well as practically, essential. The greater robustness and speed due to a reduced number of parameters of this technique are additional and appealing features.

Incorporation of detailed eye model into polygon-mesh versions of ICRP-110 reference phantoms

NASA Astrophysics Data System (ADS)

Tat Nguyen, Thang; Yeom, Yeon Soo; Kim, Han Sung; Wang, Zhao Jun; Han, Min Cheol; Kim, Chan Hyeong; Lee, Jai Ki; Zankl, Maria; Petoussi-Henss, Nina; Bolch, Wesley E.; Lee, Choonsik; Chung, Beom Sun

2015-11-01

The dose coefficients for the eye lens reported in ICRP 2010 Publication 116 were calculated using both a stylized model and the ICRP-110 reference phantoms, according to the type of radiation, energy, and irradiation geometry. To maintain consistency of lens dose assessment, in the present study we incorporated the ICRP-116 detailed eye model into the converted polygon-mesh (PM) version of the ICRP-110 reference phantoms. After the incorporation, the dose coefficients for the eye lens were calculated and compared with those of the ICRP-116 data. The results showed generally a good agreement between the newly calculated lens dose coefficients and the values of ICRP 2010 Publication 116. Significant differences were found for some irradiation cases due mainly to the use of different types of phantoms. Considering that the PM version of the ICRP-110 reference phantoms preserve the original topology of the ICRP-110 reference phantoms, it is believed that the PM version phantoms, along with the detailed eye model, provide more reliable and consistent dose coefficients for the eye lens.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eldred, Christopher; Randall, David

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restrictedmore » to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Lastly, detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.« less

Binary space partitioning trees and their uses

NASA Technical Reports Server (NTRS)

Bell, Bradley N.

1989-01-01

Binary Space Partitioning (BSP) trees have some qualities that make them useful in solving many graphics related problems. The purpose is to describe what a BSP tree is, and how it can be used to solve the problem of hidden surface removal, and constructive solid geometry. The BSP tree is based on the idea that a plane acting as a divider subdivides space into two parts with one being on the positive side and the other on the negative. A polygonal solid is then represented as the volume defined by the collective interior half spaces of the solid's bounding surfaces. The nature of how the tree is organized lends itself well for sorting polygons relative to an arbitrary point in 3 space. The speed at which the tree can be traversed for depth sorting is fast enough to provide hidden surface removal at interactive speeds. The fact that a BSP tree actually represents a polygonal solid as a bounded volume also makes it quite useful in performing the boolean operations used in constructive solid geometry. Due to the nature of the BSP tree, polygons can be classified as they are subdivided. The ability to classify polygons as they are subdivided can enhance the simplicity of implementing constructive solid geometry.

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

Arbitrary Lagrangian-Eulerian Method with Local Structured Adaptive Mesh Refinement for Modeling Shock Hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anderson, R W; Pember, R B; Elliott, N S

2001-10-22

A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditionalmore » AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.« less

Comparison of updated Lagrangian FEM with arbitrary Lagrangian Eulerian method for 3D thermo-mechanical extrusion of a tube profile

NASA Astrophysics Data System (ADS)

Kronsteiner, J.; Horwatitsch, D.; Zeman, K.

2017-10-01

Thermo-mechanical numerical modelling and simulation of extrusion processes faces several serious challenges. Large plastic deformations in combination with a strong coupling of thermal with mechanical effects leads to a high numerical demand for the solution as well as for the handling of mesh distortions. The two numerical methods presented in this paper also reflect two different ways to deal with mesh distortions. Lagrangian Finite Element Methods (FEM) tackle distorted elements by building a new mesh (called re-meshing) whereas Arbitrary Lagrangian Eulerian (ALE) methods use an "advection" step to remap the solution from the distorted to the undistorted mesh. Another difference between conventional Lagrangian and ALE methods is the separate treatment of material and mesh in ALE, allowing the definition of individual velocity fields. In theory, an ALE formulation contains the Eulerian formulation as a subset to the Lagrangian description of the material. The investigations presented in this paper were dealing with the direct extrusion of a tube profile using EN-AW 6082 aluminum alloy and a comparison of experimental with Lagrangian and ALE results. The numerical simulations cover the billet upsetting and last until one third of the billet length is extruded. A good qualitative correlation of experimental and numerical results could be found, however, major differences between Lagrangian and ALE methods concerning thermo-mechanical coupling lead to deviations in the thermal results.

FASH and MASH: female and male adult human phantoms based on polygon mesh surfaces: I. Development of the anatomy

NASA Astrophysics Data System (ADS)

Cassola, V. F.; de Melo Lima, V. J.; Kramer, R.; Khoury, H. J.

2010-01-01

Among computational models, voxel phantoms based on computer tomographic (CT), nuclear magnetic resonance (NMR) or colour photographic images of patients, volunteers or cadavers have become popular in recent years. Although being true to nature representations of scanned individuals, voxel phantoms have limitations, especially when walled organs have to be segmented or when volumes of organs or body tissues, like adipose, have to be changed. Additionally, the scanning of patients or volunteers is usually made in supine position, which causes a shift of internal organs towards the ribcage, a compression of the lungs and a reduction of the sagittal diameter especially in the abdominal region compared to the regular anatomy of a person in the upright position, which in turn can influence organ and tissue absorbed or equivalent dose estimates. This study applies tools developed recently in the areas of computer graphics and animated films to the creation and modelling of 3D human organs, tissues, skeletons and bodies based on polygon mesh surfaces. Female and male adult human phantoms, called FASH (Female Adult meSH) and MASH (Male Adult meSH), have been designed using software, such as MakeHuman, Blender, Binvox and ImageJ, based on anatomical atlases, observing at the same time organ masses recommended by the International Commission on Radiological Protection for the male and female reference adult in report no 89. 113 organs, bones and tissues have been modelled in the FASH and the MASH phantoms representing locations for adults in standing posture. Most organ and tissue masses of the voxelized versions agree with corresponding data from ICRP89 within a margin of 2.6%. Comparison with the mesh-based male RPI_AM and female RPI_AF phantoms shows differences with respect to the material used, to the software and concepts applied, and to the anatomies created.

Fast ray-tracing of human eye optics on Graphics Processing Units.

PubMed

Wei, Qi; Patkar, Saket; Pai, Dinesh K

2014-05-01

We present a new technique for simulating retinal image formation by tracing a large number of rays from objects in three dimensions as they pass through the optic apparatus of the eye to objects. Simulating human optics is useful for understanding basic questions of vision science and for studying vision defects and their corrections. Because of the complexity of computing such simulations accurately, most previous efforts used simplified analytical models of the normal eye. This makes them less effective in modeling vision disorders associated with abnormal shapes of the ocular structures which are hard to be precisely represented by analytical surfaces. We have developed a computer simulator that can simulate ocular structures of arbitrary shapes, for instance represented by polygon meshes. Topographic and geometric measurements of the cornea, lens, and retina from keratometer or medical imaging data can be integrated for individualized examination. We utilize parallel processing using modern Graphics Processing Units (GPUs) to efficiently compute retinal images by tracing millions of rays. A stable retinal image can be generated within minutes. We simulated depth-of-field, accommodation, chromatic aberrations, as well as astigmatism and correction. We also show application of the technique in patient specific vision correction by incorporating geometric models of the orbit reconstructed from clinical medical images. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

SILHOUETTE - HIDDEN LINE COMPUTER CODE WITH GENERALIZED SILHOUETTE SOLUTION

NASA Technical Reports Server (NTRS)

Hedgley, D. R.

1994-01-01

Flexibility in choosing how to display computer-generated three-dimensional drawings has become increasingly important in recent years. A major consideration is the enhancement of the realism and aesthetics of the presentation. A polygonal representation of objects, even with hidden lines removed, is not always desirable. A more pleasing pictorial representation often can be achieved by removing some of the remaining visible lines, thus creating silhouettes (or outlines) of selected surfaces of the object. Additionally, it should be noted that this silhouette feature allows warped polygons. This means that any polygon can be decomposed into constituent triangles. Considering these triangles as members of the same family will present a polygon with no interior lines, and thus removes the restriction of flat polygons. SILHOUETTE is a program for calligraphic drawings that can render any subset of polygons as a silhouette with respect to itself. The program is flexible enough to be applicable to every class of object. SILHOUETTE offers all possible combinations of silhouette and nonsilhouette specifications for an arbitrary solid. Thus, it is possible to enhance the clarity of any three-dimensional scene presented in two dimensions. Input to the program can be line segments or polygons. Polygons designated with the same number will be drawn as a silhouette of those polygons. SILHOUETTE is written in FORTRAN 77 and requires a graphics package such as DI-3000. The program has been implemented on a DEC VAX series computer running VMS and used 65K of virtual memory without a graphics package linked in. The source code is intended to be machine independent. This program is available on a 5.25 inch 360K MS-DOS format diskette (standard distribution) and is also available on a 9-track 1600 BPI ASCII CARD IMAGE magnetic tape. SILHOUETTE was developed in 1986 and was last updated in 1992.

Diffuse interface simulation of bubble rising process: a comparison of adaptive mesh refinement and arbitrary lagrange-euler methods

NASA Astrophysics Data System (ADS)

Wang, Ye; Cai, Jiejin; Li, Qiong; Yin, Huaqiang; Yang, Xingtuan

2018-06-01

Gas-liquid two phase flow exists in several industrial processes and light-water reactors (LWRs). A diffuse interface based finite element method with two different mesh generation methods namely, the Adaptive Mesh Refinement (AMR) and the Arbitrary Lagrange Euler (ALE) methods is used to model the shape and velocity changes in a rising bubble. Moreover, the calculating speed and mesh generation strategies of AMR and ALE are contrasted. The simulation results agree with the Bhagat's experiments, indicating that both mesh generation methods can simulate the characteristics of bubble accurately. We concluded that: the small bubble rises as elliptical with oscillation, whereas a larger bubble (11 mm > d > 7 mm) rises with a morphology between the elliptical and cap type with a larger oscillation. When the bubble is large (d > 11 mm), it rises up as a cap type, and the amplitude becomes smaller. Moreover, it takes longer to achieve the stable shape from the ellipsoid to the spherical cap type with the increase of the bubble diameter. The results also show that for smaller diameter case, the ALE method uses fewer grids and has a faster calculation speed, but the AMR method can solve the case of a large geometry deformation efficiently.

Resistive-force theory for mesh-like superhydrophobic surfaces

NASA Astrophysics Data System (ADS)

Schnitzer, Ory; Yariv, Ehud

2018-03-01

A common realization of superhydrophobic surfaces makes use of a mesh-like geometry, where pockets of air are trapped in a periodic array of holes in a no-slip solid substrate. We consider the small-solid-fraction limit where the ribs of the mesh are narrow. In this limit, we obtain a simple leading-order approximation for the slip-length tensor of an arbitrary mesh geometry. This approximation scales as the solid-fraction logarithm, as anticipated by Ybert et al. [Phys. Fluids 19, 123601 (2007), 10.1063/1.2815730]; in the special case of a square mesh it agrees with the analytical results obtained by Davis and Lauga [Phys. Fluids 21, 113101 (2009), 10.1063/1.3250947].

Transport of phase space densities through tetrahedral meshes using discrete flow mapping

NASA Astrophysics Data System (ADS)

Bajars, Janis; Chappell, David J.; Søndergaard, Niels; Tanner, Gregor

2017-01-01

Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximation of a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space.

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1991-01-01

A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes.

Hierarchical Regularization of Polygons for Photogrammetric Point Clouds of Oblique Images

NASA Astrophysics Data System (ADS)

Xie, L.; Hu, H.; Zhu, Q.; Wu, B.; Zhang, Y.

2017-05-01

Despite the success of multi-view stereo (MVS) reconstruction from massive oblique images in city scale, only point clouds and triangulated meshes are available from existing MVS pipelines, which are topologically defect laden, free of semantical information and hard to edit and manipulate interactively in further applications. On the other hand, 2D polygons and polygonal models are still the industrial standard. However, extraction of the 2D polygons from MVS point clouds is still a non-trivial task, given the fact that the boundaries of the detected planes are zigzagged and regularities, such as parallel and orthogonal, cannot preserve. Aiming to solve these issues, this paper proposes a hierarchical polygon regularization method for the photogrammetric point clouds from existing MVS pipelines, which comprises of local and global levels. After boundary points extraction, e.g. using alpha shapes, the local level is used to consolidate the original points, by refining the orientation and position of the points using linear priors. The points are then grouped into local segments by forward searching. In the global level, regularities are enforced through a labeling process, which encourage the segments share the same label and the same label represents segments are parallel or orthogonal. This is formulated as Markov Random Field and solved efficiently. Preliminary results are made with point clouds from aerial oblique images and compared with two classical regularization methods, which have revealed that the proposed method are more powerful in abstracting a single building and is promising for further 3D polygonal model reconstruction and GIS applications.

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods - Part 1: Derivation and properties

NASA Astrophysics Data System (ADS)

Eldred, Christopher; Randall, David

2017-02-01

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.

Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

DOE PAGES

Kauffman, Justin A.; Sheldon, Jason P.; Miller, Scott T.

2017-03-01

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusionmore » and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.« less

A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

DOE PAGES

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...

2015-02-24

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less

Jali - Unstructured Mesh Infrastructure for Multi-Physics Applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garimella, Rao V; Berndt, Markus; Coon, Ethan

2017-04-13

Jali is a parallel unstructured mesh infrastructure library designed for use by multi-physics simulations. It supports 2D and 3D arbitrary polyhedral meshes distributed over hundreds to thousands of nodes. Jali can read write Exodus II meshes along with fields and sets on the mesh and support for other formats is partially implemented or is (https://github.com/MeshToolkit/MSTK), an open source general purpose unstructured mesh infrastructure library from Los Alamos National Laboratory. While it has been made to work with other mesh frameworks such as MOAB and STKmesh in the past, support for maintaining the interface to these frameworks has been suspended formore » now. Jali supports distributed as well as on-node parallelism. Support of on-node parallelism is through direct use of the the mesh in multi-threaded constructs or through the use of "tiles" which are submeshes or sub-partitions of a partition destined for a compute node.« less

View-Dependent Simplification of Arbitrary Polygonal Environments

DTIC Science & Technology

2006-01-01

of backfacing nodes are not rendered [ Kumar 96]. 4.3 Triangle-Budget Simplification The screenspace error threshold and silhouette test allow the user...Greg Turk, and Dinesh Manocha for their invaluable guidance and support throughout this project. Funding for this work was provided by DARPA...Proceedings Visualization 95 , IEEE Computer Society Press (Atlanta, GA), 1995, pp. 296-303. [ Kumar 96] Kumar , Subodh, D. Manocha, W. Garrett, M. Lin

A simple finite element method for linear hyperbolic problems

DOE PAGES

Mu, Lin; Ye, Xiu

2017-09-14

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

A simple finite element method for linear hyperbolic problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Ye, Xiu

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

Terrain modeling for real-time simulation

NASA Astrophysics Data System (ADS)

Devarajan, Venkat; McArthur, Donald E.

1993-10-01

There are many applications, such as pilot training, mission rehearsal, and hardware-in-the- loop simulation, which require the generation of realistic images of terrain and man-made objects in real-time. One approach to meeting this requirement is to drape photo-texture over a planar polygon model of the terrain. The real time system then computes, for each pixel of the output image, the address in a texture map based on the intersection of the line-of-sight vector with the terrain model. High quality image generation requires that the terrain be modeled with a fine mesh of polygons while hardware costs limit the number of polygons which may be displayed for each scene. The trade-off between these conflicting requirements must be made in real-time because it depends on the changing position and orientation of the pilot's eye point or simulated sensor. The traditional approach is to develop a data base consisting of multiple levels of detail (LOD), and then selecting for display LODs as a function of range. This approach could lead to both anomalies in the displayed scene and inefficient use of resources. An approach has been developed in which the terrain is modeled with a set of nested polygons and organized as a tree with each node corresponding to a polygon. This tree is pruned to select the optimum set of nodes for each eye-point position. As the point of view moves, the visibility of some nodes drops below the limit of perception and may be deleted while new points must be added in regions near the eye point. An analytical model has been developed to determine the number of polygons required for display. This model leads to quantitative performance measures of the triangulation algorithm which is useful for optimizing system performance with a limited display capability.

Failure processes in soft and quasi-brittle materials with nonhomogeneous microstructures

NASA Astrophysics Data System (ADS)

Spring, Daniel W.

Material failure pervades the fields of materials science and engineering; it occurs at various scales and in various contexts. Understanding the mechanisms by which a material fails can lead to advancements in the way we design and build the world around us. For example, in structural engineering, understanding the fracture of concrete and steel can lead to improved structural systems and safer designs; in geological engineering, understanding the fracture of rock can lead to increased efficiency in oil and gas extraction; and in biological engineering, understanding the fracture of bone can lead to improvements in the design of bio-composites and medical implants. In this thesis, we numerically investigate a wide spectrum of failure behavior; in soft and quasi-brittle materials with nonhomogeneous microstructures considering a statistical distribution of material properties. The first topic we investigate considers the influence of interfacial interactions on the macroscopic constitutive response of particle reinforced elastomers. When a particle is embedded into an elastomer, the polymer chains in the elastomer tend to adsorb (or anchor) onto the surface of the particle; creating a region in the vicinity of each particle (often referred to as an interphase) with distinct properties from those in the bulk elastomer. This interphasial region has been known to exist for many decades, but is primarily omitted in computational investigations of such composites. In this thesis, we present an investigation into the influence of interphases on the macroscopic constitutive response of particle filled elastomers undergoing large deformations. In addition, at large deformations, a localized region of failure tends to accumulate around inclusions. To capture this localized region of failure (often referred to as interfacial debonding), we use cohesive zone elements which follow the Park-Paulino-Roesler traction-separation relation. To account for friction, we present a new, coupled cohesive-friction relation and detail its formulation and implementation. In the process of this investigation, we developed a small library of cohesive elements for use with a commercially available finite element analysis software package. Additionally, in this thesis, we present a series of methods for reducing mesh dependency in two-dimensional dynamic cohesive fracture simulations of quasi-brittle materials. In this setting, cracks are only permitted to propagate along element facets, thus a poorly designed discretization of the problem domain can introduce artifacts into the fracture behavior. To reduce mesh induced artifacts, we consider unstructured polygonal finite elements. A randomly-seeded polygonal mesh leads to an isotropic discretization of the problem domain, which does not bias the direction of crack propagation. However, polygonal meshes tend to limit the possible directions a crack may travel at each node, making this discretization a poor candidate for dynamic cohesive fracture simulations. To alleviate this problem, we propose two new topological operators. The first operator we propose is adaptive element-splitting, and the second is adaptive mesh refinement. Both operators are designed to improve the ability of unstructured polygonal meshes to capture crack patterns in dynamic cohesive fracture simulations. However, we demonstrate that element-splitting is more suited to pervasive fracture problems, whereas, adaptive refinement is more suited to problems exhibiting a dominant crack. Finally, we investigate the use of geometric and constitutive design features to regularize pervasive fragmentation behavior in three-dimensions. Throughout pervasive fracture simulations, many cracks initiate, propagate, branch and coalesce simultaneously. Because of the cohesive element method's unique framework, this behavior can be captured in a regularized manner. In this investigation, unstructuring techniques are used to introduce randomness into a numerical model. The behavior of quasi-brittle materials undergoing pervasive fracture and fragmentation is then examined using three examples. The examples are selected to investigate some of the significant factors influencing pervasive fracture and fragmentation behavior; including, geometric features, loading conditions, and material gradation.

WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions

NASA Astrophysics Data System (ADS)

Tsoutsanis, P.; Titarev, V. A.; Drikakis, D.

2011-02-01

The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases and the compressible Euler equations on various types of grids. Schemes of up to fifth order of spatial accuracy are considered.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Jitendra; Collier, Nathan; Bisht, Gautam

Vast carbon stocks stored in permafrost soils of Arctic tundra are under risk of release to the atmosphere under warming climate scenarios. Ice-wedge polygons in the low-gradient polygonal tundra create a complex mosaic of microtopographic features. This microtopography plays a critical role in regulating the fine-scale variability in thermal and hydrological regimes in the polygonal tundra landscape underlain by continuous permafrost. Modeling of thermal regimes of this sensitive ecosystem is essential for understanding the landscape behavior under the current as well as changing climate. Here, we present an end-to-end effort for high-resolution numerical modeling of thermal hydrology at real-world fieldmore » sites, utilizing the best available data to characterize and parameterize the models. We also develop approaches to model the thermal hydrology of polygonal tundra and apply them at four study sites near Barrow, Alaska, spanning across low to transitional to high-centered polygons, representing a broad polygonal tundra landscape. A multiphase subsurface thermal hydrology model (PFLOTRAN) was developed and applied to study the thermal regimes at four sites. Using a high-resolution lidar digital elevation model (DEM), microtopographic features of the landscape were characterized and represented in the high-resolution model mesh. The best available soil data from field observations and literature were utilized to represent the complex heterogeneous subsurface in the numerical model. Simulation results demonstrate the ability of the developed modeling approach to capture – without recourse to model calibration – several aspects of the complex thermal regimes across the sites, and provide insights into the critical role of polygonal tundra microtopography in regulating the thermal dynamics of the carbon-rich permafrost soils. Moreover, areas of significant disagreement between model results and observations highlight the importance of field-based observations of soil thermal and hydraulic properties for modeling-based studies of permafrost thermal dynamics, and provide motivation and guidance for future observations that will help address model and data gaps affecting our current understanding of the system.« less

A coupled ALE-AMR method for shock hydrodynamics

DOE PAGES

Waltz, J.; Bakosi, J.

2018-03-05

We present a numerical method combining adaptive mesh refinement (AMR) with arbitrary Lagrangian-Eulerian (ALE) mesh motion for the simulation of shock hydrodynamics on unstructured grids. The primary goal of the coupled method is to use AMR to reduce numerical error in ALE simulations at reduced computational expense relative to uniform fine mesh calculations, in the same manner that AMR has been used in Eulerian simulations. We also identify deficiencies with ALE methods that AMR is able to mitigate, and discuss the unique coupling challenges. The coupled method is demonstrated using three-dimensional unstructured meshes of up to O(10 7) tetrahedral cells.more » Convergence of ALE-AMR solutions towards both uniform fine mesh ALE results and analytic solutions is demonstrated. Speed-ups of 5-10× for a given level of error are observed relative to uniform fine mesh calculations.« less

A coupled ALE-AMR method for shock hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Waltz, J.; Bakosi, J.

We present a numerical method combining adaptive mesh refinement (AMR) with arbitrary Lagrangian-Eulerian (ALE) mesh motion for the simulation of shock hydrodynamics on unstructured grids. The primary goal of the coupled method is to use AMR to reduce numerical error in ALE simulations at reduced computational expense relative to uniform fine mesh calculations, in the same manner that AMR has been used in Eulerian simulations. We also identify deficiencies with ALE methods that AMR is able to mitigate, and discuss the unique coupling challenges. The coupled method is demonstrated using three-dimensional unstructured meshes of up to O(10 7) tetrahedral cells.more » Convergence of ALE-AMR solutions towards both uniform fine mesh ALE results and analytic solutions is demonstrated. Speed-ups of 5-10× for a given level of error are observed relative to uniform fine mesh calculations.« less

Laser Ray Tracing in a Parallel Arbitrary Lagrangian-Eulerian Adaptive Mesh Refinement Hydrocode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masters, N D; Kaiser, T B; Anderson, R W

2009-09-28

ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray-tracing in ALE-AMR. We present the equations of laser ray tracing, our approach to efficient traversal of the adaptive mesh hierarchy in which we propagate computational rays through a virtual composite mesh consisting of the finest resolution representation of the modeled space, and anticipate simulations that will be compared to experiments for code validation.

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods $-$ Part 1: Derivation and properties

DOE PAGES

Eldred, Christopher; Randall, David

2017-02-17

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restrictedmore » to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Lastly, detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.« less

Modeling the spatiotemporal variability in subsurface thermal regimes across a low-relief polygonal tundra landscape

DOE PAGES

Kumar, Jitendra; Collier, Nathan; Bisht, Gautam; ...

2016-09-27

Vast carbon stocks stored in permafrost soils of Arctic tundra are under risk of release to the atmosphere under warming climate scenarios. Ice-wedge polygons in the low-gradient polygonal tundra create a complex mosaic of microtopographic features. This microtopography plays a critical role in regulating the fine-scale variability in thermal and hydrological regimes in the polygonal tundra landscape underlain by continuous permafrost. Modeling of thermal regimes of this sensitive ecosystem is essential for understanding the landscape behavior under the current as well as changing climate. Here, we present an end-to-end effort for high-resolution numerical modeling of thermal hydrology at real-world fieldmore » sites, utilizing the best available data to characterize and parameterize the models. We also develop approaches to model the thermal hydrology of polygonal tundra and apply them at four study sites near Barrow, Alaska, spanning across low to transitional to high-centered polygons, representing a broad polygonal tundra landscape. A multiphase subsurface thermal hydrology model (PFLOTRAN) was developed and applied to study the thermal regimes at four sites. Using a high-resolution lidar digital elevation model (DEM), microtopographic features of the landscape were characterized and represented in the high-resolution model mesh. The best available soil data from field observations and literature were utilized to represent the complex heterogeneous subsurface in the numerical model. Simulation results demonstrate the ability of the developed modeling approach to capture – without recourse to model calibration – several aspects of the complex thermal regimes across the sites, and provide insights into the critical role of polygonal tundra microtopography in regulating the thermal dynamics of the carbon-rich permafrost soils. Moreover, areas of significant disagreement between model results and observations highlight the importance of field-based observations of soil thermal and hydraulic properties for modeling-based studies of permafrost thermal dynamics, and provide motivation and guidance for future observations that will help address model and data gaps affecting our current understanding of the system.« less

Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Thomas, James L. (Technical Monitor)

2003-01-01

The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.

Three-dimensional unstructured grid refinement and optimization using edge-swapping

NASA Technical Reports Server (NTRS)

Gandhi, Amar; Barth, Timothy

1993-01-01

This paper presents a three-dimensional (3-D) 'edge-swapping method based on local transformations. This method extends Lawson's edge-swapping algorithm into 3-D. The 3-D edge-swapping algorithm is employed for the purpose of refining and optimizing unstructured meshes according to arbitrary mesh-quality measures. Several criteria including Delaunay triangulations are examined. Extensions from two to three dimensions of several known properties of Delaunay triangulations are also discussed.

Development of Anthropometric Analogous Headforms. Phase 1.

DTIC Science & Technology

1994-10-31

shown in figure 5. This surface mesh can then be transformed into polygon faces that are able to be rendered by the AutoCAD rendering tools . Rendering of...computer-generated surfaces. The material removal techniques require the programming of the tool path of the cutter and in some cases requires specialized... tooling . Tool path programs are available to transfer the computer-generated surface into actual paths of the cutting tool . In cases where the

Interpretation of long- and short-wavelength magnetic anomalies

USGS Publications Warehouse

DeNoyer, John M.; Barringer, Anthony R.

1980-01-01

Magset was launched on October 30, 1979. More than a decade of examining existing data, devising appropriate models of the global magnetic field, and extending methods for interpreting long-wavelength magnetic anomalies preceded this launch Magnetic data collected by satellite can be interrupted by using a method of analysis that quantitively describes the magnetic field resulting from three-dimensional geologic structures that are bounded by an arbitrary number of polygonal faces, Each face my have any orientation and three or more sides. At each point of the external field, the component normal to each face is obtained by using an expression for the solid angle subtended by a generalized polygon. The "cross" of tangential components are relatively easy to obtain for the same polygons. No approximations have been made related to orbit height that restrict the dimensions of the polygons relative to the distance from the external field points. This permits the method to be used to model shorter wavelength anomalies obtained from aircraft or ground surveys. The magnetic fields for all the structures considered are determine in the same rectangular coordinate system. The coordinate system is in depended from the orientation of geologic trends and permits multiple structures or bodies to be included in the same magnetic field calculations. This single reference system also simplified adjustments in position and direction to account for earth curvature in regional interpretation.

Diffracted wavefield by an arbitrary aperture from Maggi-Rubinowicz transformation

NASA Astrophysics Data System (ADS)

Ganci, S.

2008-01-01

Fraunhofer diffraction patterns through apertures in opaque screens are the cases of most interest in optics. The major purpose of this paper is to establish a general and explicit formula for calculating diffracted wavefield from Maggi-Rubinowicz transformation. The 2-D integration (Rayleigh-Sommerfeld or Helmholtz-Kirchhoff integral formulas) is reduced to a 1-D integration over the rim of the aperture. Some examples for elliptical and polygonal apertures are given.

An advancing front Delaunay triangulation algorithm designed for robustness

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1992-01-01

A new algorithm is described for generating an unstructured mesh about an arbitrary two-dimensional configuration. Mesh points are generated automatically by the algorithm in a manner which ensures a smooth variation of elements, and the resulting triangulation constitutes the Delaunay triangulation of these points. The algorithm combines the mathematical elegance and efficiency of Delaunay triangulation algorithms with the desirable point placement features, boundary integrity, and robustness traditionally associated with advancing-front-type mesh generation strategies. The method offers increased robustness over previous algorithms in that it cannot fail regardless of the initial boundary point distribution and the prescribed cell size distribution throughout the flow-field.

An h-p Taylor-Galerkin finite element method for compressible Euler equations

NASA Technical Reports Server (NTRS)

Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

1991-01-01

An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

Texturing of continuous LOD meshes with the hierarchical texture atlas

NASA Astrophysics Data System (ADS)

Birkholz, Hermann

2006-02-01

For the rendering of detailed virtual environments, trade-offs have to be made between image quality and rendering time. An immersive experience of virtual reality always demands high frame-rates with the best reachable image qual-ity. Continuous Level of Detail (cLoD) triangle-meshes provide an continuous spectrum of detail for a triangle mesh that can be used to create view-dependent approximations of the environment in real-time. This enables the rendering with a constant number of triangles and thus with constant frame-rates. Normally the construction of such cLoD mesh representations leads to the loss of all texture information of the original mesh. To overcome this problem, a parameter domain can be created, in order to map the surface properties (colour, texture, normal) to it. This parameter domain can be used to map the surface properties back to arbitrary approximations of the original mesh. The parameter domain is often a simplified version of the mesh to be parameterised. This limits the reachable simplification to the domain mesh which has to map the surface of the original mesh with the least possible stretch. In this paper, a hierarchical domain mesh is presented, that scales between very coarse domain meshes and good property-mapping.

Calculus domains modelled using an original bool algebra based on polygons

NASA Astrophysics Data System (ADS)

Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.

2016-08-01

Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.

Efficient Boundary Extraction of BSP Solids Based on Clipping Operations.

PubMed

Wang, Charlie C L; Manocha, Dinesh

2013-01-01

We present an efficient algorithm to extract the manifold surface that approximates the boundary of a solid represented by a Binary Space Partition (BSP) tree. Our polygonization algorithm repeatedly performs clipping operations on volumetric cells that correspond to a spatial convex partition and computes the boundary by traversing the connected cells. We use point-based representations along with finite-precision arithmetic to improve the efficiency and generate the B-rep approximation of a BSP solid. The core of our polygonization method is a novel clipping algorithm that uses a set of logical operations to make it resistant to degeneracies resulting from limited precision of floating-point arithmetic. The overall BSP to B-rep conversion algorithm can accurately generate boundaries with sharp and small features, and is faster than prior methods. At the end of this paper, we use this algorithm for a few geometric processing applications including Boolean operations, model repair, and mesh reconstruction.

A hybrid framework for coupling arbitrary summation-by-parts schemes on general meshes

NASA Astrophysics Data System (ADS)

Lundquist, Tomas; Malan, Arnaud; Nordström, Jan

2018-06-01

We develop a general interface procedure to couple both structured and unstructured parts of a hybrid mesh in a non-collocated, multi-block fashion. The target is to gain optimal computational efficiency in fluid dynamics simulations involving complex geometries. While guaranteeing stability, the proposed procedure is optimized for accuracy and requires minimal algorithmic modifications to already existing schemes. Initial numerical investigations confirm considerable efficiency gains compared to non-hybrid calculations of up to an order of magnitude.

Emerging trend prediction in biomedical literature.

PubMed

Moerchen, Fabian; Fradkin, Dmitriy; Dejori, Mathaeus; Wachmann, Bernd

2008-11-06

We present a study on how to predict new emerging trends in the biomedical domain based on textual data. We thereby propose a way of anticipating the transformation of arbitrary information into ground truth knowledge by predicting the inclusion of new terms into the MeSH ontology. We also discuss the preparation of a dataset for the evaluation of emerging trend prediction algorithms that is based on PubMed abstracts and related MeSH terms. The results suggest that early prediction of emerging trends is possible.

Numerical modeling of pulsed laser-material interaction and of laser plume dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Qiang; Shi, Yina

2015-03-10

We have developed two-dimensional Arbitrary Lagrangian Eulerian (ALE) code which is used to study the physical processes, the plasma absorption, the crater profile, and the temperature distribution on metallic target and below the surface. The ALE method overcomes problems with Lagrangian moving mesh distortion by mesh smoothing and conservative quantities remapping from Lagrangian mesh to smoothed one. A new second order accurate diffusion solver has been implemented for the thermal conduction and radiation transport on distorted mesh. The results of numerical simulation of pulsed laser ablation are presented. The influences of different processes, such as time evolution of the surfacemore » temperature, interspecies interactions (elastic collisions, recombination-dissociation reaction), interaction with an ambient gas are examined. The study presents particular interest for the analysis of experimental results obtained during pulsed laser ablation.« less

Entanglement polygon inequality in qubit systems

NASA Astrophysics Data System (ADS)

Qian, Xiao-Feng; Alonso, Miguel A.; Eberly, J. H.

2018-06-01

We prove a set of tight entanglement inequalities for arbitrary N-qubit pure states. By focusing on all bi-partite marginal entanglements between each single qubit and its remaining partners, we show that the inequalities provide an upper bound for each marginal entanglement, while the known monogamy relation establishes the lower bound. The restrictions and sharing properties associated with the inequalities are further analyzed with a geometric polytope approach, and examples of three-qubit GHZ-class and W-class entangled states are presented to illustrate the results.

Optimal Filling of Shapes

NASA Astrophysics Data System (ADS)

Phillips, Carolyn L.; Anderson, Joshua A.; Huber, Greg; Glotzer, Sharon C.

2012-05-01

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal disks. We consider the properties of ideal distributions of N disks as N→∞. We note an analogy with energy landscapes.

Geometric Transforms for Fast Geometric Algorithms.

DTIC Science & Technology

1979-12-01

representation is not an important issue in a real RAM.) For more complicated geometrical objects such as polygons, polyhedrons , and Voronoi diagrams the issue...of N disks canl be represented as a convex polyhedron in O(N log N) time. Proof: We illustrate thle construction in Figurc 3-1 1. We first embed the N...or intersection of N arbitrary planar disks by a convex polyhedron in O(N log N) time. 0. Figure 3-11: General case for intersection or union of N

Approximate calculation of multispar cantilever and semicantilever wings with parallel ribs under direct and indirect loading

NASA Technical Reports Server (NTRS)

Sanger, Eugen

1932-01-01

A method is presented for approximate static calculation, which is based on the customary assumption of rigid ribs, while taking into account the systematic errors in the calculation results due to this arbitrary assumption. The procedure is given in greater detail for semicantilever and cantilever wings with polygonal spar plan form and for wings under direct loading only. The last example illustrates the advantages of the use of influence lines for such wing structures and their practical interpretation.

Transparent electrodes fabricated via the self-assembly of silver nanowires using a bubble template.

PubMed

Tokuno, Takehiro; Nogi, Masaya; Jiu, Jinting; Sugahara, Tohru; Suganuma, Katsuaki

2012-06-26

To shore up the demand of transparent electrodes for wide applications such as organic light emitting diodes and solar cells, transparent electrodes are required as an alternative for indium tin oxide electrodes. Herein the self-assembly method with a bubble template paves the way for cost-effective fabrication of transparent electrodes with high conductivity and transparency using self-assembly of silver nanowires (AgNWs) in a bubble template. AgNWs were first dispersed in water that was bubbled with a surfactant and a thickening agent. Furthermore, these AgNWs were assembled by lining along the bubble ridges. When the bubbles containing the AgNWs were sandwiched between two glass substrates, the bubble ridges including the AgNWs formed continuous polygonal structures. Mesh structures were formed on both glass substrates after air-drying. The mesh structures evolved into mesh transparent electrodes following heat-treatment. The AgNW mesh structure exhibited a low sheet resistance of 6.2 Ω/square with a transparency of 84% after heat treatment at 200 °C for 20 min. The performance is higher than that of transparent electrodes with random networks of AgNWs. Furthermore, the conductivity and transparency of the mesh transparent electrodes can be adjusted by changing the amount of the AgNW suspension and the space between the two glass substrates.

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

PubMed

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, available to the scientific community, to generate, visualize, and save the adaptive resolution meshes.

Dynamic Mesh Adaptation for Front Evolution Using Discontinuous Galerkin Based Weighted Condition Number Mesh Relaxation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert

2016-06-21

A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as amore » volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.« less

Design of an essentially non-oscillatory reconstruction procedure on finite-element type meshes

NASA Technical Reports Server (NTRS)

Abgrall, R.

1991-01-01

An essentially non-oscillatory reconstruction for functions defined on finite-element type meshes was designed. Two related problems are studied: the interpolation of possibly unsmooth multivariate functions on arbitrary meshes and the reconstruction of a function from its average in the control volumes surrounding the nodes of the mesh. Concerning the first problem, we have studied the behavior of the highest coefficients of the Lagrange interpolation function which may admit discontinuities of locally regular curves. This enables us to choose the best stencil for the interpolation. The choice of the smallest possible number of stencils is addressed. Concerning the reconstruction problem, because of the very nature of the mesh, the only method that may work is the so called reconstruction via deconvolution method. Unfortunately, it is well suited only for regular meshes as we show, but we also show how to overcome this difficulty. The global method has the expected order of accuracy but is conservative up to a high order quadrature formula only. Some numerical examples are given which demonstrate the efficiency of the method.

Gas flow calculation method of a ramjet engine

NASA Astrophysics Data System (ADS)

Kostyushin, Kirill; Kagenov, Anuar; Eremin, Ivan; Zhiltsov, Konstantin; Shuvarikov, Vladimir

2017-11-01

At the present study calculation methodology of gas dynamics equations in ramjet engine is presented. The algorithm is based on Godunov`s scheme. For realization of calculation algorithm, the system of data storage is offered, the system does not depend on mesh topology, and it allows using the computational meshes with arbitrary number of cell faces. The algorithm of building a block-structured grid is given. Calculation algorithm in the software package "FlashFlow" is implemented. Software package is verified on the calculations of simple configurations of air intakes and scramjet models.

A Walking Method for Non-Decomposition Intersection and Union of Arbitrary Polygons and Polyhedrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Graham, M.; Yao, J.

We present a method for computing the intersection and union of non- convex polyhedrons without decomposition in O(n log n) time, where n is the total number of faces of both polyhedrons. We include an accompanying Python package which addresses many of the practical issues associated with implementation and serves as a proof of concept. The key to the method is that by considering the edges of the original ob- jects and the intersections between faces as walking routes, we can e ciently nd the boundary of the intersection of arbitrary objects using directional walks, thus handling the concave casemore » in a natural manner. The method also easily extends to plane slicing and non-convex polyhedron unions, and both the polyhedron and its constituent faces may be non-convex.« less

Enriching Triangle Mesh Animations with Physically Based Simulation.

PubMed

Li, Yijing; Xu, Hongyi; Barbic, Jernej

2017-10-01

We present a system to combine arbitrary triangle mesh animations with physically based Finite Element Method (FEM) simulation, enabling control over the combination both in space and time. The input is a triangle mesh animation obtained using any method, such as keyframed animation, character rigging, 3D scanning, or geometric shape modeling. The input may be non-physical, crude or even incomplete. The user provides weights, specified using a minimal user interface, for how much physically based simulation should be allowed to modify the animation in any region of the model, and in time. Our system then computes a physically-based animation that is constrained to the input animation to the amount prescribed by these weights. This permits smoothly turning physics on and off over space and time, making it possible for the output to strictly follow the input, to evolve purely based on physically based simulation, and anything in between. Achieving such results requires a careful combination of several system components. We propose and analyze these components, including proper automatic creation of simulation meshes (even for non-manifold and self-colliding undeformed triangle meshes), converting triangle mesh animations into animations of the simulation mesh, and resolving collisions and self-collisions while following the input.

Adaptive mesh optimization and nonrigid motion recovery based image registration for wide-field-of-view ultrasound imaging.

PubMed

Tan, Chaowei; Wang, Bo; Liu, Paul; Liu, Dong

2008-01-01

Wide field of view (WFOV) imaging mode obtains an ultrasound image over an area much larger than the real time window normally available. As the probe is moved over the region of interest, new image frames are combined with prior frames to form a panorama image. Image registration techniques are used to recover the probe motion, eliminating the need for a position sensor. Speckle patterns, which are inherent in ultrasound imaging, change, or become decorrelated, as the scan plane moves, so we pre-smooth the image to reduce the effects of speckle in registration, as well as reducing effects from thermal noise. Because we wish to track the movement of features such as structural boundaries, we use an adaptive mesh over the entire smoothed image to home in on areas with feature. Motion estimation using blocks centered at the individual mesh nodes generates a field of motion vectors. After angular correction of motion vectors, we model the overall movement between frames as a nonrigid deformation. The polygon filling algorithm for precise, persistence-based spatial compounding constructs the final speckle reduced WFOV image.

Three new models for evaluation of standard involute spur gear mesh stiffness

NASA Astrophysics Data System (ADS)

Liang, Xihui; Zhang, Hongsheng; Zuo, Ming J.; Qin, Yong

2018-02-01

Time-varying mesh stiffness is one of the main internal excitation sources of gear dynamics. Accurate evaluation of gear mesh stiffness is crucial for gear dynamic analysis. This study is devoted to developing new models for spur gear mesh stiffness evaluation. Three models are proposed. The proposed model 1 can give very accurate mesh stiffness result but the gear bore surface must be assumed to be rigid. Enlighted by the proposed model 1, our research discovers that the angular deflection pattern of the gear bore surface of a pair of meshing gears under a constant torque basically follows a cosine curve. Based on this finding, two other models are proposed. The proposed model 2 evaluates gear mesh stiffness by using angular deflections at different circumferential angles of an end surface circle of the gear bore. The proposed model 3 requires using only the angular deflection at an arbitrary circumferential angle of an end surface circle of the gear bore but this model can only be used for a gear with the same tooth profile among all teeth. The proposed models are accurate in gear mesh stiffness evaluation and easy to use. Finite element analysis is used to validate the accuracy of the proposed models.

Efficiently computing exact geodesic loops within finite steps.

PubMed

Xin, Shi-Qing; He, Ying; Fu, Chi-Wing

2012-06-01

Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.

A comparative study on different methods of automatic mesh generation of human femurs.

PubMed

Viceconti, M; Bellingeri, L; Cristofolini, L; Toni, A

1998-01-01

The aim of this study was to evaluate comparatively five methods for automating mesh generation (AMG) when used to mesh a human femur. The five AMG methods considered were: mapped mesh, which provides hexahedral elements through a direct mapping of the element onto the geometry; tetra mesh, which generates tetrahedral elements from a solid model of the object geometry; voxel mesh which builds cubic 8-node elements directly from CT images; and hexa mesh that automatically generated hexahedral elements from a surface definition of the femur geometry. The various methods were tested against two reference models: a simplified geometric model and a proximal femur model. The first model was useful to assess the inherent accuracy of the meshes created by the AMG methods, since an analytical solution was available for the elastic problem of the simplified geometric model. The femur model was used to test the AMG methods in a more realistic condition. The femoral geometry was derived from a reference model (the "standardized femur") and the finite element analyses predictions were compared to experimental measurements. All methods were evaluated in terms of human and computer effort needed to carry out the complete analysis, and in terms of accuracy. The comparison demonstrated that each tested method deserves attention and may be the best for specific situations. The mapped AMG method requires a significant human effort but is very accurate and it allows a tight control of the mesh structure. The tetra AMG method requires a solid model of the object to be analysed but is widely available and accurate. The hexa AMG method requires a significant computer effort but can also be used on polygonal models and is very accurate. The voxel AMG method requires a huge number of elements to reach an accuracy comparable to that of the other methods, but it does not require any pre-processing of the CT dataset to extract the geometry and in some cases may be the only viable solution.

High-Order Moving Overlapping Grid Methodology in a Spectral Element Method

NASA Astrophysics Data System (ADS)

Merrill, Brandon E.

A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. Mesh movement is enabled through the Arbitrary Lagrangian-Eulerian formulation of the governing equations, which allows for prescription of arbitrary velocity values at discrete mesh points. The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver. Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data. Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies, show near linear strong scaling, even for moderately large processor counts. The moving overlapping mesh methodology is utilized to investigate the effect of an upstream turbulent wake on a three-dimensional oscillating NACA0012 extruded airfoil. A direct numerical simulation (DNS) at Reynolds Number 44,000 is performed for steady inflow incident upon the airfoil oscillating between angle of attack 5.6° and 25° with reduced frequency k=0.16. Results are contrasted with subsequent DNS of the same oscillating airfoil in a turbulent wake generated by a stationary upstream cylinder.

Mesh Oriented datABase

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tautges, Timothy J.

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 handlesmore » rather than pointers, to allow the underlying representation of an entity to change without changing the handle to that entity. Sets are arbitrary groupings of mesh entities and other sets. Sets also support parent/child relationships as a relation distinct from sets containing other sets. The directed-graph provided by set parent/child relationships is useful for modeling topological relations from a geometric model or other metadata. Tags are named data which can be assigned to the mesh as a whole, individual entities, or sets. Tags are a mechanism for attaching data to individual entities and sets are a mechanism for describing relations between entities; the combination of these two mechanisms isa powerful yet simple interface for representing metadata or application-specific data. For example, sets and tags can be used together to describe geometric topology, boundary condition, and inter-processor interface groupings in a mesh. MOAB is used in several ways in various applications. MOAB serves as the underlying mesh data representation in the VERDE mesh verification code. MOAB can also be used as a mesh input mechanism, using mesh readers induded with MOAB, or as a t’anslator between mesh formats, using readers and writers included with MOAB.« less

An automatic generation of non-uniform mesh for CFD analyses of image-based multiscale human airway models

NASA Astrophysics Data System (ADS)

Miyawaki, Shinjiro; Tawhai, Merryn H.; Hoffman, Eric A.; Lin, Ching-Long

2014-11-01

The authors have developed a method to automatically generate non-uniform CFD mesh for image-based human airway models. The sizes of generated tetrahedral elements vary in both radial and longitudinal directions to account for boundary layer and multiscale nature of pulmonary airflow. The proposed method takes advantage of our previously developed centerline-based geometry reconstruction method. In order to generate the mesh branch by branch in parallel, we used the open-source programs Gmsh and TetGen for surface and volume meshes, respectively. Both programs can specify element sizes by means of background mesh. The size of an arbitrary element in the domain is a function of wall distance, element size on the wall, and element size at the center of airway lumen. The element sizes on the wall are computed based on local flow rate and airway diameter. The total number of elements in the non-uniform mesh (10 M) was about half of that in the uniform mesh, although the computational time for the non-uniform mesh was about twice longer (170 min). The proposed method generates CFD meshes with fine elements near the wall and smooth variation of element size in longitudinal direction, which are required, e.g., for simulations with high flow rate. NIH Grants R01-HL094315, U01-HL114494, and S10-RR022421. Computer time provided by XSEDE.

A Sketching Interface for Freeform 3D Modeling

NASA Astrophysics Data System (ADS)

Igarashi, Takeo

This chapter introduces Teddy, a sketch-based modeling system to quickly and easily design freeform models such as stuffed animals and other rotund objects. The user draws several 2D freeform strokes interactively on the screen and the system automatically constructs plausible 3D polygonal surfaces. Our system supports several modeling operations, including the operation to construct a 3D polygonal surface from a 2D silhouette drawn by the user: it inflates the region surrounded by the silhouette making a wide area fat, and a narrow area thin. Teddy, our prototype system, is implemented as a Java program, and the mesh construction is done in real-time on a standard PC. Our informal user study showed that a first-time user masters the operations within 10 minutes, and can construct interesting 3D models within minutes. We also report the result of a case study where a high school teacher taught various 3D concepts in geography using the system.

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

All-quad meshing without cleanup

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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

Conforming and nonconforming virtual element methods for elliptic problems

DOE PAGES

Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J.

2016-08-03

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1- and L 2-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

Acoustic Panel Liner for an Engine Nacelle

NASA Technical Reports Server (NTRS)

Nark, Douglas M. (Inventor); Ayle, Earl (Inventor); Jones, Michael G. (Inventor); Ichihashi, Fumitaka (Inventor)

2016-01-01

An acoustic panel liner includes a face sheet, back plate, and liner core positioned there-between, which may be used in an engine nacelle. Elongated chambers contain variable amounts of septa at a calibrated depth or depths. The septa may have varying DC flow resistance. The chambers may have a hexagonal or other polygonal cross sections. The septa, such as mesh caps, may be bonded to an inner wall of a corresponding chamber. The insertion depths may be the same or different. If different, the pattern of distribution of the depths may be randomized.

Conforming and nonconforming virtual element methods for elliptic problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J.

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1- and L 2-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

Conical twist fields and null polygonal Wilson loops

NASA Astrophysics Data System (ADS)

Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Fioravanti, Davide

2018-06-01

Using an extension of the concept of twist field in QFT to space-time (external) symmetries, we study conical twist fields in two-dimensional integrable QFT. These create conical singularities of arbitrary excess angle. We show that, upon appropriate identification between the excess angle and the number of sheets, they have the same conformal dimension as branch-point twist fields commonly used to represent partition functions on Riemann surfaces, and that both fields have closely related form factors. However, we show that conical twist fields are truly different from branch-point twist fields. They generate different operator product expansions (short distance expansions) and form factor expansions (large distance expansions). In fact, we verify in free field theories, by re-summing form factors, that the conical twist fields operator product expansions are correctly reproduced. We propose that conical twist fields are the correct fields in order to understand null polygonal Wilson loops/gluon scattering amplitudes of planar maximally supersymmetric Yang-Mills theory.

Molecular Polygons Probe the Role of Intramolecular Strain in the Photophysics of π-Conjugated Chromophores.

PubMed

Wilhelm, Philipp; Vogelsang, Jan; Poluektov, Georgiy; Schönfelder, Nina; Keller, Tristan J; Jester, Stefan-Sven; Höger, Sigurd; Lupton, John M

2017-01-24

π-Conjugated segments, chromophores, are the electronically active units of polymer materials used in organic electronics. To elucidate the effect of the bending of these linear moieties on elementary electronic properties, such as luminescence color and radiative rate, we introduce a series of molecular polygons. The π-system in these molecules becomes so distorted in bichromophores (digons) that these absorb and emit light of arbitrary polarization: any part of the chain absorbs and emits radiation with equal probability. Bending leads to a cancellation of transition dipole moment (TDM), increasing excited-state lifetime. Simultaneously, fluorescence shifts to the red as radiative transitions require mixing of the excited state with vibrational modes. However, strain can become so large that excited-state localization on shorter units of the chain occurs, compensating TDM cancellation. The underlying correlations between shape and photophysics can only be resolved in single molecules. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

NASA Astrophysics Data System (ADS)

Meierbachtol, Collin S.; Svyatskiy, Daniil; Delzanno, Gian Luca; Vernon, Louis J.; Moulton, J. David

2017-12-01

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. Despite 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 an 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. 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.

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

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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

A novel consistent and well-balanced algorithm for simulations of multiphase flows on unstructured grids

NASA Astrophysics Data System (ADS)

Patel, Jitendra Kumar; Natarajan, Ganesh

2017-12-01

We discuss the development and assessment of a robust numerical algorithm for simulating multiphase flows with complex interfaces and high density ratios on arbitrary polygonal meshes. The algorithm combines the volume-of-fluid method with an incremental projection approach for incompressible multiphase flows in a novel hybrid staggered/non-staggered framework. The key principles that characterise the algorithm are the consistent treatment of discrete mass and momentum transport and the similar discretisation of force terms appearing in the momentum equation. The former is achieved by invoking identical schemes for convective transport of volume fraction and momentum in the respective discrete equations while the latter is realised by representing the gravity and surface tension terms as gradients of suitable scalars which are then discretised in identical fashion resulting in a balanced formulation. The hybrid staggered/non-staggered framework employed herein solves for the scalar normal momentum at the cell faces, while the volume fraction is computed at the cell centroids. This is shown to naturally lead to similar terms for pressure and its correction in the momentum and pressure correction equations respectively, which are again treated discretely in a similar manner. We show that spurious currents that corrupt the solution may arise both from an unbalanced formulation where forces (gravity and surface tension) are discretised in dissimilar manner and from an inconsistent approach where different schemes are used to convect the mass and momentum, with the latter prominent in flows which are convection-dominant with high density ratios. Interestingly, the inconsistent approach is shown to perform as well as the consistent approach even for high density ratio flows in some cases while it exhibits anomalous behaviour for other scenarios, even at low density ratios. Using a plethora of test problems of increasing complexity, we conclusively demonstrate that the consistent transport and balanced force treatment results in a numerically stable solution procedure and physically consistent results. The algorithm proposed in this study qualifies as a robust approach to simulate multiphase flows with high density ratios on unstructured meshes and may be realised in existing flow solvers with relative ease.

Matrix multiplication on the Intel Touchstone Delta

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huss-Lederman, S.; Jacobson, E.M.; Tsao, A.

1993-12-31

Matrix multiplication is a key primitive in block matrix algorithms such as those found in LAPACK. We present results from our study of matrix multiplication algorithms on the Intel Touchstone Delta, a distributed memory message-passing architecture with a two-dimensional mesh topology. We obtain an implementation that uses communication primitives highly suited to the Delta and exploits the single node assembly-coded matrix multiplication. Our algorithm is completely general, able to deal with arbitrary mesh aspect ratios and matrix dimensions, and has achieved parallel efficiency of 86% with overall peak performance in excess of 8 Gflops on 256 nodes for an 8800more » {times} 8800 matrix. We describe our algorithm design and implementation, and present performance results that demonstrate scalability and robust behavior over varying mesh topologies.« less

Unified algorithm of cone optics to compute solar flux on central receiver

NASA Astrophysics Data System (ADS)

Grigoriev, Victor; Corsi, Clotilde

2017-06-01

Analytical algorithms to compute flux distribution on central receiver are considered as a faster alternative to ray tracing. They have quite too many modifications, with HFLCAL and UNIZAR being the most recognized and verified. In this work, a generalized algorithm is presented which is valid for arbitrary sun shape of radial symmetry. Heliostat mirrors can have a nonrectangular profile, and the effects of shading and blocking, strong defocusing and astigmatism can be taken into account. The algorithm is suitable for parallel computing and can benefit from hardware acceleration of polygon texturing.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rebay, S.

This work is devoted to the description of an efficient unstructured mesh generation method entirely based on the Delaunay triangulation. The distinctive characteristic of the proposed method is that point positions and connections are computed simultaneously. This result is achieved by taking advantage of the sequential way in which the Bowyer-Watson algorithm computes the Delaunay triangulation. Two methods are proposed which have great geometrical flexibility, in that they allow us to treat domains of arbitrary shape and topology and to generate arbitrarily nonuniform meshes. The methods are computationally efficient and are applicable both in two and three dimensions. 11 refs.,more » 20 figs., 1 tab.« less

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Lesoinne, Michel

1993-01-01

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

DOE PAGES

Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert

2017-01-27

A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fractionmore » or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.« less

Visualization of Uncertainty

NASA Astrophysics Data System (ADS)

Jones, P. W.; Strelitz, R. A.

2012-12-01

The output of a simulation is best comprehended through the agency and methods of visualization, but a vital component of good science is knowledge of uncertainty. While great strides have been made in the quantification of uncertainty, especially in simulation, there is still a notable gap: there is no widely accepted means of simultaneously viewing the data and the associated uncertainty in one pane. Visualization saturates the screen, using the full range of color, shadow, opacity and tricks of perspective to display even a single variable. There is no room in the visualization expert's repertoire left for uncertainty. We present a method of visualizing uncertainty without sacrificing the clarity and power of the underlying visualization that works as well in 3-D and time-varying visualizations as it does in 2-D. At its heart, it relies on a principal tenet of continuum mechanics, replacing the notion of value at a point with a more diffuse notion of density as a measure of content in a region. First, the uncertainties calculated or tabulated at each point are transformed into a piecewise continuous field of uncertainty density . We next compute a weighted Voronoi tessellation of a user specified N convex polygonal/polyhedral cells such that each cell contains the same amount of uncertainty as defined by . The problem thus devolves into minimizing . Computation of such a spatial decomposition is O(N*N ), and can be computed iteratively making it possible to update easily over time as well as faster. The polygonal mesh does not interfere with the visualization of the data and can be easily toggled on or off. In this representation, a small cell implies a great concentration of uncertainty, and conversely. The content weighted polygons are identical to the cartogram familiar to the information visualization community in the depiction of things voting results per stat. Furthermore, one can dispense with the mesh or edges entirely to be replaced by symbols or glyphs at the generating points (effectively the center of the polygon). This methodology readily admits to rigorous statistical analysis using standard components found in R and thus entirely compatible with the visualization package we use (Visit and/or ParaView), the language we use (Python) and the UVCDAT environment that provides the programmer and analyst workbench. We will demonstrate the power and effectiveness of this methodology in climate studies. We will further argue that our method of defining (or predicting) values in a region has many advantages over the traditional visualization notion of value at a point.

Automated quadrilateral surface discretization method and apparatus usable to generate mesh in a finite element analysis system

DOEpatents

Blacker, Teddy D.

1994-01-01

An automatic quadrilateral surface discretization method and apparatus is provided for automatically discretizing a geometric region without decomposing the region. The automated quadrilateral surface discretization method and apparatus automatically generates a mesh of all quadrilateral elements which is particularly useful in finite element analysis. The generated mesh of all quadrilateral elements is boundary sensitive, orientation insensitive and has few irregular nodes on the boundary. A permanent boundary of the geometric region is input and rows are iteratively layered toward the interior of the geometric region. Also, an exterior permanent boundary and an interior permanent boundary for a geometric region may be input and the rows are iteratively layered inward from the exterior boundary in a first counter clockwise direction while the rows are iteratively layered from the interior permanent boundary toward the exterior of the region in a second clockwise direction. As a result, a high quality mesh for an arbitrary geometry may be generated with a technique that is robust and fast for complex geometric regions and extreme mesh gradations.

Hexahedral mesh generation via the dual arrangement of surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 compatiblemore » 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.« less

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, available to the scientific community, to generate, visualize, and save the adaptive resolution meshes. PMID:28690511

Analysis of Slope Limiters on Irregular Grids

NASA Technical Reports Server (NTRS)

Berger, Marsha; Aftosmis, Michael J.

2005-01-01

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. Many slope limiters in standard use do not preserve linear solutions on irregular grids impacting both accuracy and convergence. We rewrite some well-known limiters to highlight their underlying symmetry, and use this form to examine the proper - ties of both traditional and novel limiter formulations on non-uniform meshes. A consistent method of handling stretched meshes is developed which is both linearity preserving for arbitrary mesh stretchings and reduces to common limiters on uniform meshes. In multiple dimensions we analyze the monotonicity region of the gradient vector and show that the multidimensional limiting problem may be cast as the solution of a linear programming problem. For some special cases we present a new directional limiting formulation that preserves linear solutions in multiple dimensions on irregular grids. Computational results using model problems and complex three-dimensional examples are presented, demonstrating accuracy, monotonicity and robustness.

Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes

NASA Astrophysics Data System (ADS)

Amsallem, David; Tezaur, Radek; Farhat, Charbel

2016-12-01

A comprehensive approach for real-time computations using a database of parametric, linear, projection-based reduced-order models (ROMs) based on arbitrary underlying meshes is proposed. In the offline phase of this approach, the parameter space is sampled and linear ROMs defined by linear reduced operators are pre-computed at the sampled parameter points and stored. Then, these operators and associated ROMs are transformed into counterparts that satisfy a certain notion of consistency. In the online phase of this approach, a linear ROM is constructed in real-time at a queried but unsampled parameter point by interpolating the pre-computed linear reduced operators on matrix manifolds and therefore computing an interpolated linear ROM. The proposed overall model reduction framework is illustrated with two applications: a parametric inverse acoustic scattering problem associated with a mockup submarine, and a parametric flutter prediction problem associated with a wing-tank system. The second application is implemented on a mobile device, illustrating the capability of the proposed computational framework to operate in real-time.

Progress in the Simulation of Steady and Time-Dependent Flows with 3D Parallel Unstructured Cartesian Methods

NASA Technical Reports Server (NTRS)

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

2002-01-01

The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.

Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers

NASA Technical Reports Server (NTRS)

Sozer, Emre; Brehm, Christoph; Kiris, Cetin C.

2014-01-01

A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties

Two-dimensional mesh embedding for Galerkin B-spline methods

NASA Technical Reports Server (NTRS)

Shariff, Karim; Moser, Robert D.

1995-01-01

A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

AN EXTENSION OF THE ATHENA++ CODE FRAMEWORK FOR GRMHD BASED ON ADVANCED RIEMANN SOLVERS AND STAGGERED-MESH CONSTRAINED TRANSPORT

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Christopher J.; Stone, James M.; Gammie, Charles F.

2016-08-01

We present a new general relativistic magnetohydrodynamics (GRMHD) code integrated into the Athena++ framework. Improving upon the techniques used in most GRMHD codes, ours allows the use of advanced, less diffusive Riemann solvers, in particular HLLC and HLLD. We also employ a staggered-mesh constrained transport algorithm suited for curvilinear coordinate systems in order to maintain the divergence-free constraint of the magnetic field. Our code is designed to work with arbitrary stationary spacetimes in one, two, or three dimensions, and we demonstrate its reliability through a number of tests. We also report on its promising performance and scalability.

An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies

NASA Technical Reports Server (NTRS)

Quirk, James J.

1992-01-01

In this paper we describe an approach for dealing with arbitrary complex, two dimensional geometries, the so-called cartesian boundary method. Conceptually, the cartesian boundary method is quite simple. Solid bodies blank out areas of a background, cartesian mesh, and the resultant cut cells are singled out for special attention. However, there are several obstacles that must be overcome in order to achieve a practical scheme. We present a general strategy that overcomes these obstacles, together with some details of our successful conversion of an adaptive mesh algorithm from a body-fitted code to a cartesian boundary code.

Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Di Pietro, Daniele A.; Droniou, Jérôme; Manzini, Gianmarco

Here, in this work we develop arbitrary-order Discontinuous Skeletal Gradient Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal refers to the fact that the globally coupled unknowns are broken polynomials on the mesh skeleton. The key ingredient is a high-order gradient reconstruction composed of two terms: (i) a consistent contribution obtained mimicking an integration by parts formula inside each element and (ii) a stabilising term for which sufficient design conditions are provided. An example of stabilisation that satisfies the design conditions is proposed based on a local lifting of high-order residuals on a Raviart–Thomas–Nédélec subspace. We prove that the novelmore » DSGDs satisfy coercivity, consistency, limit-conformity, and compactness requirements that ensure convergence for a variety of elliptic and parabolic problems. Lastly, links with Hybrid High-Order, non-conforming Mimetic Finite Difference and non-conforming Virtual Element methods are also studied. Numerical examples complete the exposition.« less

Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes

DOE PAGES

Di Pietro, Daniele A.; Droniou, Jérôme; Manzini, Gianmarco

2017-11-21

Here, in this work we develop arbitrary-order Discontinuous Skeletal Gradient Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal refers to the fact that the globally coupled unknowns are broken polynomials on the mesh skeleton. The key ingredient is a high-order gradient reconstruction composed of two terms: (i) a consistent contribution obtained mimicking an integration by parts formula inside each element and (ii) a stabilising term for which sufficient design conditions are provided. An example of stabilisation that satisfies the design conditions is proposed based on a local lifting of high-order residuals on a Raviart–Thomas–Nédélec subspace. We prove that the novelmore » DSGDs satisfy coercivity, consistency, limit-conformity, and compactness requirements that ensure convergence for a variety of elliptic and parabolic problems. Lastly, links with Hybrid High-Order, non-conforming Mimetic Finite Difference and non-conforming Virtual Element methods are also studied. Numerical examples complete the exposition.« less

High-performance parallel analysis of coupled problems for aircraft propulsion

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Lanteri, S.; Maman, N.; Piperno, S.; Gumaste, U.

1994-01-01

This research program deals with the application of high-performance computing methods for the analysis of complete jet engines. We have entitled this program by applying the two dimensional parallel aeroelastic codes to the interior gas flow problem of a bypass jet engine. The fluid mesh generation, domain decomposition, and solution capabilities were successfully tested. We then focused attention on methodology for the partitioned analysis of the interaction of the gas flow with a flexible structure and with the fluid mesh motion that results from these structural displacements. This is treated by a new arbitrary Lagrangian-Eulerian (ALE) technique that models the fluid mesh motion as that of a fictitious mass-spring network. New partitioned analysis procedures to treat this coupled three-component problem are developed. These procedures involved delayed corrections and subcycling. Preliminary results on the stability, accuracy, and MPP computational efficiency are reported.

Mimetic finite difference method

NASA Astrophysics Data System (ADS)

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

An investigation into scalability and compliance for triple patterning with stitches for metal 1 at the 14nm node

NASA Astrophysics Data System (ADS)

Cork, Christopher; Miloslavsky, Alexander; Friedberg, Paul; Luk-Pat, Gerry

2013-04-01

Lithographers had hoped that single patterning would be enabled at the 20nm node by way of EUV lithography. However, due to delays in EUV readiness, double patterning with 193i lithography is currently relied upon for volume production for the 20nm node's metal 1 layer. At the 14nm and likely at the 10nm node, LE-LE-LE triple patterning technology (TPT) is one of the favored options [1,2] for patterning local interconnect and Metal 1 layers. While previous research has focused on TPT for contact mask, metal layers offer new challenges and opportunities, in particular the ability to decompose design polygons across more than one mask. The extra flexibility offered by the third mask and ability to leverage polygon stitching both serve to improve compliance. However, ensuring TPT compliance - the task of finding a 3-color mask decomposition for a design - is still a difficult task. Moreover, scalability concerns multiply the difficulty of triple patterning decomposition which is an NP-complete problem. Indeed previous work shows that network sizes above a few thousand nodes or polygons start to take significantly longer times to compute [3], making full chip decomposition for arbitrary layouts impractical. In practice Metal 1 layouts can be considered as two separate problem domains, namely: decomposition of standard cells and decomposition of IP blocks. Standard cells typically include only a few 10's of polygons and should be amenable to fast decomposition. Successive design iterations should resolve compliance issues and improve packing density. Density improvements are multiplied repeatedly as standard cells are placed multiple times. IP blocks, on the other hand, may involve very large networks. This paper evaluates multiple approaches to triple patterning decomposition for the Metal 1 layer. The benefits of polygon stitching, in particular, the ability to resolve commonly encountered non-compliant layout configurations and improve packing density, are weighed against the increased difficulty in finding an optimized, legal decomposition and coping with the increased scalability challenges.

A Finite Element Method for Simulation of Compressible Cavitating Flows

NASA Astrophysics Data System (ADS)

Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad

2016-11-01

This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.

Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2017-04-01

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

Interference Analysis for Highly Directional 60 GHz Mesh Networks: The Case for Rethinking Medium Access Control

DTIC Science & Technology

2010-11-24

Helmken, “Performance analysis of coherent DS - CDMA systems in a Nakagami fading channel with arbitrary parameters,” Vehicular Technology, IEEE...Transactions on, vol. 46, no. 2, pp. 289–297, may 1997. [26] M. Sunay and P. McLane, “Calculating error probabilities for DS - CDMA systems: when not to use

Translation and integration of numerical atomic orbitals in linear molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heinäsmäki, Sami, E-mail: sami.heinasmaki@gmail.com

2014-02-14

We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.

A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2014-10-01

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with stiff relaxation source terms.

A 3D finite element ALE method using an approximate Riemann solution

DOE PAGES

Chiravalle, V. P.; Morgan, N. R.

2016-08-09

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

A 3D finite element ALE method using an approximate Riemann solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiravalle, V. P.; Morgan, N. R.

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

A multi-dimensional high-order DG-ALE method based on gas-kinetic theory with application to oscillating bodies

NASA Astrophysics Data System (ADS)

Ren, Xiaodong; Xu, Kun; Shyy, Wei

2016-07-01

This paper presents a multi-dimensional high-order discontinuous Galerkin (DG) method in an arbitrary Lagrangian-Eulerian (ALE) formulation to simulate flows over variable domains with moving and deforming meshes. It is an extension of the gas-kinetic DG method proposed by the authors for static domains (X. Ren et al., 2015 [22]). A moving mesh gas kinetic DG method is proposed for both inviscid and viscous flow computations. A flux integration method across a translating and deforming cell interface has been constructed. Differently from the previous ALE-type gas kinetic method with piecewise constant mesh velocity at each cell interface within each time step, the mesh velocity variation inside a cell and the mesh moving and rotating at a cell interface have been accounted for in the finite element framework. As a result, the current scheme is applicable for any kind of mesh movement, such as translation, rotation, and deformation. The accuracy and robustness of the scheme have been improved significantly in the oscillating airfoil calculations. All computations are conducted in a physical domain rather than in a reference domain, and the basis functions move with the grid movement. Therefore, the numerical scheme can preserve the uniform flow automatically, and satisfy the geometric conservation law (GCL). The numerical accuracy can be maintained even for a largely moving and deforming mesh. Several test cases are presented to demonstrate the performance of the gas-kinetic DG-ALE method.

Syringe-Injectable Electronics with a Plug-and-Play Input/Output Interface.

PubMed

Schuhmann, Thomas G; Yao, Jun; Hong, Guosong; Fu, Tian-Ming; Lieber, Charles M

2017-09-13

Syringe-injectable mesh electronics represent a new paradigm for brain science and neural prosthetics by virtue of the stable seamless integration of the electronics with neural tissues, a consequence of the macroporous mesh electronics structure with all size features similar to or less than individual neurons and tissue-like flexibility. These same properties, however, make input/output (I/O) connection to measurement electronics challenging, and work to-date has required methods that could be difficult to implement by the life sciences community. Here we present a new syringe-injectable mesh electronics design with plug-and-play I/O interfacing that is rapid, scalable, and user-friendly to nonexperts. The basic design tapers the ultraflexible mesh electronics to a narrow stem that routes all of the device/electrode interconnects to I/O pads that are inserted into a standard zero insertion force (ZIF) connector. Studies show that the entire plug-and-play mesh electronics can be delivered through capillary needles with precise targeting using microliter-scale injection volumes similar to the standard mesh electronics design. Electrical characterization of mesh electronics containing platinum (Pt) electrodes and silicon (Si) nanowire field-effect transistors (NW-FETs) demonstrates the ability to interface arbitrary devices with a contact resistance of only 3 Ω. Finally, in vivo injection into mice required only minutes for I/O connection and yielded expected local field potential (LFP) recordings from a compact head-stage compatible with chronic studies. Our results substantially lower barriers for use by new investigators and open the door for increasingly sophisticated and multifunctional mesh electronics designs for both basic and translational studies.

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

NASA Technical Reports Server (NTRS)

Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.

2012-01-01

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

The mutual inductance calculation between circular and quadrilateral coils at arbitrary attitudes using a rotation matrix for airborne transient electromagnetic systems

NASA Astrophysics Data System (ADS)

Ji, Yanju; Wang, Hongyuan; Lin, Jun; Guan, Shanshan; Feng, Xue; Li, Suyi

2014-12-01

Performance testing and calibration of airborne transient electromagnetic (ATEM) systems are conducted to obtain the electromagnetic response of ground loops. It is necessary to accurately calculate the mutual inductance between transmitting coils, receiving coils and ground loops to compute the electromagnetic responses. Therefore, based on Neumann's formula and the measured attitudes of the coils, this study deduces the formula for the mutual inductance calculation between circular and quadrilateral coils, circular and circular coils, and quadrilateral and quadrilateral coils using a rotation matrix, and then proposes a method to calculate the mutual inductance between two coils at arbitrary attitudes (roll, pitch, and yaw). Using coil attitude simulated data of an ATEM system, we calculate the mutual inductance of transmitting coils and ground loops at different attitudes, analyze the impact of coil attitudes on mutual inductance, and compare the computational accuracy and speed of the proposed method with those of other methods using the same data. The results show that the relative error of the calculation is smaller and that the speed-up is significant compared to other methods. Moreover, the proposed method is also applicable to the mutual inductance calculation of polygonal and circular coils at arbitrary attitudes and is highly expandable.

Evaluation of the Anisotropic Radiative Conductivity of a Low-Density Carbon Fiber Material from Realistic Microscale Imaging

NASA Technical Reports Server (NTRS)

Nouri, Nima; Panerai, Francesco; Tagavi, Kaveh A.; Mansour, Nagi N.; Martin, Alexandre

2015-01-01

The radiative heat transfer inside a low-density carbon fiber insulator is analyzed using a three-dimensional direct simulation model. A robust procedure is presented for the numerical calculation of the geometric configuration factor to compute the radiative energy exchange processes among the small discretized surface areas of the fibrous material. The methodology is applied to a polygonal mesh of a fibrous insulator obtained from three-dimensional microscale imaging of the real material. The anisotropic values of the radiative conductivity are calculated for that geometry. The results yield both directional and thermal dependence of the radiative conductivity.

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

NASA Astrophysics Data System (ADS)

Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael

2018-06-01

In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.

Design quadrilateral apertures in binary computer-generated holograms of large space bandwidth product.

PubMed

Wang, Jing; Sheng, Yunlong

2016-09-20

A new approach for designing the binary computer-generated hologram (CGH) of a very large number of pixels is proposed. Diffraction of the CGH apertures is computed by the analytical Abbe transform and by considering the aperture edges as the basic diffracting elements. The computation cost is independent of the CGH size. The arbitrary-shaped polygonal apertures in the CGH consist of quadrilateral apertures, which are designed by assigning the binary phases using the parallel genetic algorithm with a local search, followed by optimizing the locations of the co-vertices with a direct search. The design results in high performance with low image reconstruction error.

Unstructured Finite Elements and Dynamic Meshing for Explicit Phase Tracking in Multiphase Problems

NASA Astrophysics Data System (ADS)

Chandra, Anirban; Yang, Fan; Zhang, Yu; Shams, Ehsan; Sahni, Onkar; Oberai, Assad; Shephard, Mark

2017-11-01

Multi-phase processes involving phase change at interfaces, such as evaporation of a liquid or combustion of a solid, represent an interesting class of problems with varied applications. Large density ratio across phases, discontinuous fields at the interface and rapidly evolving geometries are some of the inherent challenges which influence the numerical modeling of multi-phase phase change problems. In this work, a mathematically consistent and robust computational approach to address these issues is presented. We use stabilized finite element methods on mixed topology unstructured grids for solving the compressible Navier-Stokes equations. Appropriate jump conditions derived from conservations laws across the interface are handled by using discontinuous interpolations, while the continuity of temperature and tangential velocity is enforced using a penalty parameter. The arbitrary Lagrangian-Eulerian (ALE) technique is utilized to explicitly track the interface motion. Mesh at the interface is constrained to move with the interface while elsewhere it is moved using the linear elasticity analogy. Repositioning is applied to the layered mesh that maintains its structure and normal resolution. In addition, mesh modification is used to preserve the quality of the volumetric mesh. This work is supported by the U.S. Army Grants W911NF1410301 and W911NF16C0117.

ALEGRA -- A massively parallel h-adaptive code for solid dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Summers, R.M.; Wong, M.K.; Boucheron, E.A.

1997-12-31

ALEGRA is a multi-material, arbitrary-Lagrangian-Eulerian (ALE) code for solid dynamics designed to run on massively parallel (MP) computers. It combines the features of modern Eulerian shock codes, such as CTH, with modern Lagrangian structural analysis codes using an unstructured grid. ALEGRA is being developed for use on the teraflop supercomputers to conduct advanced three-dimensional (3D) simulations of shock phenomena important to a variety of systems. ALEGRA was designed with the Single Program Multiple Data (SPMD) paradigm, in which the mesh is decomposed into sub-meshes so that each processor gets a single sub-mesh with approximately the same number of elements. Usingmore » this approach the authors have been able to produce a single code that can scale from one processor to thousands of processors. A current major effort is to develop efficient, high precision simulation capabilities for ALEGRA, without the computational cost of using a global highly resolved mesh, through flexible, robust h-adaptivity of finite elements. H-adaptivity is the dynamic refinement of the mesh by subdividing elements, thus changing the characteristic element size and reducing numerical error. The authors are working on several major technical challenges that must be met to make effective use of HAMMER on MP computers.« less

Three-dimensional local ALE-FEM method for fluid flow in domains containing moving boundaries/objects interfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carrington, David Bradley; Monayem, A. K. M.; Mazumder, H.

2015-03-05

A three-dimensional finite element method for the numerical simulations of fluid flow in domains containing moving rigid objects or boundaries is developed. The method falls into the general category of Arbitrary Lagrangian Eulerian methods; it is based on a fixed mesh that is locally adapted in the immediate vicinity of the moving interfaces and reverts to its original shape once the moving interfaces go past the elements. The moving interfaces are defined by separate sets of marker points so that the global mesh is independent of interface movement and the possibility of mesh entanglement is eliminated. The results is amore » fully robust formulation capable of calculating on domains of complex geometry with moving boundaries or devises that can also have a complex geometry without danger of the mesh becoming unsuitable due to its continuous deformation thus eliminating the need for repeated re-meshing and interpolation. Moreover, the boundary conditions on the interfaces are imposed exactly. This work is intended to support the internal combustion engines simulator KIVA developed at Los Alamos National Laboratories. The model's capabilities are illustrated through application to incompressible flows in different geometrical settings that show the robustness and flexibility of the technique to perform simulations involving moving boundaries in a three-dimensional domain.« less

TESS: A RELATIVISTIC HYDRODYNAMICS CODE ON A MOVING VORONOI MESH

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duffell, Paul C.; MacFadyen, Andrew I., E-mail: pcd233@nyu.edu, E-mail: macfadyen@nyu.edu

2011-12-01

We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finite-volume form. The mesh-generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluidsmore » on a dynamic Voronoi mesh. When run in Lagrangian mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical, and cylindrical coordinates and is modular so that auxiliary physics solvers are readily integrated into the TESS framework and so that this can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.« less

Kinematics, structural mechanics, and design of origami structures with smooth folds

NASA Astrophysics Data System (ADS)

Peraza Hernandez, Edwin Alexander

Origami provides novel approaches to the fabrication, assembly, and functionality of engineering structures in various fields such as aerospace, robotics, etc. With the increase in complexity of the geometry and materials for origami structures that provide engineering utility, computational models and design methods for such structures have become essential. Currently available models and design methods for origami structures are generally limited to the idealization of the folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures having non-negligible thickness or maximum curvature at the folds restricted by material limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate representations of structural response and a new approach is needed. The first contribution of this dissertation is a model for the kinematics of origami structures having realistic folds of non-zero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of the smooth folds and the constraints on their associated kinematic variables are presented. A numerical implementation of the model allowing for kinematic simulation of structures having arbitrary fold patterns is also described. Examples illustrating the capability of the model to capture realistic structural folding response are provided. Subsequently, a method for solving the origami design problem of determining the geometry of a single planar sheet and its pattern of smooth folds that morphs into a given three-dimensional goal shape, discretized as a polygonal mesh, is presented. The design parameterization of the planar sheet and the constraints that allow for a valid pattern of smooth folds and approximation of the goal shape in a known folded configuration are presented. Various testing examples considering goal shapes of diverse geometries are provided. Afterwards, a model for the structural mechanics of origami continuum bodies with smooth folds is presented. Such a model entails the integration of the presented kinematic model and existing plate theories in order to obtain a structural representation for folds having non-zero thickness and comprised of arbitrary materials. The model is validated against finite element analysis. The last contribution addresses the design and analysis of active material-based self-folding structures that morph via simultaneous folding towards a given three-dimensional goal shape starting from a planar configuration. Implementation examples including shape memory alloy (SMA)-based self-folding structures are provided.

Analysis of electrophoresis performance

NASA Technical Reports Server (NTRS)

Roberts, Glyn O.

1988-01-01

A flexible efficient computer code is being developed to simulate electrophoretic separation phenomena, in either a cylindrical or a rectangular geometry. The code will computer the evolution in time of the concentrations of an arbitrary number of chemical species, and of the temperature, pH distribution, conductivity, electric field, and fluid motion. Use of nonuniform meshes and fast accurate implicit time-stepping will yield accurate answers at economical cost.

Adaptive Meshing of Ship Air-Wake Flowfields

DTIC Science & Technology

2014-10-21

performs cut- cell operations at geometry boundaries. A second-order spatial finite-volume scheme has been incorporated with explicit first order...The cells intersected by the geometry are handled using the “cut- cell ” approach, which is basically creating arbitrary polyhedral elements with...appropriate surface boundary conditions. Any cells completely outside the computational domain are tagged external and not solved in the flow solution

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - III. Viscoelastic attenuation

NASA Astrophysics Data System (ADS)

Käser, Martin; Dumbser, Michael; de la Puente, Josep; Igel, Heiner

2007-01-01

We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on 3-D unstructured tetrahedral meshes. Using the velocity-stress formulation provides a linear hyperbolic system of equations with source terms that is completed by additional equations for the anelastic functions including the strain history of the material. These additional equations result from the rheological model of the generalized Maxwell body and permit the incorporation of realistic attenuation properties of viscoelastic material accounting for the behaviour of elastic solids and viscous fluids. The proposed method combines the Discontinuous Galerkin (DG) finite element (FE) method with the ADER approach using Arbitrary high order DERivatives for flux calculations. The DG approach, in contrast to classical FE methods, uses a piecewise polynomial approximation of the numerical solution which allows for discontinuities at element interfaces. Therefore, the well-established theory of numerical fluxes across element interfaces obtained by the solution of Riemann problems can be applied as in the finite volume framework. The main idea of the ADER time integration approach is a Taylor expansion in time in which all time derivatives are replaced by space derivatives using the so-called Cauchy-Kovalewski procedure which makes extensive use of the governing PDE. Due to the ADER time integration technique the same approximation order in space and time is achieved automatically and the method is a one-step scheme advancing the solution for one time step without intermediate stages. To this end, we introduce a new unrolled recursive algorithm for efficiently computing the Cauchy-Kovalewski procedure by making use of the sparsity of the system matrices. The numerical convergence analysis demonstrates that the new schemes provide very high order accuracy even on unstructured tetrahedral meshes while computational cost and storage space for a desired accuracy can be reduced when applying higher degree approximation polynomials. In addition, we investigate the increase in computing time, when the number of relaxation mechanisms due to the generalized Maxwell body are increased. An application to a well-acknowledged test case and comparisons with analytic and reference solutions, obtained by different well-established numerical methods, confirm the performance of the proposed method. Therefore, the development of the highly accurate ADER-DG approach for tetrahedral meshes including viscoelastic material provides a novel, flexible and efficient numerical technique to approach 3-D wave propagation problems including realistic attenuation and complex geometry.

Multiresolution Distance Volumes for Progressive Surface Compression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laney, D E; Bertram, M; Duchaineau, M A

2002-04-18

We present a surface compression method that stores surfaces as wavelet-compressed signed-distance volumes. Our approach enables the representation of surfaces with complex topology and arbitrary numbers of components within a single multiresolution data structure. This data structure elegantly handles topological modification at high compression rates. Our method does not require the costly and sometimes infeasible base mesh construction step required by subdivision surface approaches. We present several improvements over previous attempts at compressing signed-distance functions, including an 0(n) distance transform, a zero set initialization method for triangle meshes, and a specialized thresholding algorithm. We demonstrate the potential of sampled distancemore » volumes for surface compression and progressive reconstruction for complex high genus surfaces.« less

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1996-01-01

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

3D hierarchical interface-enriched finite element method: Implementation and applications

NASA Astrophysics Data System (ADS)

Soghrati, Soheil; Ahmadian, Hossein

2015-10-01

A hierarchical interface-enriched finite element method (HIFEM) is proposed for the mesh-independent treatment of 3D problems with intricate morphologies. The HIFEM implements a recursive algorithm for creating enrichment functions that capture gradient discontinuities in nonconforming finite elements cut by arbitrary number and configuration of materials interfaces. The method enables the mesh-independent simulation of multiphase problems with materials interfaces that are in close proximity or contact while providing a straightforward general approach for evaluating the enrichments. In this manuscript, we present a detailed discussion on the implementation issues and required computational geometry considerations associated with the HIFEM approximation of thermal and mechanical responses of 3D problems. A convergence study is provided to investigate the accuracy and convergence rate of the HIFEM and compare them with standard FEM benchmark solutions. We will also demonstrate the application of this mesh-independent method for simulating the thermal and mechanical responses of two composite materials systems with complex microstructures.

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 3: Advanced Fan Section Grid Generator Final Report and Computer Program User's Manual

NASA Technical Reports Server (NTRS)

Crook, Andrew J.; Delaney, Robert A.

1991-01-01

A procedure is studied for generating three-dimensional grids for advanced turbofan engine fan section geometries. The procedure constructs a discrete mesh about engine sections containing the fan stage, an arbitrary number of axisymmetric radial flow splitters, a booster stage, and a bifurcated core/bypass flow duct with guide vanes. The mesh is an h-type grid system, the points being distributed with a transfinite interpolation scheme with axial and radial spacing being user specified. Elliptic smoothing of the grid in the meridional plane is a post-process option. The grid generation scheme is consistent with aerodynamic analyses utilizing the average-passage equation system developed by Dr. John Adamczyk of NASA Lewis. This flow solution scheme requires a series of blade specific grids each having a common axisymmetric mesh, but varying in the circumferential direction according to the geometry of the specific blade row.

A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong Luo; Luqing Luo; Robert Nourgaliev

2012-11-01

A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems onmore » arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.« less

Direct Replacement of Arbitrary Grid-Overlapping by Non-Structured Grid

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing

1994-01-01

A new approach that uses nonstructured mesh to replace the arbitrarily overlapped structured regions of embedded grids is presented. The present methodology uses the Chimera composite overlapping mesh system so that the physical domain of the flowfield is subdivided into regions which can accommodate easily-generated grid for complex configuration. In addition, a Delaunay triangulation technique generates nonstructured triangular mesh which wraps over the interconnecting region of embedded grids. It is designed that the present approach, termed DRAGON grid, has three important advantages: eliminating some difficulties of the Chimera scheme, such as the orphan points and/or bad quality of interpolation stencils; making grid communication in a fully conservative way; and implementation into three dimensions is straightforward. A computer code based on a time accurate, finite volume, high resolution scheme for solving the compressible Navier-Stokes equations has been further developed to include both the Chimera overset grid and the nonstructured mesh schemes. For steady state problems, the local time stepping accelerates convergence based on a Courant - Friedrichs - Leury (CFL) number near the local stability limit. Numerical tests on representative steady and unsteady supersonic inviscid flows with strong shock waves are demonstrated.

Recent advances in high-order WENO finite volume methods for compressible multiphase flows

NASA Astrophysics Data System (ADS)

Dumbser, Michael

2013-10-01

We present two new families of better than second order accurate Godunov-type finite volume methods for the solution of nonlinear hyperbolic partial differential equations with nonconservative products. One family is based on a high order Arbitrary-Lagrangian-Eulerian (ALE) formulation on moving meshes, which allows to resolve the material contact wave in a very sharp way when the mesh is moved at the speed of the material interface. The other family of methods is based on a high order Adaptive Mesh Refinement (AMR) strategy, where the mesh can be strongly refined in the vicinity of the material interface. Both classes of schemes have several building blocks in common, in particular: a high order WENO reconstruction operator to obtain high order of accuracy in space; the use of an element-local space-time Galerkin predictor step which evolves the reconstruction polynomials in time and that allows to reach high order of accuracy in time in one single step; the use of a path-conservative approach to treat the nonconservative terms of the PDE. We show applications of both methods to the Baer-Nunziato model for compressible multiphase flows.

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Legat, Vincent; Vallaeys, Valentin; Naithani, Jaya; Thiery, Wim; Remacle, Jean-François; Deleersnijder, Eric

2018-03-01

The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces. The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian-Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level. The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

The NonConforming Virtual Element Method for the Stokes Equations

DOE PAGES

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

2016-01-01

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

Stereo matching and view interpolation based on image domain triangulation.

PubMed

Fickel, Guilherme Pinto; Jung, Claudio R; Malzbender, Tom; Samadani, Ramin; Culbertson, Bruce

2013-09-01

This paper presents a new approach for stereo matching and view interpolation problems based on triangular tessellations suitable for a linear array of rectified cameras. The domain of the reference image is initially partitioned into triangular regions using edge and scale information, aiming to place vertices along image edges and increase the number of triangles in textured regions. A region-based matching algorithm is then used to find an initial disparity for each triangle, and a refinement stage is applied to change the disparity at the vertices of the triangles, generating a piecewise linear disparity map. A simple post-processing procedure is applied to connect triangles with similar disparities generating a full 3D mesh related to each camera (view), which are used to generate new synthesized views along the linear camera array. With the proposed framework, view interpolation reduces to the trivial task of rendering polygonal meshes, which can be done very fast, particularly when GPUs are employed. Furthermore, the generated views are hole-free, unlike most point-based view interpolation schemes that require some kind of post-processing procedures to fill holes.

Electromagnetic Scattering From a Polygonal Thin Metallic Plate Using Quadrilateral Meshing

NASA Technical Reports Server (NTRS)

Deshpande, Manohar D.

2003-01-01

The problem of electromagnetic (EM) scattering from irregularly shaped, thin, metallic flat plates in free space is solved using the electric field integral equation (EFIE) approach in conjunction with the method of moments (MoM) with quadrilateral meshing. An irregularly shaped thin plate is discretized into quadrilateral patches and the unknown electric surface current over the plate is expressed in terms of proper basis functions over these patches. The basis functions for the electric surface current density that satisfy the proper boundary conditions on these quadrilateral patches are derived. The unknown surface current density on these quadrilateral patches is determined by setting up and solving the electric field integral equation by the application of the MoM. From the knowledge of the surface current density, the EM scattering from various irregularly shaped plates is determined and compared with the earlier published results. The novelty in the present approach is the use of quadrilateral patches instead of well known and often used triangular patches. The numerical results obtained using the quadrilateral patches compare favorably with measured results.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nivarti, Girish V., E-mail: g.nivarti@alumni.ubc.ca; Salehi, M. Mahdi; Bushe, W. Kendal

2015-01-15

Highlights: •An algorithm for partitioning computational meshes is proposed. •The Morton order space-filling curve is modified to achieve improved locality. •A spatial locality metric is defined to compare results with existing approaches. •Results indicate improved performance of the algorithm in complex geometries. -- Abstract: A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton ordermore » curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.« less

An unstructured mesh arbitrary Lagrangian-Eulerian unsteady incompressible flow solver and its application to insect flight aerodynamics

NASA Astrophysics Data System (ADS)

Su, Xiaohui; Cao, Yuanwei; Zhao, Yong

2016-06-01

In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.

Higher-Order Advection-Based Remap of Magnetic Fields in an Arbitrary Lagrangian-Eulerian Code

NASA Astrophysics Data System (ADS)

Cornille, Brian; White, Dan

2017-10-01

We will present methods formulated for the Eulerian advection stage of an arbitrary Lagrangian-Eulerian code for the new addition of magnetohydrodynamic (MHD) effects. The various physical fields are advanced in time using a Lagrangian formulation of the system. When this Lagrangian motion produces substantial distortion of the mesh, it can be difficult or impossible to progress the simulation forward. This is overcome by relaxation of the mesh while the physical fields are frozen. The code has already successfully been extended to include evolution of magnetic field diffusion during the Lagrangian motion stage. This magnetic field is discretized using an H(div) compatible finite element basis. The advantage of this basis is that the divergence-free constraint of magnetic fields is maintained exactly during the Lagrangian motion evolution. Our goal is to preserve this property during Eulerian advection as well. We will demonstrate this property and the importance of MHD effects in several numerical experiments. In pulsed-power experiments magnetic fields may be imposed or spontaneously generated. When these magnetic fields are present, the evolution of the experiment may differ from a comparable configuration without magnetic fields. Prepared by LLNL under Contract DE-AC52-07NA27344. Supported by DOE CSGF under Grant Number DE-FG02-97ER25308.

Segmentation of 3d Models for Cultural Heritage Structural Analysis - Some Critical Issues

NASA Astrophysics Data System (ADS)

Gonizzi Barsanti, S.; Guidi, G.; De Luca, L.

2017-08-01

Cultural Heritage documentation and preservation has become a fundamental concern in this historical period. 3D modelling offers a perfect aid to record ancient buildings and artefacts and can be used as a valid starting point for restoration, conservation and structural analysis, which can be performed by using Finite Element Methods (FEA). The models derived from reality-based techniques, made up of the exterior surfaces of the objects captured at high resolution, are - for this reason - made of millions of polygons. Such meshes are not directly usable in structural analysis packages and need to be properly pre-processed in order to be transformed in volumetric meshes suitable for FEA. In addition, dealing with ancient objects, a proper segmentation of 3D volumetric models is needed to analyse the behaviour of the structure with the most suitable level of detail for the different sections of the structure under analysis. Segmentation of 3D models is still an open issue, especially when dealing with ancient, complicated and geometrically complex objects that imply the presence of anomalies and gaps, due to environmental agents such as earthquakes, pollution, wind and rain, or human factors. The aims of this paper is to critically analyse some of the different methodologies and algorithms available to segment a 3D point cloud or a mesh, identifying difficulties and problems by showing examples on different structures.

Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.

2015-07-01

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshes.

Monogamy Relations of Measurement-Induced Disturbance

NASA Astrophysics Data System (ADS)

Liu, Feng; Li, Fei; Wei, Yun-Xia; Ma, Hong-Yang

2017-06-01

The standard monogamy imposes severe limitations to sharing quantum correlations in multipartite quantum systems, which is a star topology and is established by Coffman, Kundu and Wootters. In this work, we discuss some monogamy relations beyond it, and focus on the measurement-induced disturbance (MID) which quantifies the multipartite quantum correlation. We prove exactly that MID obeys the property of discarding quantum systems never increases in an arbitrary quantum state. Moreover, we define a new kind of sharper monogamy relation which shows that the sum of all bipartite MID can not exceed the amount of total MID. This restriction is similarly called a mesh monogamy. We numerically study how MID is distributed in a 4-qubit mixed state, and which relation exists between the mesh monogamy of MID and the level of obeying the standard monogamy.

Evaluation of a transient, simultaneous, arbitrary Lagrange-Euler based multi-physics method for simulating the mitral heart valve.

PubMed

Espino, Daniel M; Shepherd, Duncan E T; Hukins, David W L

2014-01-01

A transient multi-physics model of the mitral heart valve has been developed, which allows simultaneous calculation of fluid flow and structural deformation. A recently developed contact method has been applied to enable simulation of systole (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the mitral valve within the heart walls in two dimensions. Only the mitral valve undergoes deformation. A moving arbitrary Lagrange-Euler mesh is used to allow true fluid-structure interaction (FSI). The FSI model requires blood flow to induce valve closure by inducing strains in the region of 10-20%. Model predictions were found to be consistent with existing literature and will undergo further development.

EMPHASIS/Nevada UTDEM user guide. Version 2.0.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turner, C. David; Seidel, David Bruce; Pasik, Michael Francis

The Unstructured Time-Domain ElectroMagnetics (UTDEM) portion of the EMPHASIS suite solves Maxwell's equations using finite-element techniques on unstructured meshes. This document provides user-specific information to facilitate the use of the code for applications of interest. UTDEM is a general-purpose code for solving Maxwell's equations on arbitrary, unstructured tetrahedral meshes. The geometries and the meshes thereof are limited only by the patience of the user in meshing and by the available computing resources for the solution. UTDEM solves Maxwell's equations using finite-element method (FEM) techniques on tetrahedral elements using vector, edge-conforming basis functions. EMPHASIS/Nevada Unstructured Time-Domain ElectroMagnetic Particle-In-Cell (UTDEM PIC) ismore » a superset of the capabilities found in UTDEM. It adds the capability to simulate systems in which the effects of free charge are important and need to be treated in a self-consistent manner. This is done by integrating the equations of motion for macroparticles (a macroparticle is an object that represents a large number of real physical particles, all with the same position and momentum) being accelerated by the electromagnetic forces upon the particle (Lorentz force). The motion of these particles results in a current, which is a source for the fields in Maxwell's equations.« less

A new adaptive mesh refinement strategy for numerically solving evolutionary PDE's

NASA Astrophysics Data System (ADS)

Burgarelli, Denise; Kischinhevsky, Mauricio; Biezuner, Rodney Josue

2006-11-01

A graph-based implementation of quadtree meshes for dealing with adaptive mesh refinement (AMR) in the numerical solution of evolutionary partial differential equations is discussed using finite volume methods. The technique displays a plug-in feature that allows replacement of a group of cells in any region of interest for another one with arbitrary refinement, and with only local changes occurring in the data structure. The data structure is also specially designed to minimize the number of operations needed in the AMR. Implementation of the new scheme allows flexibility in the levels of refinement of adjacent regions. Moreover, storage requirements and computational cost compare competitively with mesh refinement schemes based on hierarchical trees. Low storage is achieved for only the children nodes are stored when a refinement takes place. These nodes become part of a graph structure, thus motivating the denomination autonomous leaves graph (ALG) for the new scheme. Neighbors can then be reached without accessing their parent nodes. Additionally, linear-system solvers based on the minimization of functionals can be easily employed. ALG was not conceived with any particular problem or geometry in mind and can thus be applied to the study of several phenomena. Some test problems are used to illustrate the effectiveness of the technique.

Electromagnetic forward modelling for realistic Earth models using unstructured tetrahedral meshes and a meshfree approach

NASA Astrophysics Data System (ADS)

Farquharson, C.; Long, J.; Lu, X.; Lelievre, P. G.

2017-12-01

Real-life geology is complex, and so, even when allowing for the diffusive, low resolution nature of geophysical electromagnetic methods, we need Earth models that can accurately represent this complexity when modelling and inverting electromagnetic data. This is particularly the case for the scales, detail and conductivity contrasts involved in mineral and hydrocarbon exploration and development, but also for the larger scale of lithospheric studies. Unstructured tetrahedral meshes provide a flexible means of discretizing a general, arbitrary Earth model. This is important when wanting to integrate a geophysical Earth model with a geological Earth model parameterized in terms of surfaces. Finite-element and finite-volume methods can be derived for computing the electric and magnetic fields in a model parameterized using an unstructured tetrahedral mesh. A number of such variants have been proposed and have proven successful. However, the efficiency and accuracy of these methods can be affected by the "quality" of the tetrahedral discretization, that is, how many of the tetrahedral cells in the mesh are long, narrow and pointy. This is particularly the case if one wants to use an iterative technique to solve the resulting linear system of equations. One approach to deal with this issue is to develop sophisticated model and mesh building and manipulation capabilities in order to ensure that any mesh built from geological information is of sufficient quality for the electromagnetic modelling. Another approach is to investigate other methods of synthesizing the electromagnetic fields. One such example is a "meshfree" approach in which the electromagnetic fields are synthesized using a mesh that is distinct from the mesh used to parameterized the Earth model. There are then two meshes, one describing the Earth model and one used for the numerical mathematics of computing the fields. This means that there are no longer any quality requirements on the model mesh, which makes the process of building a geophysical Earth model from a geological model much simpler. In this presentation we will explore the issues that arise when working with realistic Earth models and when synthesizing geophysical electromagnetic data for them. We briefly consider meshfree methods as a possible means of alleviating some of these issues.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.

1990-01-01

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry

NASA Astrophysics Data System (ADS)

Al-Marouf, M.; Samtaney, R.

2017-05-01

We present an embedded ghost fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

Digital relief generation from 3D models

NASA Astrophysics Data System (ADS)

Wang, Meili; Sun, Yu; Zhang, Hongming; Qian, Kun; Chang, Jian; He, Dongjian

2016-09-01

It is difficult to extend image-based relief generation to high-relief generation, as the images contain insufficient height information. To generate reliefs from three-dimensional (3D) models, it is necessary to extract the height fields from the model, but this can only generate bas-reliefs. To overcome this problem, an efficient method is proposed to generate bas-reliefs and high-reliefs directly from 3D meshes. To produce relief features that are visually appropriate, the 3D meshes are first scaled. 3D unsharp masking is used to enhance the visual features in the 3D mesh, and average smoothing and Laplacian smoothing are implemented to achieve better smoothing results. A nonlinear variable scaling scheme is then employed to generate the final bas-reliefs and high-reliefs. Using the proposed method, relief models can be generated from arbitrary viewing positions with different gestures and combinations of multiple 3D models. The generated relief models can be printed by 3D printers. The proposed method provides a means of generating both high-reliefs and bas-reliefs in an efficient and effective way under the appropriate scaling factors.

Efficient low-bit-rate adaptive mesh-based motion compensation technique

NASA Astrophysics Data System (ADS)

Mahmoud, Hanan A.; Bayoumi, Magdy A.

2001-08-01

This paper proposes a two-stage global motion estimation method using a novel quadtree block-based motion estimation technique and an active mesh model. In the first stage, motion parameters are estimated by fitting block-based motion vectors computed using a new efficient quadtree technique, that divides a frame into equilateral triangle blocks using the quad-tree structure. Arbitrary partition shapes are achieved by allowing 4-to-1, 3-to-1 and 2-1 merge/combine of sibling blocks having the same motion vector . In the second stage, the mesh is constructed using an adaptive triangulation procedure that places more triangles over areas with high motion content, these areas are estimated during the first stage. finally the motion compensation is achieved by using a novel algorithm that is carried by both the encoder and the decoder to determine the optimal triangulation of the resultant partitions followed by affine mapping at the encoder. Computer simulation results show that the proposed method gives better performance that the conventional ones in terms of the peak signal-to-noise ration (PSNR) and the compression ratio (CR).

Full-color digitized holography for large-scale holographic 3D imaging of physical and nonphysical objects.

PubMed

Matsushima, Kyoji; Sonobe, Noriaki

2018-01-01

Digitized holography techniques are used to reconstruct three-dimensional (3D) images of physical objects using large-scale computer-generated holograms (CGHs). The object field is captured at three wavelengths over a wide area at high densities. Synthetic aperture techniques using single sensors are used for image capture in phase-shifting digital holography. The captured object field is incorporated into a virtual 3D scene that includes nonphysical objects, e.g., polygon-meshed CG models. The synthetic object field is optically reconstructed as a large-scale full-color CGH using red-green-blue color filters. The CGH has a wide full-parallax viewing zone and reconstructs a deep 3D scene with natural motion parallax.

Interface projection techniques for fluid-structure interaction modeling with moving-mesh methods

NASA Astrophysics Data System (ADS)

Tezduyar, Tayfun E.; Sathe, Sunil; Pausewang, Jason; Schwaab, Matthew; Christopher, Jason; Crabtree, Jason

2008-12-01

The stabilized space-time fluid-structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM) was applied to a number of 3D examples, including arterial fluid mechanics and parachute aerodynamics. Here we focus on the interface projection techniques that were developed as supplementary methods targeting the computational challenges associated with the geometric complexities of the fluid-structure interface. Although these supplementary techniques were developed in conjunction with the SSTFSI method and in the context of air-fabric interactions, they can also be used in conjunction with other moving-mesh methods, such as the Arbitrary Lagrangian-Eulerian (ALE) method, and in the context of other classes of FSI applications. The supplementary techniques currently consist of using split nodal values for pressure at the edges of the fabric and incompatible meshes at the air-fabric interfaces, the FSI Geometric Smoothing Technique (FSI-GST), and the Homogenized Modeling of Geometric Porosity (HMGP). Using split nodal values for pressure at the edges and incompatible meshes at the interfaces stabilizes the structural response at the edges of the membrane used in modeling the fabric. With the FSI-GST, the fluid mechanics mesh is sheltered from the consequences of the geometric complexity of the structure. With the HMGP, we bypass the intractable complexities of the geometric porosity by approximating it with an “equivalent”, locally-varying fabric porosity. As test cases demonstrating how the interface projection techniques work, we compute the air-fabric interactions of windsocks, sails and ringsail parachutes.

MAGNA (Materially and Geometrically Nonlinear Analysis). Part II. Preprocessor Manual.

DTIC Science & Technology

1982-12-01

AGRID can accept a virtually arbitrary collection of point coor- dinates which lie on a surface of interest, and generate a regular grid of mesh points...in the form of a collection of such patches to be translated into an assemblage of biquadratic surface elements (see Subsection 2.1, Figure 2.2...using IMPRESS can be converted for use with the present preprocessor by means of the IMPRINT translator. IMPRINT is a collection of conversion routines

Computing Gravitational Fields of Finite-Sized Bodies

NASA Technical Reports Server (NTRS)

Quadrelli, Marco

2005-01-01

A computer program utilizes the classical theory of gravitation, implemented by means of the finite-element method, to calculate the near gravitational fields of bodies of arbitrary size, shape, and mass distribution. The program was developed for application to a spacecraft and to floating proof masses and associated equipment carried by the spacecraft for detecting gravitational waves. The program can calculate steady or time-dependent gravitational forces, moments, and gradients thereof. Bodies external to a proof mass can be moving around the proof mass and/or deformed under thermoelastic loads. An arbitrarily shaped proof mass is represented by a collection of parallelepiped elements. The gravitational force and moment acting on each parallelepiped element of a proof mass, including those attributable to the self-gravitational field of the proof mass, are computed exactly from the closed-form equation for the gravitational potential of a parallelepiped. The gravitational field of an arbitrary distribution of mass external to a proof mass can be calculated either by summing the fields of suitably many point masses or by higher-order Gauss-Legendre integration over all elements surrounding the proof mass that are part of a finite-element mesh. This computer program is compatible with more general finite-element codes, such as NASTRAN, because it is configured to read a generic input data file, containing the detailed description of the finiteelement mesh.

Advanced DPSM approach for modeling ultrasonic wave scattering in an arbitrary geometry

NASA Astrophysics Data System (ADS)

Yadav, Susheel K.; Banerjee, Sourav; Kundu, Tribikram

2011-04-01

Several techniques are used to diagnose structural damages. In the ultrasonic technique structures are tested by analyzing ultrasonic signals scattered by damages. The interpretation of these signals requires a good understanding of the interaction between ultrasonic waves and structures. Therefore, researchers need analytical or numerical techniques to have a clear understanding of the interaction between ultrasonic waves and structural damage. However, modeling of wave scattering phenomenon by conventional numerical techniques such as finite element method requires very fine mesh at high frequencies necessitating heavy computational power. Distributed point source method (DPSM) is a newly developed robust mesh free technique to simulate ultrasonic, electrostatic and electromagnetic fields. In most of the previous studies the DPSM technique has been applied to model two dimensional surface geometries and simple three dimensional scatterer geometries. It was difficult to perform the analysis for complex three dimensional geometries. This technique has been extended to model wave scattering in an arbitrary geometry. In this paper a channel section idealized as a thin solid plate with several rivet holes is formulated. The simulation has been carried out with and without cracks near the rivet holes. Further, a comparison study has been also carried out to characterize the crack. A computer code has been developed in C for modeling the ultrasonic field in a solid plate with and without cracks near the rivet holes.

How Misapplication of the Hydrologic Unit Framework ...

EPA Pesticide Factsheets

Hydrologic units provide a convenient nationwide set of geographic polygons based on an arbitrary subdivision of the drainage of land surface areas at several hierarchical levels. Half or more of these units, however, are not true watersheds as the official name of the framework, Watershed Boundary Dataset (WBD), implies. Hydrologic units and watersheds are commonly treated as synonymous, and this misuse and misunderstanding can have some serious consequences. We discuss some of the strengths and limitations of watersheds and hydrologic units as spatial frameworks. Using examples from the Northwest and Southeast U.S., we explain how the misuse of the hydrologic unit framework has affected the meaning of watersheds and can impair the understanding of the associations of spatial geographic phenomena relative to a potentially infinite number of points on streams due to their linear nature. Watersheds are a fundamental geographic unit used to study the effects of natural and anthropogenic characteristics on the quality and quantity of water. Most scientists and resource managers historically have been in agreement on the spatial meaning of the term ‘watershed’ – that is, the topographic area within which water drains to a specific point on a stream, river, or particular waterbody. The Hydrologic Unit Code (HUC) framework, however, has changed this understanding. Hydrologic units provide a convenient nationwide set of geographic polygons based on an arbitra

MOAB : a mesh-oriented database.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tautges, Timothy James; Ernst, Corey; Stimpson, Clint

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 storemore » 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-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 included with MOAB, or as a translator between mesh formats, using readers and writers included with MOAB. The remainder of this report is organized as follows. Section 2, 'Getting Started', provides a few simple examples of using MOAB to perform simple tasks on a mesh. Section 3 discusses the MOAB data model in more detail, including some aspects of the implementation. Section 4 summarizes the MOAB function API. Section 5 describes some of the tools included with MOAB, and the implementation of mesh readers/writers for MOAB. Section 6 contains a brief description of MOAB's relation to the TSTT mesh interface. Section 7 gives a conclusion and future plans for MOAB development. Section 8 gives references cited in this report. A reference description of the full MOAB API is contained in Section 9.« less

Three-dimensional contour edge detection algorithm

NASA Astrophysics Data System (ADS)

Wang, Yizhou; Ong, Sim Heng; Kassim, Ashraf A.; Foong, Kelvin W. C.

2000-06-01

This paper presents a novel algorithm for automatically extracting 3D contour edges, which are points of maximum surface curvature in a surface range image. The 3D image data are represented as a surface polygon mesh. The algorithm transforms the range data, obtained by scanning a dental plaster cast, into a 2D gray scale image by linearly converting the z-value of each vertex to a gray value. The Canny operator is applied to the median-filtered image to obtain the edge pixels and their orientations. A vertex in the 3D object corresponding to the detected edge pixel and its neighbors in the direction of the edge gradient are further analyzed with respect to their n-curvatures to extract the real 3D contour edges. This algorithm provides a fast method of reducing and sorting the unwieldy data inherent in the surface mesh representation. It employs powerful 2D algorithms to extract features from the transformed 3D models and refers to the 3D model for further analysis of selected data. This approach substantially reduces the computational burden without losing accuracy. It is also easily extended to detect 3D landmarks and other geometrical features, thus making it applicable to a wide range of applications.

An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

NASA Astrophysics Data System (ADS)

Papoutsakis, Andreas; Sazhin, Sergei S.; Begg, Steven; Danaila, Ionut; Luddens, Francky

2018-06-01

We present an Adaptive Mesh Refinement (AMR) method suitable for hybrid unstructured meshes that allows for local refinement and de-refinement of the computational grid during the evolution of the flow. The adaptive implementation of the Discontinuous Galerkin (DG) method introduced in this work (ForestDG) is based on a topological representation of the computational mesh by a hierarchical structure consisting of oct- quad- and binary trees. Adaptive mesh refinement (h-refinement) enables us to increase the spatial resolution of the computational mesh in the vicinity of the points of interest such as interfaces, geometrical features, or flow discontinuities. The local increase in the expansion order (p-refinement) at areas of high strain rates or vorticity magnitude results in an increase of the order of accuracy in the region of shear layers and vortices. A graph of unitarian-trees, representing hexahedral, prismatic and tetrahedral elements is used for the representation of the initial domain. The ancestral elements of the mesh can be split into self-similar elements allowing each tree to grow branches to an arbitrary level of refinement. The connectivity of the elements, their genealogy and their partitioning are described by linked lists of pointers. An explicit calculation of these relations, presented in this paper, facilitates the on-the-fly splitting, merging and repartitioning of the computational mesh by rearranging the links of each node of the tree with a minimal computational overhead. The modal basis used in the DG implementation facilitates the mapping of the fluxes across the non conformal faces. The AMR methodology is presented and assessed using a series of inviscid and viscous test cases. Also, the AMR methodology is used for the modelling of the interaction between droplets and the carrier phase in a two-phase flow. This approach is applied to the analysis of a spray injected into a chamber of quiescent air, using the Eulerian-Lagrangian approach. This enables us to refine the computational mesh in the vicinity of the droplet parcels and accurately resolve the coupling between the two phases.

Pellet Cladding Mechanical Interaction Modeling Using the Extended Finite Element Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spencer, Benjamin W.; Jiang, Wen; Dolbow, John E.

As a brittle material, the ceramic UO2 used as light water reactor fuel experiences significant fracturing throughout its life, beginning with the first rise to power of fresh fuel. This has multiple effects on the thermal and mechanical response of the fuel/cladding system. One such effect that is particularly important is that when there is mechanical contact between the fuel and cladding, cracks that extending from the outer surface of the fuel into the volume of the fuel cause elevated stresses in the adjacent cladding, which can potentially lead to cladding failure. Modeling the thermal and mechanical response of themore » cladding in the vicinity of these surface-breaking cracks in the fuel can provide important insights into this behavior to help avoid operating conditions that could lead to cladding failure. Such modeling has traditionally been done in the context of finite-element-based fuel performance analysis by modifying the fuel mesh to introduce discrete cracks. While this approach is effective in capturing the important behavior at the fuel/cladding interface, there are multiple drawbacks to explicitly incorporating the cracks in the finite element mesh. Because the cracks are incorporated in the original mesh, the mesh must be modified for cracks of specified location and depth, so it is difficult to account for crack propagation and the formation of new cracks at other locations. The extended finite element method (XFEM) has emerged in recent years as a powerful method to represent arbitrary, evolving, discrete discontinuities within the context of the finite element method. Development work is underway by the authors to implement XFEM in the BISON fuel performance code, and this capability has previously been demonstrated in simulations of fracture propagation in ceramic nuclear fuel. These preliminary demonstrations have included only the fuel, and excluded the cladding for simplicity. This paper presents initial results of efforts to apply XFEM to model stress concentrations induced by fuel fractures at the fuel/cladding interface during pellet cladding mechanical interaction (PCMI). This is accomplished by enhancing the thermal and mechanical contact enforcement algorithms employed by BISON to permit their use in conjunction with XFEM. The results from this methodology are demonstrated to be equivalent to those from using meshed discrete cracks. While the results of the two methods are equivalent for the case of a stationary crack, it is demonstrated that XFEM provides the additional flexibility of allowing arbitrary crack initiation and propagation during the analysis, and minimizes model setup effort for cases with stationary cracks.« less

The anatomy of floating shock fitting. [shock waves computation for flow field

NASA Technical Reports Server (NTRS)

Salas, M. D.

1975-01-01

The floating shock fitting technique is examined. Second-order difference formulas are developed for the computation of discontinuities. A procedure is developed to compute mesh points that are crossed by discontinuities. The technique is applied to the calculation of internal two-dimensional flows with arbitrary number of shock waves and contact surfaces. A new procedure, based on the coalescence of characteristics, is developed to detect the formation of shock waves. Results are presented to validate and demonstrate the versatility of the technique.

A hybridized discontinuous Galerkin framework for high-order particle-mesh operator splitting of the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias

2018-04-01

A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.

Establishing mesh topology in multi-material cells: enabling technology for robust and accurate multi-material simulations

DOE PAGES

Kikinzon, Evgeny; Shashkov, Mikhail Jurievich; Garimella, Rao Veerabhadra

2018-05-29

Real world problems are typically multi-material, combining materials such as gases, liquids and solids that have very different properties. The material interfaces may be fixed in time or can be a part of the solution, as in fluid-structure interactions or air-water dynamics, and therefore move and change shape. In such problems the computational mesh may be non-conformal to interfaces due to complexity of these interfaces, presence of small fractions of materials, or because the mesh does not move with the flow, as in the arbitrary Lagrangian–Eulerian (ALE) methods. In order to solve problems of interest on such meshes, interface reconstructionmore » methods are usually used to recover an approximation of material regions within the cells. For a cell intersecting multiple material regions, these approximations of contained subregions can be considered as single-material subcells in a local mesh that we call a minimesh. In this paper, we discuss some of the requirements that discretization methods have on topological information in the resulting hierarchical meshes and present an approach that allows incorporating the buildup of sufficiently detailed topology into the nested dissections based PLIC-type reconstruction algorithms (e.g. Volume-of-Fluid, Moment-of-Fluid) in an efficient and robust manner. Specifically, we describe the X-MOF interface reconstruction algorithm in 2D, which extends the Moment-Of-Fluid (MOF) method to include the topology of minimeshes created inside of multi-material cells and parent-child relations between corresponding mesh entities on different hierarchy levels. X-MOF retains the property of being local to a cell and not requiring external communication, which makes it suitable for massively parallel applications. Here, we demonstrate some scaling results for the X-MOF implementation in Tangram, a modern interface reconstruction framework for exascale computing.« less

Quinoa - Adaptive Computational Fluid Dynamics, 0.2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bakosi, Jozsef; Gonzalez, Francisco; Rogers, Brandon

Quinoa is a set of computational tools that enables research and numerical analysis in fluid dynamics. At this time it remains a test-bed to experiment with various algorithms using fully asynchronous runtime systems. Currently, Quinoa consists of the following tools: (1) Walker, a numerical integrator for systems of stochastic differential equations in time. It is a mathematical tool to analyze and design the behavior of stochastic differential equations. It allows the estimation of arbitrary coupled statistics and probability density functions and is currently used for the design of statistical moment approximations for multiple mixing materials in variable-density turbulence. (2) Inciter,more » an overdecomposition-aware finite element field solver for partial differential equations using 3D unstructured grids. Inciter is used to research asynchronous mesh-based algorithms and to experiment with coupling asynchronous to bulk-synchronous parallel code. Two planned new features of Inciter, compared to the previous release (LA-CC-16-015), to be implemented in 2017, are (a) a simple Navier-Stokes solver for ideal single-material compressible gases, and (b) solution-adaptive mesh refinement (AMR), which enables dynamically concentrating compute resources to regions with interesting physics. Using the NS-AMR problem we plan to explore how to scale such high-load-imbalance simulations, representative of large production multiphysics codes, to very large problems on very large computers using an asynchronous runtime system. (3) RNGTest, a test harness to subject random number generators to stringent statistical tests enabling quantitative ranking with respect to their quality and computational cost. (4) UnitTest, a unit test harness, running hundreds of tests per second, capable of testing serial, synchronous, and asynchronous functions. (5) MeshConv, a mesh file converter that can be used to convert 3D tetrahedron meshes from and to either of the following formats: Gmsh, (http://www.geuz.org/gmsh), Netgen, (http://sourceforge.net/apps/mediawiki/netgen-mesher), ExodusII, (http://sourceforge.net/projects/exodusii), HyperMesh, (http://www.altairhyperworks.com/product/HyperMesh).« less

Establishing mesh topology in multi-material cells: enabling technology for robust and accurate multi-material simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kikinzon, Evgeny; Shashkov, Mikhail Jurievich; Garimella, Rao Veerabhadra

Real world problems are typically multi-material, combining materials such as gases, liquids and solids that have very different properties. The material interfaces may be fixed in time or can be a part of the solution, as in fluid-structure interactions or air-water dynamics, and therefore move and change shape. In such problems the computational mesh may be non-conformal to interfaces due to complexity of these interfaces, presence of small fractions of materials, or because the mesh does not move with the flow, as in the arbitrary Lagrangian–Eulerian (ALE) methods. In order to solve problems of interest on such meshes, interface reconstructionmore » methods are usually used to recover an approximation of material regions within the cells. For a cell intersecting multiple material regions, these approximations of contained subregions can be considered as single-material subcells in a local mesh that we call a minimesh. In this paper, we discuss some of the requirements that discretization methods have on topological information in the resulting hierarchical meshes and present an approach that allows incorporating the buildup of sufficiently detailed topology into the nested dissections based PLIC-type reconstruction algorithms (e.g. Volume-of-Fluid, Moment-of-Fluid) in an efficient and robust manner. Specifically, we describe the X-MOF interface reconstruction algorithm in 2D, which extends the Moment-Of-Fluid (MOF) method to include the topology of minimeshes created inside of multi-material cells and parent-child relations between corresponding mesh entities on different hierarchy levels. X-MOF retains the property of being local to a cell and not requiring external communication, which makes it suitable for massively parallel applications. Here, we demonstrate some scaling results for the X-MOF implementation in Tangram, a modern interface reconstruction framework for exascale computing.« less

Identifying Blocks Formed by Curbed Fractures Using Exact Arithmetic

NASA Astrophysics Data System (ADS)

Zheng, Y.; Xia, L.; Yu, Q.; Zhang, X.

2015-12-01

Identifying blocks formed by fractures is important in rock engineering. Most studies assume the fractures to be perfect planar whereas curved fractures are rarely considered. However, large fractures observed in the field are often curved. This paper presents a new method for identifying rock blocks formed by both curved and planar fractures based on the element-block-assembling approach. The curved and planar fractures are represented as triangle meshes and planar discs, respectively. In the beginning of the identification method, the intersection segments between different triangle meshes are calculated and the intersected triangles are re-meshed to construct a piecewise linear complex (PLC). Then, the modeling domain is divided into tetrahedral subdomains under the constraint of the PLC and these subdomains are further decomposed into element blocks by extended planar fractures. Finally, the element blocks are combined and the subdomains are assembled to form complex blocks. The combination of two subdomains is skipped if and only if the common facet lies on a curved fracture. In this study, the exact arithmetic is used to handle the computational errors, which may threat the robustness of the block identification program when the degenerated cases are encountered. Specifically, a real number is represented as the ratio between two integers and the basic arithmetic such as addition, subtraction, multiplication and division between different real numbers can be performed exactly if an arbitrary precision integer package is used. In this way, the exact construction of blocks can be achieved without introducing computational errors. Several analytical examples are given in this paper and the results show effectiveness of this method in handling arbitrary shaped blocks. Moreover, there is no limitation on the number of blocks in a block system. The results also show (suggest) that the degenerated cases can be handled without affecting the robustness of the identification program.

Research on bulbous bow optimization based on the improved PSO algorithm

NASA Astrophysics Data System (ADS)

Zhang, Sheng-long; Zhang, Bao-ji; Tezdogan, Tahsin; Xu, Le-ping; Lai, Yu-yang

2017-08-01

In order to reduce the total resistance of a hull, an optimization framework for the bulbous bow optimization was presented. The total resistance in calm water was selected as the objective function, and the overset mesh technique was used for mesh generation. RANS method was used to calculate the total resistance of the hull. In order to improve the efficiency and smoothness of the geometric reconstruction, the arbitrary shape deformation (ASD) technique was introduced to change the shape of the bulbous bow. To improve the global search ability of the particle swarm optimization (PSO) algorithm, an improved particle swarm optimization (IPSO) algorithm was proposed to set up the optimization model. After a series of optimization analyses, the optimal hull form was found. It can be concluded that the simulation based design framework built in this paper is a promising method for bulbous bow optimization.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

Numerical integration of discontinuous functions: moment fitting and smart octree

NASA Astrophysics Data System (ADS)

Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander

2017-11-01

A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Speed-up of the volumetric method of moments for the approximate RCS of large arbitrary-shaped dielectric targets

NASA Astrophysics Data System (ADS)

Moreno, Javier; Somolinos, Álvaro; Romero, Gustavo; González, Iván; Cátedra, Felipe

2017-08-01

A method for the rigorous computation of the electromagnetic scattering of large dielectric volumes is presented. One goal is to simplify the analysis of large dielectric targets with translational symmetries taken advantage of their Toeplitz symmetry. Then, the matrix-fill stage of the Method of Moments is efficiently obtained because the number of coupling terms to compute is reduced. The Multilevel Fast Multipole Method is applied to solve the problem. Structured meshes are obtained efficiently to approximate the dielectric volumes. The regular mesh grid is achieved by using parallelepipeds whose centres have been identified as internal to the target. The ray casting algorithm is used to classify the parallelepiped centres. It may become a bottleneck when too many points are evaluated in volumes defined by parametric surfaces, so a hierarchical algorithm is proposed to minimize the number of evaluations. Measurements and analytical results are included for validation purposes.

A Cartesian grid approach with hierarchical refinement for compressible flows

NASA Technical Reports Server (NTRS)

Quirk, James J.

1994-01-01

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

Tempest: Mesoscale test case suite results and the effect of order-of-accuracy on pressure gradient force errors

NASA Astrophysics Data System (ADS)

Guerra, J. E.; Ullrich, P. A.

2014-12-01

Tempest is a new non-hydrostatic atmospheric modeling framework that allows for investigation and intercomparison of high-order numerical methods. It is composed of a dynamical core based on a finite-element formulation of arbitrary order operating on cubed-sphere and Cartesian meshes with topography. The underlying technology is briefly discussed, including a novel Hybrid Finite Element Method (HFEM) vertical coordinate coupled with high-order Implicit/Explicit (IMEX) time integration to control vertically propagating sound waves. Here, we show results from a suite of Mesoscale testing cases from the literature that demonstrate the accuracy, performance, and properties of Tempest on regular Cartesian meshes. The test cases include wave propagation behavior, Kelvin-Helmholtz instabilities, and flow interaction with topography. Comparisons are made to existing results highlighting improvements made in resolving atmospheric dynamics in the vertical direction where many existing methods are deficient.

Seismic waves in heterogeneous material: subcell resolution of the discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Castro, Cristóbal E.; Käser, Martin; Brietzke, Gilbert B.

2010-07-01

We present an important extension of the arbitrary high-order discontinuous Galerkin (DG) finite-element method to model 2-D elastic wave propagation in highly heterogeneous material. In this new approach we include space-variable coefficients to describe smooth or discontinuous material variations inside each element using the same numerical approximation strategy as for the velocity-stress variables in the formulation of the elastic wave equation. The combination of the DG method with a time integration scheme based on the solution of arbitrary accuracy derivatives Riemann problems still provides an explicit, one-step scheme which achieves arbitrary high-order accuracy in space and time. Compared to previous formulations the new scheme contains two additional terms in the form of volume integrals. We show that the increasing computational cost per element can be overcompensated due to the improved material representation inside each element as coarser meshes can be used which reduces the total number of elements and therefore computational time to reach a desired error level. We confirm the accuracy of the proposed scheme performing convergence tests and several numerical experiments considering smooth and highly heterogeneous material. As the approximation of the velocity and stress variables in the wave equation and of the material properties in the model can be chosen independently, we investigate the influence of the polynomial material representation on the accuracy of the synthetic seismograms with respect to computational cost. Moreover, we study the behaviour of the new method on strong material discontinuities, in the case where the mesh is not aligned with such a material interface. In this case second-order linear material approximation seems to be the best choice, with higher-order intra-cell approximation leading to potential instable behaviour. For all test cases we validate our solution against the well-established standard fourth-order finite difference and spectral element method.

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong Luo; Luqing Luo; Robert Nourgaliev

2010-09-01

A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier–Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier–Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi–Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier–Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier–Stokes equations.« less

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong Luo; Luqing Luo; Robert Nourgaliev

2010-01-01

A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.« less

Release of RANKERN 16A

NASA Astrophysics Data System (ADS)

Bird, Adam; Murphy, Christophe; Dobson, Geoff

2017-09-01

RANKERN 16 is the latest version of the point-kernel gamma radiation transport Monte Carlo code from AMEC Foster Wheeler's ANSWERS Software Service. RANKERN is well established in the UK shielding community for radiation shielding and dosimetry assessments. Many important developments have been made available to users in this latest release of RANKERN. The existing general 3D geometry capability has been extended to include import of CAD files in the IGES format providing efficient full CAD modelling capability without geometric approximation. Import of tetrahedral mesh and polygon surface formats has also been provided. An efficient voxel geometry type has been added suitable for representing CT data. There have been numerous input syntax enhancements and an extended actinide gamma source library. This paper describes some of the new features and compares the performance of the new geometry capabilities.

A Numerical Investigation of Two-Different Drosophila Forward Flight Modes

NASA Astrophysics Data System (ADS)

Sahin, Mehmet; Dilek, Ezgi; Erzincanli, Belkis

2016-11-01

The parallel large-scale unstructured finite volume method based on an Arbitrary Lagrangian-Eulerian (ALE) formulation has been applied in order to investigate the near wake structure of Drosophila in forward flight. DISTENE MeshGems-Hexa algorithm based on the octree method is used to generate the all hexahedral mesh for the wing-body combination. The mesh deformation algorithm is based on the indirect radial basis function (RBF) method at each time level while avoiding remeshing in order to enhance numerical robustness. The large-scale numerical simulations are carried out for a flapping Drosophila in forward flight. In the first case, the wing tip-path plane is tilted forward to generate forward force. In the second case, paddling wing motion is used to generate the forward fore. The λ2-criterion proposed by Jeong and Hussain (1995) is used for investigating the time variation of the Eulerian coherent structures in the near wake. The present simulations reveal highly detailed near wake topology for a hovering Drosophila. This is very useful in terms of understanding physics in biological flights which can provide a very useful tool for designing bio-inspired MAVs.

An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm in curvilinear geometry

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.; Barnes, D. C.

2012-03-01

A recent proof-of-principle study proposes an energy- and charge-conserving, fully implicit particle-in-cell algorithm in one dimension [1], which is able to use timesteps comparable to the dynamical timescale of interest. Here, we generalize the method to employ non-uniform meshes via a curvilinear map. The key enabling technology is a hybrid particle pusher [2], with particle positions updated in logical space and particle velocities updated in physical space. The self-adaptive, charge-conserving particle mover of Ref. [1] is extended to the non-uniform mesh case. The fully implicit implementation, using a Jacobian-free Newton-Krylov iterative solver, remains exactly charge- and energy-conserving. The extension of the formulation to multiple dimensions will be discussed. We present numerical experiments of 1D electrostatic, long-timescale ion-acoustic wave and ion-acoustic shock wave simulations, demonstrating that charge and energy are conserved to round-off for arbitrary mesh non-uniformity, and that the total momentum remains well conserved.[4pt] [1] Chen, Chac'on, Barnes, J. Comput. Phys. 230 (2011). [0pt] [2] Camporeale and Delzanno, Bull. Am. Phys. Soc. 56(6) (2011); Wang, et al., J. Plasma Physics, 61 (1999).

Momentum Advection on a Staggered Mesh

NASA Astrophysics Data System (ADS)

Benson, David J.

1992-05-01

Eulerian and ALE (arbitrary Lagrangian-Eulerian) hydrodynamics programs usually split a timestep into two parts. The first part is a Lagrangian step, which calculates the incremental motion of the material. The second part is referred to as the Eulerian step, the advection step, or the remap step, and it accounts for the transport of material between cells. In most finite difference and finite element formulations, all the solution variables except the velocities are cell-centered while the velocities are edge- or vertex-centered. As a result, the advection algorithm for the momentum is, by necessity, different than the algorithm used for the other variables. This paper reviews three momentum advection methods and proposes a new one. One method, pioneered in YAQUI, creates a new staggered mesh, while the other two, used in SALE and SHALE, are cell-centered. The new method is cell-centered and its relationship to the other methods is discussed. Both pure advection and strong shock calculations are presented to substantiate the mathematical analysis. From the standpoint of numerical accuracy, both the staggered mesh and the cell-centered algorithms can give good results, while the computational costs are highly dependent on the overall architecture of a code.

Multi-resolution MPS method

NASA Astrophysics Data System (ADS)

Tanaka, Masayuki; Cardoso, Rui; Bahai, Hamid

2018-04-01

In this work, the Moving Particle Semi-implicit (MPS) method is enhanced for multi-resolution problems with different resolutions at different parts of the domain utilising a particle splitting algorithm for the finer resolution and a particle merging algorithm for the coarser resolution. The Least Square MPS (LSMPS) method is used for higher stability and accuracy. Novel boundary conditions are developed for the treatment of wall and pressure boundaries for the Multi-Resolution LSMPS method. A wall is represented by polygons for effective simulations of fluid flows with complex wall geometries and the pressure boundary condition allows arbitrary inflow and outflow, making the method easier to be used in flow simulations of channel flows. By conducting simulations of channel flows and free surface flows, the accuracy of the proposed method was verified.

SU-F-BRB-05: Collision Avoidance Mapping Using Consumer 3D Camera

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cardan, R; Popple, R

2015-06-15

Purpose: To develop a fast and economical method of scanning a patient’s full body contour for use in collision avoidance mapping without the use of ionizing radiation. Methods: Two consumer level 3D cameras used in electronic gaming were placed in a CT simulator room to scan a phantom patient set up in a high collision probability position. A registration pattern and computer vision algorithms were used to transform the scan into the appropriate coordinate systems. The cameras were then used to scan the surface of a gantry in the treatment vault. Each scan was converted into a polygon mesh formore » collision testing in a general purpose polygon interference algorithm. All clinically relevant transforms were applied to the gantry and patient support to create a map of all possible collisions. The map was then tested for accuracy by physically testing the collisions with the phantom in the vault. Results: The scanning fidelity of both the gantry and patient was sufficient to produce a collision prediction accuracy of 97.1% with 64620 geometry states tested in 11.5 s. The total scanning time including computation, transformation, and generation was 22.3 seconds. Conclusion: Our results demonstrate an economical system to generate collision avoidance maps. Future work includes testing the speed of the framework in real-time collision avoidance scenarios. Research partially supported by a grant from Varian Medical Systems.« less

Inlet Spillage Drag Predictions Using the AIRPLANE Code

NASA Technical Reports Server (NTRS)

Thomas, Scott D.; Won, Mark A.; Cliff, Susan E.

1999-01-01

AIRPLANE (Jameson/Baker) is a steady inviscid unstructured Euler flow solver. It has been validated on many HSR geometries. It is implemented as MESHPLANE, an unstructured mesh generator, and FLOPLANE, an iterative flow solver. The surface description from an Intergraph CAD system goes into MESHPLANE as collections of polygonal curves to generate the 3D mesh. The flow solver uses a multistage time stepping scheme with residual averaging to approach steady state, but R is not time accurate. The flow solver was ported from Cray to IBM SP2 by Wu-Sun Cheng (IBM); it could only be run on 4 CPUs at a time because of memory limitations. Meshes for the four cases had about 655,000 points in the flow field, about 3.9 million tetrahedra, about 77,500 points on the surface. The flow solver took about 23 wall seconds per iteration when using 4 CPUs. It took about eight and a half wall hours to run 1,300 iterations at a time (the queue limit is 10 hours). A revised version of FLOPLANE (Thomas) was used on up to 64 CPUs to finish up some calculations at the end. We had to turn on more communication when using more processors to eliminate noise that was contaminating the flow field; this added about 50% to the elapsed wall time per iteration when using 64 CPUs. This study involved computing lift and drag for a wing/body/nacelle configuration at Mach 0.9 and 4 degrees pitch. Four cases were considered, corresponding to four nacelle mass flow conditions.

a Geometric Processing Workflow for Transforming Reality-Based 3d Models in Volumetric Meshes Suitable for Fea

NASA Astrophysics Data System (ADS)

Gonizzi Barsanti, S.; Guidi, G.

2017-02-01

Conservation of Cultural Heritage is a key issue and structural changes and damages can influence the mechanical behaviour of artefacts and buildings. The use of Finite Elements Methods (FEM) for mechanical analysis is largely used in modelling stress behaviour. The typical workflow involves the use of CAD 3D models made by Non-Uniform Rational B-splines (NURBS) surfaces, representing the ideal shape of the object to be simulated. Nowadays, 3D documentation of CH has been widely developed through reality-based approaches, but the models are not suitable for a direct use in FEA: the mesh has in fact to be converted to volumetric, and the density has to be reduced since the computational complexity of a FEA grows exponentially with the number of nodes. The focus of this paper is to present a new method aiming at generate the most accurate 3D representation of a real artefact from highly accurate 3D digital models derived from reality-based techniques, maintaining the accuracy of the high-resolution polygonal models in the solid ones. The approach proposed is based on a wise use of retopology procedures and a transformation of this model to a mathematical one made by NURBS surfaces suitable for being processed by volumetric meshers typically embedded in standard FEM packages. The strong simplification with little loss of consistency possible with the retopology step is used for maintaining as much coherence as possible between the original acquired mesh and the simplified model, creating in the meantime a topology that is more favourable for the automatic NURBS conversion.

Microtopographic characterization of ice-wedge polygon landscape in Barrow, Alaska: a digital map of troughs, rims, centers derived from high resolution (0.25 m) LiDAR data

DOE Data Explorer

Gangodagamage, Chandana; Wullschleger, Stan

2014-07-03

The dataset represents microtopographic characterization of the ice-wedge polygon landscape in Barrow, Alaska. Three microtopographic features are delineated using 0.25 m high resolution digital elevation dataset derived from LiDAR. The troughs, rims, and centers are the three categories in this classification scheme. The polygon troughs are the surface expression of the ice-wedges that are in lower elevations than the interior polygon. The elevated shoulders of the polygon interior immediately adjacent to the polygon troughs are the polygon rims for the low center polygons. In case of high center polygons, these features are the topographic highs. In this classification scheme, both topographic highs and rims are considered as polygon rims. The next version of the dataset will include more refined classification scheme including separate classes for rims ad topographic highs. The interior part of the polygon just adjacent to the polygon rims are the polygon centers.

Symmetry- and essentially-bound-preserving flux-corrected remapping of momentum in staggered ALE hydrodynamics

NASA Astrophysics Data System (ADS)

Velechovský, J.; Kuchařík, M.; Liska, R.; Shashkov, M.; Váchal, P.

2013-12-01

We present a new flux-corrected approach for remapping of velocity in the framework of staggered arbitrary Lagrangian-Eulerian methods. The main focus of the paper is the definition and preservation of coordinate invariant local bounds for velocity vector and development of momentum remapping method such that the radial symmetry of the radially symmetric flows is preserved when remapping from one equiangular polar mesh to another. The properties of this new method are demonstrated on a set of selected numerical cyclic remapping tests and a full hydrodynamic example.

N-MODY: A Code for Collisionless N-body Simulations in Modified Newtonian Dynamics

NASA Astrophysics Data System (ADS)

Londrillo, Pasquale; Nipoti, Carlo

2011-02-01

N-MODY is a parallel particle-mesh code for collisionless N-body simulations in modified Newtonian dynamics (MOND). N-MODY is based on a numerical potential solver in spherical coordinates that solves the non-linear MOND field equation, and is ideally suited to simulate isolated stellar systems. N-MODY can be used also to compute the MOND potential of arbitrary static density distributions. A few applications of N-MODY indicate that some astrophysically relevant dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter.

Developing a Learning Algorithm-Generated Empirical Relaxer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitchell, Wayne; Kallman, Josh; Toreja, Allen

2016-03-30

One of the main difficulties when running Arbitrary Lagrangian-Eulerian (ALE) simulations is determining how much to relax the mesh during the Eulerian step. This determination is currently made by the user on a simulation-by-simulation basis. We present a Learning Algorithm-Generated Empirical Relaxer (LAGER) which uses a regressive random forest algorithm to automate this decision process. We also demonstrate that LAGER successfully relaxes a variety of test problems, maintains simulation accuracy, and has the potential to significantly decrease both the person-hours and computational hours needed to run a successful ALE simulation.

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

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

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

3D unstructured-mesh radiation transport codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morel, J.

1997-12-31

Three unstructured-mesh radiation transport codes are currently being developed at Los Alamos National Laboratory. The first code is ATTILA, which uses an unstructured tetrahedral mesh in conjunction with standard Sn (discrete-ordinates) angular discretization, standard multigroup energy discretization, and linear-discontinuous spatial differencing. ATTILA solves the standard first-order form of the transport equation using source iteration in conjunction with diffusion-synthetic acceleration of the within-group source iterations. DANTE is designed to run primarily on workstations. The second code is DANTE, which uses a hybrid finite-element mesh consisting of arbitrary combinations of hexahedra, wedges, pyramids, and tetrahedra. DANTE solves several second-order self-adjoint forms of the transport equation including the even-parity equation, the odd-parity equation, and a new equation called the self-adjoint angular flux equation. DANTE also offers three angular discretization options:more » $$S{_}n$$ (discrete-ordinates), $$P{_}n$$ (spherical harmonics), and $$SP{_}n$$ (simplified spherical harmonics). DANTE is designed to run primarily on massively parallel message-passing machines, such as the ASCI-Blue machines at LANL and LLNL. The third code is PERICLES, which uses the same hybrid finite-element mesh as DANTE, but solves the standard first-order form of the transport equation rather than a second-order self-adjoint form. DANTE uses a standard $$S{_}n$$ discretization in angle in conjunction with trilinear-discontinuous spatial differencing, and diffusion-synthetic acceleration of the within-group source iterations. PERICLES was initially designed to run on workstations, but a version for massively parallel message-passing machines will be built. The three codes will be described in detail and computational results will be presented.« less

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

Weakly supervised automatic segmentation and 3D modeling of the knee joint from MR images

NASA Astrophysics Data System (ADS)

Amami, Amal; Ben Azouz, Zouhour

2013-12-01

Automatic segmentation and 3D modeling of the knee joint from MR images, is a challenging task. Most of the existing techniques require the tedious manual segmentation of a training set of MRIs. We present an approach that necessitates the manual segmentation of one MR image. It is based on a volumetric active appearance model. First, a dense tetrahedral mesh is automatically created on a reference MR image that is arbitrary selected. Second, a pairwise non-rigid registration between each MRI from a training set and the reference MRI is computed. The non-rigid registration is based on a piece-wise affine deformation using the created tetrahedral mesh. The minimum description length is then used to bring all the MR images into a correspondence. An average image and tetrahedral mesh, as well as a set of main modes of variations, are generated using the established correspondence. Any manual segmentation of the average MRI can be mapped to other MR images using the AAM. The proposed approach has the advantage of simultaneously generating 3D reconstructions of the surface as well as a 3D solid model of the knee joint. The generated surfaces and tetrahedral meshes present the interesting property of fulfilling a correspondence between different MR images. This paper shows preliminary results of the proposed approach. It demonstrates the automatic segmentation and 3D reconstruction of a knee joint obtained by mapping a manual segmentation of a reference image.

Method and system for detecting polygon boundaries of structures in images as particle tracks through fields of corners and pixel gradients

DOEpatents

Paglieroni, David W [Pleasanton, CA; Manay, Siddharth [Livermore, CA

2011-12-20

A stochastic method and system for detecting polygon structures in images, by detecting a set of best matching corners of predetermined acuteness .alpha. of a polygon model from a set of similarity scores based on GDM features of corners, and tracking polygon boundaries as particle tracks using a sequential Monte Carlo approach. The tracking involves initializing polygon boundary tracking by selecting pairs of corners from the set of best matching corners to define a first side of a corresponding polygon boundary; tracking all intermediate sides of the polygon boundaries using a particle filter, and terminating polygon boundary tracking by determining the last side of the tracked polygon boundaries to close the polygon boundaries. The particle tracks are then blended to determine polygon matches, which may be made available, such as to a user, for ranking and inspection.

A conservative MHD scheme on unstructured Lagrangian grids for Z-pinch hydrodynamic simulations

NASA Astrophysics Data System (ADS)

Wu, Fuyuan; Ramis, Rafael; Li, Zhenghong

2018-03-01

A new algorithm to model resistive magnetohydrodynamics (MHD) in Z-pinches has been developed. Two-dimensional axisymmetric geometry with azimuthal magnetic field Bθ is considered. Discretization is carried out using unstructured meshes made up of arbitrarily connected polygons. The algorithm is fully conservative for mass, momentum, and energy. Matter energy and magnetic energy are managed separately. The diffusion of magnetic field is solved using a derivative of the Symmetric-Semi-Implicit scheme, Livne et al. (1985) [23], where unconditional stability is obtained without needing to solve large sparse systems of equations. This MHD package has been integrated into the radiation-hydrodynamics code MULTI-2D, Ramis et al. (2009) [20], that includes hydrodynamics, laser energy deposition, heat conduction, and radiation transport. This setup allows to simulate Z-pinch configurations relevant for Inertial Confinement Fusion.

Numerical Experiments on Advective Transport in Large Three-Dimensional Discrete Fracture Networks

NASA Astrophysics Data System (ADS)

Makedonska, N.; Painter, S. L.; Karra, S.; Gable, C. W.

2013-12-01

Modeling of flow and solute transport in discrete fracture networks is an important approach for understanding the migration of contaminants in impermeable hard rocks such as granite, where fractures provide dominant flow and transport pathways. The discrete fracture network (DFN) model attempts to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. An integrated DFN meshing [1], flow, and particle tracking [2] simulation capability that enables accurate flow and particle tracking simulation on large DFNs has recently been developed. The new capability has been used in numerical experiments on advective transport in large DFNs with tens of thousands of fractures and millions of computational cells. The modeling procedure starts from the fracture network generation using a stochastic model derived from site data. A high-quality computational mesh is then generated [1]. Flow is then solved using the highly parallel PFLOTRAN [3] code. PFLOTRAN uses the finite volume approach, which is locally mass conserving and thus eliminates mass balance problems during particle tracking. The flow solver provides the scalar fluxes on each control volume face. From the obtained fluxes the Darcy velocity is reconstructed for each node in the network [4]. Velocities can then be continuously interpolated to any point in the domain of interest, thus enabling random walk particle tracking. In order to describe the flow field on fractures intersections, the control volume cells on intersections are split into four planar polygons, where each polygon corresponds to a piece of a fracture near the intersection line. Thus, computational nodes lying on fracture intersections have four associated velocities, one on each side of the intersection in each fracture plane [2]. This information is used to route particles arriving at the fracture intersection to the appropriate downstream fracture segment. Verified for small DFNs, the new simulation capability allows accurate particle tracking on more realistic representations of fractured rock sites. In the current work we focus on travel time statistics and spatial dispersion and show numerical results in DFNs of different sizes, fracture densities, and transmissivity distributions. [1] Hyman J.D., Gable C.W., Painter S.L., Automated meshing of stochastically generated discrete fracture networks, Abstract H33G-1403, 2011 AGU, San Francisco, CA, 5-9 Dec. [2] N. Makedonska, S. L. Painter, T.-L. Hsieh, Q.M. Bui, and C. W. Gable., Development and verification of a new particle tracking capability for modeling radionuclide transport in discrete fracture networks, Abstract, 2013 IHLRWM, Albuquerque, NM, Apr. 28 - May 3. [3] Lichtner, P.C., Hammond, G.E., Bisht, G., Karra, S., Mills, R.T., and Kumar, J. (2013) PFLOTRAN User's Manual: A Massively Parallel Reactive Flow Code. [4] Painter S.L., Gable C.W., Kelkar S., Pathline tracing on fully unstructured control-volume grids, Computational Geosciences, 16 (4), 2012, 1125-1134.

A Frost Enhanced Landscape

NASA Image and Video Library

2015-12-23

The arc of hills in this image from NASA Mars Reconnaissance Orbiter spacecraft is the rim of an old and infilled impact crater. The sediments that were deposited within the crater have since formed polygonal cracks due to repeated cycles of freezing and thawing. The process of polygon formation is common at these polar latitudes, but polygons are not always as striking as they are here. In this image, the polygons have been highlighted by persistent frost in the cracks. The crater rim constrains the polygon formation within the crater close to the rim, creating a spoke and ring pattern of cracks. This leads to more rectangular polygons than those near the center of the crater. The polygons close to the center of the crater display a more typical pattern. A closer look shows some of these central polygons, which have smaller polygons within them, and smaller polygons within those smaller polygons, which makes for a natural fractal. http://photojournal.jpl.nasa.gov/catalog/PIA20289

Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation

NASA Technical Reports Server (NTRS)

Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David

1996-01-01

This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.

Recent developments in multidimensional transport methods for the APOLLO 2 lattice code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zmijarevic, I.; Sanchez, R.

1995-12-31

A usual method of preparation of homogenized cross sections for reactor coarse-mesh calculations is based on two-dimensional multigroup transport treatment of an assembly together with an appropriate leakage model and reaction-rate-preserving homogenization technique. The actual generation of assembly spectrum codes based on collision probability methods is capable of treating complex geometries (i.e., irregular meshes of arbitrary shape), thus avoiding the modeling error that was introduced in codes with traditional tracking routines. The power and architecture of current computers allow the treatment of spatial domains comprising several mutually interacting assemblies using fine multigroup structure and retaining all geometric details of interest.more » Increasing safety requirements demand detailed two- and three-dimensional calculations for very heterogeneous problems such as control rod positioning, broken Pyrex rods, irregular compacting of mixed- oxide (MOX) pellets at an MOX-UO{sub 2} interface, and many others. An effort has been made to include accurate multi- dimensional transport methods in the APOLLO 2 lattice code. These include extension to three-dimensional axially symmetric geometries of the general-geometry collision probability module TDT and the development of new two- and three-dimensional characteristics methods for regular Cartesian meshes. In this paper we discuss the main features of recently developed multidimensional methods that are currently being tested.« less

Multi-Material ALE with AMR for Modeling Hot Plasmas and Cold Fragmenting Materials

NASA Astrophysics Data System (ADS)

Alice, Koniges; Nathan, Masters; Aaron, Fisher; David, Eder; Wangyi, Liu; Robert, Anderson; David, Benson; Andrea, Bertozzi

2015-02-01

We have developed a new 3D multi-physics multi-material code, ALE-AMR, which combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR) to connect the continuum to the microstructural regimes. The code is unique in its ability to model hot radiating plasmas and cold fragmenting solids. New numerical techniques were developed for many of the physics packages to work efficiently on a dynamically moving and adapting mesh. We use interface reconstruction based on volume fractions of the material components within mixed zones and reconstruct interfaces as needed. This interface reconstruction model is also used for void coalescence and fragmentation. A flexible strength/failure framework allows for pluggable material models, which may require material history arrays to determine the level of accumulated damage or the evolving yield stress in J2 plasticity models. For some applications laser rays are propagating through a virtual composite mesh consisting of the finest resolution representation of the modeled space. A new 2nd order accurate diffusion solver has been implemented for the thermal conduction and radiation transport packages. One application area is the modeling of laser/target effects including debris/shrapnel generation. Other application areas include warm dense matter, EUV lithography, and material wall interactions for fusion devices.

Multi-resolutional shape features via non-Euclidean wavelets: Applications to statistical analysis of cortical thickness

PubMed Central

Kim, Won Hwa; Singh, Vikas; Chung, Moo K.; Hinrichs, Chris; Pachauri, Deepti; Okonkwo, Ozioma C.; Johnson, Sterling C.

2014-01-01

Statistical analysis on arbitrary surface meshes such as the cortical surface is an important approach to understanding brain diseases such as Alzheimer’s disease (AD). Surface analysis may be able to identify specific cortical patterns that relate to certain disease characteristics or exhibit differences between groups. Our goal in this paper is to make group analysis of signals on surfaces more sensitive. To do this, we derive multi-scale shape descriptors that characterize the signal around each mesh vertex, i.e., its local context, at varying levels of resolution. In order to define such a shape descriptor, we make use of recent results from harmonic analysis that extend traditional continuous wavelet theory from the Euclidean to a non-Euclidean setting (i.e., a graph, mesh or network). Using this descriptor, we conduct experiments on two different datasets, the Alzheimer’s Disease NeuroImaging Initiative (ADNI) data and images acquired at the Wisconsin Alzheimer’s Disease Research Center (W-ADRC), focusing on individuals labeled as having Alzheimer’s disease (AD), mild cognitive impairment (MCI) and healthy controls. In particular, we contrast traditional univariate methods with our multi-resolution approach which show increased sensitivity and improved statistical power to detect a group-level effects. We also provide an open source implementation. PMID:24614060

Numerical electromagnetic frequency domain analysis with discrete exterior calculus

NASA Astrophysics Data System (ADS)

Chen, Shu C.; Chew, Weng Cho

2017-12-01

In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations in terms of DEC for 3-D and 2-D inhomogeneous structures, and also show that the charge continuity relation is naturally satisfied. Then we introduce a general construction for signed dual volume to incorporate material information and take into account the case when circumcenters fall outside triangles or tetrahedrons, which may lead to negative dual volume without Delaunay triangulation. Then we examine the boundary terms induced by the dual mesh and provide a systematical treatment of various boundary conditions, including perfect magnetic conductor (PMC), perfect electric conductor (PEC), Dirichlet, periodic, and absorbing boundary conditions (ABC) within this method. An excellent agreement is achieved through the numerical calculation of several problems, including homogeneous waveguides, microstructured fibers, photonic crystals, scattering by a 2-D PEC, and resonant cavities.

An efficicient data structure for three-dimensional vertex based finite volume method

NASA Astrophysics Data System (ADS)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

Meshing complex macro-scale objects into self-assembling bricks

PubMed Central

Hacohen, Adar; Hanniel, Iddo; Nikulshin, Yasha; Wolfus, Shuki; Abu-Horowitz, Almogit; Bachelet, Ido

2015-01-01

Self-assembly provides an information-economical route to the fabrication of objects at virtually all scales. However, there is no known algorithm to program self-assembly in macro-scale, solid, complex 3D objects. Here such an algorithm is described, which is inspired by the molecular assembly of DNA, and based on bricks designed by tetrahedral meshing of arbitrary objects. Assembly rules are encoded by topographic cues imprinted on brick faces while attraction between bricks is provided by embedded magnets. The bricks can then be mixed in a container and agitated, leading to properly assembled objects at high yields and zero errors. The system and its assembly dynamics were characterized by video and audio analysis, enabling the precise time- and space-resolved characterization of its performance and accuracy. Improved designs inspired by our system could lead to successful implementation of self-assembly at the macro-scale, allowing rapid, on-demand fabrication of objects without the need for assembly lines. PMID:26226488

Parallel implementation of a Lagrangian-based model on an adaptive mesh in C++: Application to sea-ice

NASA Astrophysics Data System (ADS)

Samaké, Abdoulaye; Rampal, Pierre; Bouillon, Sylvain; Ólason, Einar

2017-12-01

We present a parallel implementation framework for a new dynamic/thermodynamic sea-ice model, called neXtSIM, based on the Elasto-Brittle rheology and using an adaptive mesh. The spatial discretisation of the model is done using the finite-element method. The temporal discretisation is semi-implicit and the advection is achieved using either a pure Lagrangian scheme or an Arbitrary Lagrangian Eulerian scheme (ALE). The parallel implementation presented here focuses on the distributed-memory approach using the message-passing library MPI. The efficiency and the scalability of the parallel algorithms are illustrated by the numerical experiments performed using up to 500 processor cores of a cluster computing system. The performance obtained by the proposed parallel implementation of the neXtSIM code is shown being sufficient to perform simulations for state-of-the-art sea ice forecasting and geophysical process studies over geographical domain of several millions squared kilometers like the Arctic region.

A regularized vortex-particle mesh method for large eddy simulation

NASA Astrophysics Data System (ADS)

Spietz, H. J.; Walther, J. H.; Hejlesen, M. M.

2017-11-01

We present recent developments of the remeshed vortex particle-mesh method for simulating incompressible fluid flow. The presented method relies on a parallel higher-order FFT based solver for the Poisson equation. Arbitrary high order is achieved through regularization of singular Green's function solutions to the Poisson equation and recently we have derived novel high order solutions for a mixture of open and periodic domains. With this approach the simulated variables may formally be viewed as the approximate solution to the filtered Navier Stokes equations, hence we use the method for Large Eddy Simulation by including a dynamic subfilter-scale model based on test-filters compatible with the aforementioned regularization functions. Further the subfilter-scale model uses Lagrangian averaging, which is a natural candidate in light of the Lagrangian nature of vortex particle methods. A multiresolution variation of the method is applied to simulate the benchmark problem of the flow past a square cylinder at Re = 22000 and the obtained results are compared to results from the literature.

A Reconstructed Discontinuous Galerkin Method for the Compressible Euler Equations on Arbitrary Grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong Luo; Luquing Luo; Robert Nourgaliev

2009-06-01

A reconstruction-based discontinuous Galerkin (DG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a solution polynomial of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the van Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting DG method can be regarded as an improvement of a recovery-based DG method in the sense that it shares the samemore » nice features as the recovery-based DG method, such as high accuracy and efficiency, and yet overcomes some of its shortcomings such as a lack of flexibility, compactness, and robustness. The developed DG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate the accuracy and efficiency of the method. The numerical results indicate that this reconstructed DG method is able to obtain a third-order accurate solution at a slightly higher cost than its second-order DG method and provide an increase in performance over the third order DG method in terms of computing time and storage requirement.« less

Unsteady density-current equations for highly curved terrain

NASA Technical Reports Server (NTRS)

Sivakumaran, N. S.; Dressler, R. F.

1989-01-01

New nonlinear partial differential equations containing terrain curvature and its rate of change are derived that describe the flow of an atmospheric density current. Unlike the classical hydraulic-type equations for density currents, the new equations are valid for two-dimensional, gradually varied flow over highly curved terrain, hence suitable for computing unsteady (or steady) flows over arbitrary mountain/valley profiles. The model assumes the atmosphere above the density current exerts a known arbitrary variable pressure upon the unknown interface. Later this is specialized to the varying hydrostatic pressure of the atmosphere above. The new equations yield the variable velocity distribution, the interface position, and the pressure distribution that contains a centrifugal component, often significantly larger than its hydrostatic component. These partial differential equations are hyperbolic, and the characteristic equations and characteristic directions are derived. Using these to form a characteristic mesh, a hypothetical unsteady curved-flow problem is calculated, not based upon observed data, merely as an example to illustrate the simplicity of their application to unsteady flows over mountains.

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

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis,Michael J.

2006-01-01

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Modelling the oscillations of the thermocline in a lake by means of a fully consistent and conservative 3D finite-element model with a vertically adaptive mesh

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Vallaeys, Valentin; Naithani, Jaya; Remacle, Jean-François; Legat, Vincent; Deleersnijder, Eric

2017-04-01

Vertical discretisation is crucial in the modelling of lake thermocline oscillations. For finite element methods, a simple way to increase the resolution close to the oscillating thermocline is to use vertical adaptive coordinates. With an Arbitrary Lagrangian-Eulerian (ALE) formulation, the mesh can be adapted to increase the resolution in regions with strong shear or stratification. In such an application, consistency and conservativity must be strictly enforced. SLIM 3D, a discontinuous-Galerkin finite element model for shallow-water flows (www.climate.be/slim, e.g. Kärnä et al., 2013, Delandmeter et al., 2015), was designed to be strictly consistent and conservative in its discrete formulation. In this context, special care must be paid to the coupling of the external and internal modes of the model and the moving mesh algorithm. In this framework, the mesh can be adapted arbitrarily in the vertical direction. Two moving mesh algorithms were implemented: the first one computes an a-priori optimal mesh; the second one diffuses vertically the mesh (Burchard et al., 2004, Hofmeister et al., 2010). The criteria used to define the optimal mesh and the diffusion function are related to a suitable measure of shear and stratification. We will present in detail the design of the model and how the consistency and conservativity is obtained. Then we will apply it to both idealised benchmarks and the wind-forced thermocline oscillations in Lake Tanganyika (Naithani et al. 2002). References Tuomas Kärnä, Vincent Legat and Eric Deleersnijder. A baroclinic discontinuous Galerkin finite element model for coastal flows, Ocean Modelling, 61:1-20, 2013. Philippe Delandmeter, Stephen E Lewis, Jonathan Lambrechts, Eric Deleersnijder, Vincent Legat and Eric Wolanski. The transport and fate of riverine fine sediment exported to a semi-open system. Estuarine, Coastal and Shelf Science, 167:336-346, 2015. Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids in one-dimensional numerical ocean models. Ocean Modelling, 6:51-81, 2004. Richard Hofmeister, Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids for 3d numerical ocean models. Ocean Modelling, 33:70-86, 2010. Jaya Naithani, Eric Deleersnijder and Pierre-Denis Plisnier. Origin of intraseasonal variability in Lake Tanganyika. Geophysical Research Letters, 29(23), doi:10.1029/2002GL015843, 2002.

Origin of giant Martian polygons

NASA Technical Reports Server (NTRS)

Mcgill, George E.; Hills, L. S.

1992-01-01

Extensive areas of the Martian northern plains in Utopia and Acidalia planitiae are characterized by 'polygonal terrane'. Polygonal terrane consists of material cut by complex troughs defining a pattern resembling mudcracks, columnar joints, or frost-wedge polygons on earth. However, the Martian polygons are orders of magnitude larger than these potential earth analogues, leading to severe mechanical difficulties for genetic models based on simple analogy arguments. Plate-bending and finite element models indicate that shrinkage of desiccating sediment or cooling volcanics accompanied by differential compaction over buried topography can account for the stresses responsible for polygon troughs as well as the large size of the polygons. Although trough widths and depths relate primarily to shrinkage, the large scale of the polygonl pattern relates to the spacing between topographic elevations on the surface buried beneath polygonal terrane material. Geological relationships favor a sedimentary origin for polygonal terrane material, but our model is not dependent on the specific genesis. Our analysis also suggests that the polygons must have formed at a geologically rapid rate.

Microtopographic and depth controls on active layer chemistry in Arctic polygonal ground

DOE PAGES

Newman, Brent D.; Throckmorton, Heather M.; Graham, David E.; ...

2015-03-24

Polygonal ground is a signature characteristic of Arctic lowlands, and carbon release from permafrost thaw can alter feedbacks to Arctic ecosystems and climate. This study describes the first comprehensive spatial examination of active layer biogeochemistry that extends across high- and low-centered, ice wedge polygons, their features, and with depth. Water chemistry measurements of 54 analytes were made on surface and active layer pore waters collected near Barrow, Alaska, USA. Significant differences were observed between high- and low-centered polygons suggesting that polygon types may be useful for landscape-scale geochemical classification. However, differences were found for polygon features (centers and troughs) formore » analytes that were not significant for polygon type, suggesting that finer-scale features affect biogeochemistry differently from polygon types. Depth variations were also significant, demonstrating important multidimensional aspects of polygonal ground biogeochemistry. These results have major implications for understanding how polygonal ground ecosystems function, and how they may respond to future change.« less

Acoustic performance of a Herschel Quincke tube modified with an interconnecting pipe

NASA Astrophysics Data System (ADS)

Desantes, J. M.; Torregrosa, A. J.; Climent, H.; Moya, D.

2005-06-01

The classical two-duct Herschel-Quincke tube is modified by means of an additional pipe connecting both paths. A transfer matrix is obtained for a mesh system with five arbitrary branches and then particularized to the proposed scheme. Experimental attenuation measurements were performed on several prototypes, and the results compared favourably with predictions from the previous theoretical development. Finally, transmission loss contour plots were used to study the influence of the connecting pipe on the resonance frequencies. The results confirm the nontrivial character of the influence observed, and simple relationships are obtained for the general trends.

A finite element formulation for scattering from electrically large 2-dimensional structures

NASA Technical Reports Server (NTRS)

Ross, Daniel C.; Volakis, John L.

1992-01-01

A finite element formulation is given using the scattered field approach with a fictitious material absorber to truncate the mesh. The formulation includes the use of arbitrary approximation functions so that more accurate results can be achieved without any modification to the software. Additionally, non-polynomial approximation functions can be used, including complex approximation functions. The banded system that results is solved with an efficient sparse/banded iterative scheme and as a consequence, large structures can be analyzed. Results are given for simple cases to verify the formulation and also for large, complex geometries.

N-MODY: a code for collisionless N-body simulations in modified Newtonian dynamics.

NASA Astrophysics Data System (ADS)

Londrillo, P.; Nipoti, C.

We describe the numerical code N-MODY, a parallel particle-mesh code for collisionless N-body simulations in modified Newtonian dynamics (MOND). N-MODY is based on a numerical potential solver in spherical coordinates that solves the non-linear MOND field equation, and is ideally suited to simulate isolated stellar systems. N-MODY can be used also to compute the MOND potential of arbitrary static density distributions. A few applications of N-MODY indicate that some astrophysically relevant dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter.

Proteus-MOC: A 3D deterministic solver incorporating 2D method of characteristics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marin-Lafleche, A.; Smith, M. A.; Lee, C.

2013-07-01

A new transport solution methodology was developed by combining the two-dimensional method of characteristics with the discontinuous Galerkin method for the treatment of the axial variable. The method, which can be applied to arbitrary extruded geometries, was implemented in PROTEUS-MOC and includes parallelization in group, angle, plane, and space using a top level GMRES linear algebra solver. Verification tests were performed to show accuracy and stability of the method with the increased number of angular directions and mesh elements. Good scalability with parallelism in angle and axial planes is displayed. (authors)

Convex Lattice Polygons

ERIC Educational Resources Information Center

Scott, Paul

2006-01-01

A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.

Data decomposition method for parallel polygon rasterization considering load balancing

NASA Astrophysics Data System (ADS)

Zhou, Chen; Chen, Zhenjie; Liu, Yongxue; Li, Feixue; Cheng, Liang; Zhu, A.-xing; Li, Manchun

2015-12-01

It is essential to adopt parallel computing technology to rapidly rasterize massive polygon data. In parallel rasterization, it is difficult to design an effective data decomposition method. Conventional methods ignore load balancing of polygon complexity in parallel rasterization and thus fail to achieve high parallel efficiency. In this paper, a novel data decomposition method based on polygon complexity (DMPC) is proposed. First, four factors that possibly affect the rasterization efficiency were investigated. Then, a metric represented by the boundary number and raster pixel number in the minimum bounding rectangle was developed to calculate the complexity of each polygon. Using this metric, polygons were rationally allocated according to the polygon complexity, and each process could achieve balanced loads of polygon complexity. To validate the efficiency of DMPC, it was used to parallelize different polygon rasterization algorithms and tested on different datasets. Experimental results showed that DMPC could effectively parallelize polygon rasterization algorithms. Furthermore, the implemented parallel algorithms with DMPC could achieve good speedup ratios of at least 15.69 and generally outperformed conventional decomposition methods in terms of parallel efficiency and load balancing. In addition, the results showed that DMPC exhibited consistently better performance for different spatial distributions of polygons.

Global tectonic reconstructions with continuously deforming and evolving rigid plates

NASA Astrophysics Data System (ADS)

Gurnis, Michael; Yang, Ting; Cannon, John; Turner, Mark; Williams, Simon; Flament, Nicolas; Müller, R. Dietmar

2018-07-01

Traditional plate reconstruction methodologies do not allow for plate deformation to be considered. Here we present software to construct and visualize global tectonic reconstructions with deforming plates within the context of rigid plates. Both deforming and rigid plates are defined by continuously evolving polygons. The deforming regions are tessellated with triangular meshes such that either strain rate or cumulative strain can be followed. The finite strain history, crustal thickness and stretching factor of points within the deformation zones are tracked as Lagrangian points. Integrating these tools within the interactive platform GPlates enables specialized users to build and refine deforming plate models and integrate them with other models in time and space. We demonstrate the integrated platform with regional reconstructions of Cenozoic western North America, the Mesozoic South American Atlantic margin, and Cenozoic southeast Asia, embedded within global reconstructions, using different data and reconstruction strategies.

Getting in touch--3D printing in forensic imaging.

PubMed

Ebert, Lars Chr; Thali, Michael J; Ross, Steffen

2011-09-10

With the increasing use of medical imaging in forensics, as well as the technological advances in rapid prototyping, we suggest combining these techniques to generate displays of forensic findings. We used computed tomography (CT), CT angiography, magnetic resonance imaging (MRI) and surface scanning with photogrammetry in conjunction with segmentation techniques to generate 3D polygon meshes. Based on these data sets, a 3D printer created colored models of the anatomical structures. Using this technique, we could create models of bone fractures, vessels, cardiac infarctions, ruptured organs as well as bitemark wounds. The final models are anatomically accurate, fully colored representations of bones, vessels and soft tissue, and they demonstrate radiologically visible pathologies. The models are more easily understood by laypersons than volume rendering or 2D reconstructions. Therefore, they are suitable for presentations in courtrooms and for educational purposes. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Polygons and Their Circles

ERIC Educational Resources Information Center

Stephenson, Paul

2009-01-01

In order to find its circumference, Archimedes famously boxed the circle between two polygons. Ending the first of a series of articles (MT179) with an aside, Francis Lopez-Real reverses the situation to ask: Which polygons can be boxed between two circles? (The official term for such polygons is "bicentric".) The sides of these polygons are…

JIGSAW-GEO (1.0): Locally Orthogonal Staggered Unstructured Grid Generation for General Circulation Modelling on the Sphere

NASA Technical Reports Server (NTRS)

Engwirda, Darren

2017-01-01

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered VoronoiDelaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

NASA Astrophysics Data System (ADS)

Engwirda, Darren

2017-06-01

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi-Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2017-10-01

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total Lagrangian formulations that are based on a fixed computational grid and which instead evolve the mapping of the reference configuration to the current one. Our new Lagrangian-type DG scheme adopts the novel a posteriori sub-cell finite volume limiter method recently developed in [62] for fixed unstructured grids. In this approach, the validity of the candidate solution produced in each cell by an unlimited ADER-DG scheme is verified against a set of physical and numerical detection criteria, such as the positivity of pressure and density, the absence of floating point errors (NaN) and the satisfaction of a relaxed discrete maximum principle (DMP) in the sense of polynomials. Those cells which do not satisfy all of the above criteria are flagged as troubled cells and are recomputed at the aid of a more robust second order TVD finite volume scheme. To preserve the subcell resolution capability of the original DG scheme, the FV limiter is run on a sub-grid that is 2 N + 1 times finer compared to the mesh of the original unlimited DG scheme. The new subcell averages are then gathered back into a high order DG polynomial by a usual conservative finite volume reconstruction operator. The numerical convergence rates of the new ALE ADER-DG schemes are studied up to fourth order in space and time and several test problems are simulated in order to check the accuracy and the robustness of the proposed numerical method in the context of the Euler and Navier-Stokes equations for compressible gas dynamics, considering both inviscid and viscous fluids. Finally, an application inspired by Inertial Confinement Fusion (ICF) type flows is considered by solving the Euler equations and the PDE of viscous and resistive magnetohydrodynamics (VRMHD).

A physical optics/equivalent currents model for the RCS of trihedral corner reflectors

NASA Technical Reports Server (NTRS)

Balanis, Constantine A.; Polycarpou, Anastasis C.

1993-01-01

The scattering in the interior regions of both square and triangular trihedral corner reflectors is examined. The theoretical model presented combines geometrical and physical optics (GO and PO), used to account for reflection terms, with equivalent edge currents (EEC), used to account for first-order diffractions from the edges. First-order, second-order, and third-order reflection terms are included. Calculating the first-order reflection terms involves integrating over the entire surface of the illuminated plate. Calculating the second- and third-order reflection terms, however, is much more difficult because the illuminated area is an arbitrary polygon whose shape is dependent upon the incident angles. The method for determining the area of integration is detailed. Extensive comparisons between the high-frequency model, Finite-Difference Time-Domain (FDTD) and experimental data are used for validation of the radar cross section (RCS) of both square and triangular trihedral reflectors.

A hybridized formulation for the weak Galerkin mixed finite element method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

A hybridized formulation for the weak Galerkin mixed finite element method

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2016-01-14

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

Interactions between Polygonal Normal Faults and Larger Normal Faults, Offshore Nova Scotia, Canada

NASA Astrophysics Data System (ADS)

Pham, T. Q. H.; Withjack, M. O.; Hanafi, B. R.

2017-12-01

Polygonal faults, small normal faults with polygonal arrangements that form in fine-grained sedimentary rocks, can influence ground-water flow and hydrocarbon migration. Using well and 3D seismic-reflection data, we have examined the interactions between polygonal faults and larger normal faults on the passive margin of offshore Nova Scotia, Canada. The larger normal faults strike approximately E-W to NE-SW. Growth strata indicate that the larger normal faults were active in the Late Cretaceous (i.e., during the deposition of the Wyandot Formation) and during the Cenozoic. The polygonal faults were also active during the Cenozoic because they affect the top of the Wyandot Formation, a fine-grained carbonate sedimentary rock, and the overlying Cenozoic strata. Thus, the larger normal faults and the polygonal faults were both active during the Cenozoic. The polygonal faults far from the larger normal faults have a wide range of orientations. Near the larger normal faults, however, most polygonal faults have preferred orientations, either striking parallel or perpendicular to the larger normal faults. Some polygonal faults nucleated at the tip of a larger normal fault, propagated outward, and linked with a second larger normal fault. The strike of these polygonal faults changed as they propagated outward, ranging from parallel to the strike of the original larger normal fault to orthogonal to the strike of the second larger normal fault. These polygonal faults hard-linked the larger normal faults at and above the level of the Wyandot Formation but not below it. We argue that the larger normal faults created stress-enhancement and stress-reorientation zones for the polygonal faults. Numerous small, polygonal faults formed in the stress-enhancement zones near the tips of larger normal faults. Stress-reorientation zones surrounded the larger normal faults far from their tips. Fewer polygonal faults are present in these zones, and, more importantly, most polygonal faults in these zones were either parallel or perpendicular to the larger faults.

A Mixed-dimensional Model for Determining the Impact of Permafrost Polygonal Ground Degradation on Arctic Hydrology.

NASA Astrophysics Data System (ADS)

Coon, E.; Jan, A.; Painter, S. L.; Moulton, J. D.; Wilson, C. J.

2017-12-01

Many permafrost-affected regions in the Arctic manifest a polygonal patterned ground, which contains large carbon stores and is vulnerability to climate change as warming temperatures drive melting ice wedges, polygon degradation, and thawing of the underlying carbon-rich soils. Understanding the fate of this carbon is difficult. The system is controlled by complex, nonlinear physics coupling biogeochemistry, thermal-hydrology, and geomorphology, and there is a strong spatial scale separation between microtopograpy (at the scale of an individual polygon) and the scale of landscape change (at the scale of many thousands of polygons). Physics-based models have come a long way, and are now capable of representing the diverse set of processes, but only on individual polygons or a few polygons. Empirical models have been used to upscale across land types, including ecotypes evolving from low-centered (pristine) polygons to high-centered (degraded) polygon, and do so over large spatial extent, but are limited in their ability to discern causal process mechanisms. Here we present a novel strategy that looks to use physics-based models across scales, bringing together multiple capabilities to capture polygon degradation under a warming climate and its impacts on thermal-hydrology. We use fine-scale simulations on individual polygons to motivate a mixed-dimensional strategy that couples one-dimensional columns representing each individual polygon through two-dimensional surface flow. A subgrid model is used to incorporate the effects of surface microtopography on surface flow; this model is described and calibrated to fine-scale simulations. And critically, a subsidence model that tracks volume loss in bulk ice wedges is used to alter the subsurface structure and subgrid parameters, enabling the inclusion of the feedbacks associated with polygon degradation. This combined strategy results in a model that is able to capture the key features of polygon permafrost degradation, but in a simulation across a large spatial extent of polygonal tundra.

Parallel grid library for rapid and flexible simulation development

NASA Astrophysics Data System (ADS)

Honkonen, I.; von Alfthan, S.; Sandroos, A.; Janhunen, P.; Palmroth, M.

2013-04-01

We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as cell data. The amount of data in grid cells can vary both in space and time allowing dccrg to be used in very different types of simulations, for example in fluid and particle codes. Dccrg transfers the data between neighboring cells on different processes transparently and asynchronously allowing one to overlap computation and communication. This enables excellent scalability at least up to 32 k cores in magnetohydrodynamic tests depending on the problem and hardware. In the version of dccrg presented here part of the mesh metadata is replicated between MPI processes reducing the scalability of adaptive mesh refinement (AMR) to between 200 and 600 processes. Dccrg is free software that anyone can use, study and modify and is available at https://gitorious.org/dccrg. Users are also kindly requested to cite this work when publishing results obtained with dccrg. Catalogue identifier: AEOM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License version 3 No. of lines in distributed program, including test data, etc.: 54975 No. of bytes in distributed program, including test data, etc.: 974015 Distribution format: tar.gz Programming language: C++. Computer: PC, cluster, supercomputer. Operating system: POSIX. The code has been parallelized using MPI and tested with 1-32768 processes RAM: 10 MB-10 GB per process Classification: 4.12, 4.14, 6.5, 19.3, 19.10, 20. External routines: MPI-2 [1], boost [2], Zoltan [3], sfc++ [4] Nature of problem: Grid library supporting arbitrary data in grid cells, parallel adaptive mesh refinement, transparent remote neighbor data updates and load balancing. Solution method: The simulation grid is represented by an adjacency list (graph) with vertices stored into a hash table and edges into contiguous arrays. Message Passing Interface standard is used for parallelization. Cell data is given as a template parameter when instantiating the grid. Restrictions: Logically cartesian grid. Running time: Running time depends on the hardware, problem and the solution method. Small problems can be solved in under a minute and very large problems can take weeks. The examples and tests provided with the package take less than about one minute using default options. In the version of dccrg presented here the speed of adaptive mesh refinement is at most of the order of 106 total created cells per second. http://www.mpi-forum.org/. http://www.boost.org/. K. Devine, E. Boman, R. Heaphy, B. Hendrickson, C. Vaughan, Zoltan data management services for parallel dynamic applications, Comput. Sci. Eng. 4 (2002) 90-97. http://dx.doi.org/10.1109/5992.988653. https://gitorious.org/sfc++.

Properties of Tangential and Cyclic Polygons: An Application of Circulant Matrices

ERIC Educational Resources Information Center

Leung, Allen; Lopez-Real, Francis

2003-01-01

In this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon P[subscript n] with n even is…

Perceptions and Expected Immediate Reactions to Severe Storm Displays.

PubMed

Jon, Ihnji; Huang, Shih-Kai; Lindell, Michael K

2017-11-09

The National Weather Service has adopted warning polygons that more specifically indicate the risk area than its previous county-wide warnings. However, these polygons are not defined in terms of numerical strike probabilities (p s ). To better understand people's interpretations of warning polygons, 167 participants were shown 23 hypothetical scenarios in one of three information conditions-polygon-only (Condition A), polygon + tornadic storm cell (Condition B), and polygon + tornadic storm cell + flanking nontornadic storm cells (Condition C). Participants judged each polygon's p s and reported the likelihood of taking nine different response actions. The polygon-only condition replicated the results of previous studies; p s was highest at the polygon's centroid and declined in all directions from there. The two conditions displaying storm cells differed from the polygon-only condition only in having p s just as high at the polygon's edge nearest the storm cell as at its centroid. Overall, p s values were positively correlated with expectations of continuing normal activities, seeking information from social sources, seeking shelter, and evacuating by car. These results indicate that participants make more appropriate p s judgments when polygons are presented in their natural context of radar displays than when they are presented in isolation. However, the fact that p s judgments had moderately positive correlations with both sheltering (a generally appropriate response) and evacuation (a generally inappropriate response) suggests that experiment participants experience the same ambivalence about these two protective actions as people threatened by actual tornadoes. © 2017 Society for Risk Analysis.

FASH and MASH: female and male adult human phantoms based on polygon mesh surfaces: II. Dosimetric calculations

NASA Astrophysics Data System (ADS)

Kramer, R.; Cassola, V. F.; Khoury, H. J.; Vieira, J. W.; de Melo Lima, V. J.; Robson Brown, K.

2010-01-01

Female and male adult human phantoms, called FASH (Female Adult meSH) and MASH (Male Adult meSH), have been developed in the first part of this study using 3D animation software and anatomical atlases to replace the image-based FAX06 and the MAX06 voxel phantoms. 3D modelling methods allow for phantom development independent from medical images of patients, volunteers or cadavers. The second part of this study investigates the dosimetric implications for organ and tissue equivalent doses due to the anatomical differences between the new and the old phantoms. These differences are mainly caused by the supine position of human bodies during scanning in order to acquire digital images for voxel phantom development. Compared to an upright standing person, in image-based voxel phantoms organs are often coronally shifted towards the head and sometimes the sagittal diameter of the trunk is reduced by a gravitational change of the fat distribution. In addition, volumes of adipose and muscle tissue shielding internal organs are sometimes too small, because adaptation of organ volumes to ICRP-based organ masses often occurs at the expense of general soft tissues, such as adipose, muscle or unspecified soft tissue. These effects have dosimetric consequences, especially for partial body exposure, such as in x-ray diagnosis, but also for whole body external exposure and for internal exposure. Using the EGSnrc Monte Carlo code, internal and external exposure to photons and electrons has been simulated with both pairs of phantoms. The results show differences between organ and tissue equivalent doses for the upright standing FASH/MASH and the image-based supine FAX06/MAX06 phantoms of up to 80% for external exposure and up to 100% for internal exposure. Similar differences were found for external exposure between FASH/MASH and REGINA/REX, the reference voxel phantoms of the International Commission on Radiological Protection. Comparison of effective doses for external photon exposure showed good agreement between FASH/MASH and REGINA/REX, but large differences between FASH/MASH and the mesh-based RPI_AM and the RPI_AF phantoms, developed at the Rensselaer Polytechnic Institute (RPI).

Extrusion-Based 3D Printing of Hierarchically Porous Advanced Battery Electrodes.

PubMed

Lacey, Steven D; Kirsch, Dylan J; Li, Yiju; Morgenstern, Joseph T; Zarket, Brady C; Yao, Yonggang; Dai, Jiaqi; Garcia, Laurence Q; Liu, Boyang; Gao, Tingting; Xu, Shaomao; Raghavan, Srinivasa R; Connell, John W; Lin, Yi; Hu, Liangbing

2018-03-01

A highly porous 2D nanomaterial, holey graphene oxide (hGO), is synthesized directly from holey graphene powder and employed to create an aqueous 3D printable ink without the use of additives or binders. Stable dispersions of hydrophilic hGO sheets in water (≈100 mg mL -1 ) can be readily achieved. The shear-thinning behavior of the aqueous hGO ink enables extrusion-based printing of fine filaments into complex 3D architectures, such as stacked mesh structures, on arbitrary substrates. The freestanding 3D printed hGO meshes exhibit trimodal porosity: nanoscale (4-25 nm through-holes on hGO sheets), microscale (tens of micrometer-sized pores introduced by lyophilization), and macroscale (<500 µm square pores of the mesh design), which are advantageous for high-performance energy storage devices that rely on interfacial reactions to promote full active-site utilization. To elucidate the benefit of (nano)porosity and structurally conscious designs, the additive-free architectures are demonstrated as the first 3D printed lithium-oxygen (Li-O 2 ) cathodes and characterized alongside 3D printed GO-based materials without nanoporosity as well as nanoporous 2D vacuum filtrated films. The results indicate the synergistic effect between 2D nanomaterials, hierarchical porosity, and overall structural design, as well as the promise of a freeform generation of high-energy-density battery systems. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Centroid of a Polygon--Three Views.

ERIC Educational Resources Information Center

Shilgalis, Thomas W.; Benson, Carol T.

2001-01-01

Investigates the idea of the center of mass of a polygon and illustrates centroids of polygons. Connects physics, mathematics, and technology to produces results that serve to generalize the notion of centroid to polygons other than triangles. (KHR)

System and method for the adaptive mapping of matrix data to sets of polygons

NASA Technical Reports Server (NTRS)

Burdon, David (Inventor)

2003-01-01

A system and method for converting bitmapped data, for example, weather data or thermal imaging data, to polygons is disclosed. The conversion of the data into polygons creates smaller data files. The invention is adaptive in that it allows for a variable degree of fidelity of the polygons. Matrix data is obtained. A color value is obtained. The color value is a variable used in the creation of the polygons. A list of cells to check is determined based on the color value. The list of cells to check is examined in order to determine a boundary list. The boundary list is then examined to determine vertices. The determination of the vertices is based on a prescribed maximum distance. When drawn, the ordered list of vertices create polygons which depict the cell data. The data files which include the vertices for the polygons are much smaller than the corresponding cell data files. The fidelity of the polygon representation can be adjusted by repeating the logic with varying fidelity values to achieve a given maximum file size or a maximum number of vertices per polygon.

A fast ergodic algorithm for generating ensembles of equilateral random polygons

NASA Astrophysics Data System (ADS)

Varela, R.; Hinson, K.; Arsuaga, J.; Diao, Y.

2009-03-01

Knotted structures are commonly found in circular DNA and along the backbone of certain proteins. In order to properly estimate properties of these three-dimensional structures it is often necessary to generate large ensembles of simulated closed chains (i.e. polygons) of equal edge lengths (such polygons are called equilateral random polygons). However finding efficient algorithms that properly sample the space of equilateral random polygons is a difficult problem. Currently there are no proven algorithms that generate equilateral random polygons with its theoretical distribution. In this paper we propose a method that generates equilateral random polygons in a 'step-wise uniform' way. We prove that this method is ergodic in the sense that any given equilateral random polygon can be generated by this method and we show that the time needed to generate an equilateral random polygon of length n is linear in terms of n. These two properties make this algorithm a big improvement over the existing generating methods. Detailed numerical comparisons of our algorithm with other widely used algorithms are provided.

The ADER-DG method for seismic wave propagation and earthquake rupture dynamics

NASA Astrophysics Data System (ADS)

Pelties, Christian; Gabriel, Alice; Ampuero, Jean-Paul; de la Puente, Josep; Käser, Martin

2013-04-01

We will present the Arbitrary high-order DERivatives Discontinuous Galerkin (ADER-DG) method for solving the combined elastodynamic wave propagation and dynamic rupture problem. The ADER-DG method enables high-order accuracy in space and time while being implemented on unstructured tetrahedral meshes. A tetrahedral element discretization provides rapid and automatized mesh generation as well as geometrical flexibility. Features as mesh coarsening and local time stepping schemes can be applied to reduce computational efforts without introducing numerical artifacts. The method is well suited for parallelization and large scale high-performance computing since only directly neighboring elements exchange information via numerical fluxes. The concept of fluxes is a key ingredient of the numerical scheme as it governs the numerical dispersion and diffusion properties and allows to accommodate for boundary conditions, empirical friction laws of dynamic rupture processes, or the combination of different element types and non-conforming mesh transitions. After introducing fault dynamics into the ADER-DG framework, we will demonstrate its specific advantages in benchmarking test scenarios provided by the SCEC/USGS Spontaneous Rupture Code Verification Exercise. An important result of the benchmark is that the ADER-DG method avoids spurious high-frequency contributions in the slip rate spectra and therefore does not require artificial Kelvin-Voigt damping, filtering or other modifications of the produced synthetic seismograms. To demonstrate the capabilities of the proposed scheme we simulate an earthquake scenario, inspired by the 1992 Landers earthquake, that includes branching and curved fault segments. Furthermore, topography is respected in the discretized model to capture the surface waves correctly. The advanced geometrical flexibility combined with an enhanced accuracy will make the ADER-DG method a useful tool to study earthquake dynamics on complex fault systems in realistic rheologies.

Solution of internal ballistic problem for SRM with grain of complex shape during main firing phase

NASA Astrophysics Data System (ADS)

Kiryushkin, A. E.; Minkov, L. L.

2017-10-01

Solid rocket motor (SRM) internal ballistics problems are related to the problems with moving boundaries. The algorithm able to solve similar problems in axisymmetric formulation on Cartesian mesh with an arbitrary order of accuracy is considered in this paper. The base of this algorithm is the ghost point extrapolation using inverse Lax-Wendroff procedure. Level set method is used as an implicit representation of the domain boundary. As an example, the internal ballistics problem for SRM with umbrella type grain was solved during the main firing phase. In addition, flow parameters distribution in the combustion chamber was obtained for different time moments.

Aerodynamic interaction between vortical wakes and lifting two-dimensional bodies

NASA Technical Reports Server (NTRS)

Stremel, Paul M.

1987-01-01

Unsteady rotor wake interactions with the empenage, tail boom, and other aerodynamic surfaces of a helicopter have a significant influence on its aerodynamic performance, the ride quality, and amount of vibration. A numerical method for computing the aerodynamic interaction between an interacting vortex wake and the viscous flow about arbitrary two-dimensional bodies has been developed to address this helicopter problem. The method solves for the flow field velocities on a body-fitted computational mesh using finite-difference techniques. The interaction of a rotor wake with the flow about a 4:1 elliptic cylinder at 45-deg incidence was calculated for a Reynolds number of 3000.

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Modeling NIF experimental designs with adaptive mesh refinement and Lagrangian hydrodynamics

NASA Astrophysics Data System (ADS)

Koniges, A. E.; Anderson, R. W.; Wang, P.; Gunney, B. T. N.; Becker, R.; Eder, D. C.; MacGowan, B. J.; Schneider, M. B.

2006-06-01

Incorporation of adaptive mesh refinement (AMR) into Lagrangian hydrodynamics algorithms allows for the creation of a highly powerful simulation tool effective for complex target designs with three-dimensional structure. We are developing an advanced modeling tool that includes AMR and traditional arbitrary Lagrangian-Eulerian (ALE) techniques. Our goal is the accurate prediction of vaporization, disintegration and fragmentation in National Ignition Facility (NIF) experimental target elements. Although our focus is on minimizing the generation of shrapnel in target designs and protecting the optics, the general techniques are applicable to modern advanced targets that include three-dimensional effects such as those associated with capsule fill tubes. Several essential computations in ordinary radiation hydrodynamics need to be redesigned in order to allow for AMR to work well with ALE, including algorithms associated with radiation transport. Additionally, for our goal of predicting fragmentation, we include elastic/plastic flow into our computations. We discuss the integration of these effects into a new ALE-AMR simulation code. Applications of this newly developed modeling tool as well as traditional ALE simulations in two and three dimensions are applied to NIF early-light target designs.

A new Euler scheme based on harmonic-polygon approach for solving first order ordinary differential equation

NASA Astrophysics Data System (ADS)

Yusop, Nurhafizah Moziyana Mohd; Hasan, Mohammad Khatim; Wook, Muslihah; Amran, Mohd Fahmi Mohamad; Ahmad, Siti Rohaidah

2017-10-01

There are many benefits to improve Euler scheme for solving the Ordinary Differential Equation Problems. Among the benefits are simple implementation and low-cost computational. However, the problem of accuracy in Euler scheme persuade scholar to use complex method. Therefore, the main purpose of this research are show the construction a new modified Euler scheme that improve accuracy of Polygon scheme in various step size. The implementing of new scheme are used Polygon scheme and Harmonic mean concept that called as Harmonic-Polygon scheme. This Harmonic-Polygon can provide new advantages that Euler scheme could offer by solving Ordinary Differential Equation problem. Four set of problems are solved via Harmonic-Polygon. Findings show that new scheme or Harmonic-Polygon scheme can produce much better accuracy result.

An algorithm for calculating minimum Euclidean distance between two geographic features

NASA Astrophysics Data System (ADS)

Peuquet, Donna J.

1992-09-01

An efficient algorithm is presented for determining the shortest Euclidean distance between two features of arbitrary shape that are represented in quadtree form. These features may be disjoint point sets, lines, or polygons. It is assumed that the features do not overlap. Features also may be intertwined and polygons may be complex (i.e. have holes). Utilizing a spatial divide-and-conquer approach inherent in the quadtree data model, the basic rationale is to narrow-in on portions of each feature quickly that are on a facing edge relative to the other feature, and to minimize the number of point-to-point Euclidean distance calculations that must be performed. Besides offering an efficient, grid-based alternative solution, another unique and useful aspect of the current algorithm is that is can be used for rapidly calculating distance approximations at coarser levels of resolution. The overall process can be viewed as a top-down parallel search. Using one list of leafcode addresses for each of the two features as input, the algorithm is implemented by successively dividing these lists into four sublists for each descendant quadrant. The algorithm consists of two primary phases. The first determines facing adjacent quadrant pairs where part or all of the two features are separated between the two quadrants, respectively. The second phase then determines the closest pixel-level subquadrant pairs within each facing quadrant pair at the lowest level. The key element of the second phase is a quick estimate distance heuristic for further elimination of locations that are not as near as neighboring locations.

Numerical simulation of tunneling through arbitrary potential barriers applied on MIM and MIIM rectenna diodes

NASA Astrophysics Data System (ADS)

Abdolkader, Tarek M.; Shaker, Ahmed; Alahmadi, A. N. M.

2018-07-01

With the continuous miniaturization of electronic devices, quantum-mechanical effects such as tunneling become more effective in many device applications. In this paper, a numerical simulation tool is developed under a MATLAB environment to calculate the tunneling probability and current through an arbitrary potential barrier comparing three different numerical techniques: the finite difference method, transfer matrix method, and transmission line method. For benchmarking, the tool is applied to many case studies such as the rectangular single barrier, rectangular double barrier, and continuous bell-shaped potential barrier, each compared to analytical solutions and giving the dependence of the error on the number of mesh points. In addition, a thorough study of the J ‑ V characteristics of MIM and MIIM diodes, used as rectifiers for rectenna solar cells, is presented and simulations are compared to experimental results showing satisfactory agreement. On the undergraduate level, the tool provides a deeper insight for students to compare numerical techniques used to solve various tunneling problems and helps students to choose a suitable technique for a certain application.

New Support for Hypotheses of an Ancient Ocean on Mars

NASA Technical Reports Server (NTRS)

Oehler, Dorothy Z.; Allen, Carlton C.

2013-01-01

A new analog for the giant polygons in the Chryse-Acidalia area suggests that those features may have formed in a major body of water - likely a Late Hesperian to Early Amazonian ocean. This analog -terrestrial polygons in subsea, passive margin basins derives from 3D seismic data that show similar-scale, polygonal fault systems in the subsurface of more than 50 terrestrial offshore basins. The terrestrial and martian polygons share similar sizes, basin-wide distributions, tectonic settings, and association with expected fine-grained sediments. Late Hesperian deposition from outflow floods may have triggered formation of these polygons, by providing thick, rapidly-deposited, fine-grained sediments necessary for polygonal fracturing. The restriction of densely occurring polygons to elevations below approx. -4000 m to -4100 m supports inferences that a body of water controlled their formation. Those same elevations appear to restrict occurrence of polygons in Utopia Planitia, suggesting that this analog may apply also to Utopia and that similar processes may have occurred across the martian lowlands.

Clastic polygonal networks around Lyot crater, Mars: Possible formation mechanisms from morphometric analysis

NASA Astrophysics Data System (ADS)

Brooker, L. M.; Balme, M. R.; Conway, S. J.; Hagermann, A.; Barrett, A. M.; Collins, G. S.; Soare, R. J.

2018-03-01

Polygonal networks of patterned ground are a common feature in cold-climate environments. They can form through the thermal contraction of ice-cemented sediment (i.e. formed from fractures), or the freezing and thawing of ground ice (i.e. formed by patterns of clasts, or ground deformation). The characteristics of these landforms provide information about environmental conditions. Analogous polygonal forms have been observed on Mars leading to inferences about environmental conditions. We have identified clastic polygonal features located around Lyot crater, Mars (50°N, 30°E). These polygons are unusually large (>100 m diameter) compared to terrestrial clastic polygons, and contain very large clasts, some of which are up to 15 metres in diameter. The polygons are distributed in a wide arc around the eastern side of Lyot crater, at a consistent distance from the crater rim. Using high-resolution imaging data, we digitised these features to extract morphological information. These data are compared to existing terrestrial and Martian polygon data to look for similarities and differences and to inform hypotheses concerning possible formation mechanisms. Our results show the clastic polygons do not have any morphometric features that indicate they are similar to terrestrial sorted, clastic polygons formed by freeze-thaw processes. They are too large, do not show the expected variation in form with slope, and have clasts that do not scale in size with polygon diameter. However, the clastic networks are similar in network morphology to thermal contraction cracks, and there is a potential direct Martian analogue in a sub-type of thermal contraction polygons located in Utopia Planitia. Based upon our observations, we reject the hypothesis that polygons located around Lyot formed as freeze-thaw polygons and instead an alternative mechanism is put forward: they result from the infilling of earlier thermal contraction cracks by wind-blown material, which then became compressed and/or cemented resulting in a resistant fill. Erosion then leads to preservation of these polygons in positive relief, while later weathering results in the fracturing of the fill material to form angular clasts. These results suggest that there was an extensive area of ice-rich terrain, the extent of which is linked to ejecta from Lyot crater.

Quantitative Investigations of Polygonal Ground in Continental Antarctica: Terrestrial Analogues for Polygons on Mars

NASA Astrophysics Data System (ADS)

Sassenroth, Cynthia; Hauber, Ernst; Schmitz, Nicole; de Vera, Jean Pierre

2017-04-01

Polygonally fractured ground is widespread at middle and high latitudes on Mars. The latitude-dependence and the morphologic similarity to terrestrial patterned ground in permafrost regions may indicate a formation as thermal contraction cracks, but the exact formation mechanisms are still unclear. In particular, it is debated whether freeze-thaw processes and liquid water are required to generate the observed features. This study quantitatively investigates polygonal networks in ice-free parts of continental Antarctica to help distinguishing between different hypotheses of their origin on Mars. The study site is located in the Helliwell Hills in Northern Victoria Land ( 71.73°S/161.38°E) and was visited in the framework of the GANOVEX XI expedition during the austral summer of 2015/2016. The local bedrock consists mostly of sediments (sandstones) of the Beacon Supergroup and mafic igneous intrusions (Ferrar Dolerites). The surfaces are covered by glacial drift consisting of clasts with diverse lithologies. Thermal contraction cracks are ubiquitous. We mapped polygons in the northern part of Helliwell Hills in a GIS environment on the basis of high-resolution satellite images with a pixel size of 50 cm. The measured spatial parameters include polygon area, perimeter, length, width, circularity and aspect. We also analyzed the connectivity of enclosed polygons within a polygon network. The polygons do not display significant local relief, but overall the polygon centers are slightly higher than the bounding cracks (i.e. high-center polygons). Sizes of polygons can vary widely, dependent on the geographical location, between 10m2 and >900m2. In planar and level areas, thermal contraction cracks tend to be well connected as hexagonal or irregular polygonal networks without a preferred alignment. In contrast, polygonal networks on slopes form elongated, orthogonal primary cracks, which are either parallel or transverse to the steepest topographic gradient. During fieldwork, excavations were made in the center of polygons and across the bounding cracks. Typically, the uppermost 40 cm of regolith are dry and unconsolidated. Below that, there is commonly a sharp transition to ice-cemented material or very clear ice with no bubbles. Soil profiles were recorded, and sediment samples were taken and analyzed for their grain size composition with laser diffractometric measurement methods. External factors such as slope gradient and orientation, insolation and composition of surface and subsurface materials were included in the analysis.

Small-scale polygons on Mars

NASA Technical Reports Server (NTRS)

Lucchitta, B. K.

1984-01-01

Polygonal-fracture patterns on the martian surface were discovered on Viking Orbiter images. The polygons are 2-20 km in diameter, much larger than those of known patterned ground on Earth. New observations show, however, that polygons exist on Mars that have diameters similar to those of ice-wedge polygons on Earth (generally a few meters to more than 100 m). Various explanations for the origin of these crustal features are examined; seasonal desiccation and thermal-contraction cracking in ice-rich ground. It is difficult to ascertain whether the polygons are forming today or are relics from the past. The crispness of some crack suggests a recent origin. On the other hand the absence of upturned edges (indicating actively forming ice wedges), the locally disintegrating ground, and a few possible superposed rayed craters indicate that the polygons are not forming at the present.

Constrained map-based inventory estimation

Treesearch

Paul C. Van Deusen; Francis A. Roesch

2007-01-01

A region can conceptually be tessellated into polygons at different scales or resolutions. Likewise, samples can be taken from the region to determine the value of a polygon variable for each scale. Sampled polygons can be used to estimate values for other polygons at the same scale. However, estimates should be compatible across the different scales. Estimates are...

Area of Lattice Polygons

ERIC Educational Resources Information Center

Scott, Paul

2006-01-01

A lattice is a (rectangular) grid of points, usually pictured as occurring at the intersections of two orthogonal sets of parallel, equally spaced lines. Polygons that have lattice points as vertices are called lattice polygons. It is clear that lattice polygons come in various shapes and sizes. A very small lattice triangle may cover just 3…

A simple algorithm for computing positively weighted straight skeletons of monotone polygons.

PubMed

Biedl, Therese; Held, Martin; Huber, Stefan; Kaaser, Dominik; Palfrader, Peter

2015-02-01

We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in [Formula: see text] time and [Formula: see text] space, where n denotes the number of vertices of the polygon.

A virtual reality atlas of craniofacial anatomy.

PubMed

Smith, Darren M; Oliker, Aaron; Carter, Christina R; Kirov, Miro; McCarthy, Joseph G; Cutting, Court B

2007-11-01

Head and neck anatomy is complex and represents an educational challenge to the student. Conventional two-dimensional illustrations inherently fall short in conveying intricate anatomical relationships that exist in three dimensions. A gratis three-dimensional virtual reality atlas of craniofacial anatomy is presented in an effort to address the paucity of readily accessible and customizable three-dimensional educational material available to the student of head and neck anatomy. Three-dimensional model construction was performed in Alias Maya 4.5 and 6.0. A basic three-dimensional skull model was altered to include surgical landmarks and proportions. Some of the soft tissues were adapted from previous work, whereas others were constructed de novo. Texturing was completed with Adobe Photoshop 7.0 and Maya. The Internet application was designed in Viewpoint Enliven 1.0. A three-dimensional computer model of craniofacial anatomy (bone and soft tissue) was completed. The model is compatible with many software packages and can be accessed by means of the Internet or downloaded to a personal computer. As the three-dimensional meshes are publicly available, they can be extensively manipulated by the user, even at the polygonal level. Three-dimensional computer graphics has yet to be fully exploited for head and neck anatomy education. In this context, the authors present a publicly available computer model of craniofacial anatomy. This model may also find applications beyond clinical medicine. The model can be accessed gratis at the Plastic and Reconstructive Surgery Web site or obtained as a three-dimensional mesh, also gratis, by contacting the authors.

SU-F-T-235: Optical Scan Based Collision Avoidance Using Multiple Stereotactic Cameras During Simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cardan, R; Popple, R; Dobelbower, M

Purpose: To demonstrate the ability to quickly generate an accurate collision avoidance map using multiple stereotactic cameras during simulation. Methods: Three Kinect stereotactic cameras were placed in the CT simulation room and optically calibrated to the DICOM isocenter. Immediately before scanning, the patient was optically imaged to generate a 3D polygon mesh, which was used to calculate the collision avoidance area using our previously developed framework. The mesh was visually compared to the CT scan body contour to ensure accurate coordinate alignment. To test the accuracy of the collision calculation, the patient and machine were physically maneuvered in the treatmentmore » room to calculated collision boundaries. Results: The optical scan and collision calculation took 38.0 seconds and 2.5 seconds to complete respectively. The collision prediction accuracy was determined using a receiver operating curve (ROC) analysis, where the true positive, true negative, false positive and false negative values were 837, 821, 43, and 79 points respectively. The ROC accuracy was 93.1% over the sampled collision space. Conclusion: We have demonstrated a framework which is fast and accurate for predicting collision avoidance for treatment which can be determined during the normal simulation process. Because of the speed, the system could be used to add a layer of safety with a negligible impact on the normal patient simulation experience. This information could be used during treatment planning to explore the feasible geometries when optimizing plans. Research supported by Varian Medical Systems.« less

Fertile organs and in situ spores of a new dipteridaceous fern Hausmannia sinensis from the Jurassic of northern China.

PubMed

Wang, Yongdong; Zhang, Hong

2010-01-22

As a representative fossil member of the dipteridaceous fern, genus Hausmannia was reported worldwide from the Mesozoic strata; however, little is known about the fertile structures, including sporangia and in situ spores, of this genus. In this study, a new species Hausmannia sinensis was identified from the Middle Jurassic of Nei Mongol (Inner Mongolia), northern China. The specimens are compressions and are well preserved with details of sporangia and in situ spores. The leaf laminae are broadly fan-shaped, with an almost entire margin. Primary and lateral veins dichotomously branch to form square or polygonal meshes. Each ultimate mesh bears one to two circular sori of 0.4 mm in diameter. Sori are exindusiate; each sorus contains three to six round to ovoid sporangia. The annulus is developed and oblique, with stomial region present in proximal position. Spores are trilete, circular to oval in shape. Both proximal and distal surfaces are covered with baculate to subverrucate sculptures. Spores range from 20 to 30 microm in diameter (average 28 microm), and are comparable to the dispersed genera Baculatisporites Thomas and Pflug and Apiculatisporis Potonié and Kremp. Hausmannia sinensis represents the first compression species of genus Hausmannia form Eurasia, which shows the combination of well-preserved sori, sporangia, annuli and in situ spore characters, and is therefore helpful for further understanding the diversity and evolution of the Dipteridaceae fern lineage through time.

Fertile organs and in situ spores of a new dipteridaceous fern Hausmannia sinensis from the Jurassic of northern China

PubMed Central

Wang, Yongdong; Zhang, Hong

2010-01-01

As a representative fossil member of the dipteridaceous fern, genus Hausmannia was reported worldwide from the Mesozoic strata; however, little is known about the fertile structures, including sporangia and in situ spores, of this genus. In this study, a new species Hausmannia sinensis was identified from the Middle Jurassic of Nei Mongol (Inner Mongolia), northern China. The specimens are compressions and are well preserved with details of sporangia and in situ spores. The leaf laminae are broadly fan-shaped, with an almost entire margin. Primary and lateral veins dichotomously branch to form square or polygonal meshes. Each ultimate mesh bears one to two circular sori of 0.4 mm in diameter. Sori are exindusiate; each sorus contains three to six round to ovoid sporangia. The annulus is developed and oblique, with stomial region present in proximal position. Spores are trilete, circular to oval in shape. Both proximal and distal surfaces are covered with baculate to subverrucate sculptures. Spores range from 20 to 30 μm in diameter (average 28 μm), and are comparable to the dispersed genera Baculatisporites Thomas and Pflug and Apiculatisporis Potonié and Kremp. Hausmannia sinensis represents the first compression species of genus Hausmannia form Eurasia, which shows the combination of well-preserved sori, sporangia, annuli and in situ spore characters, and is therefore helpful for further understanding the diversity and evolution of the Dipteridaceae fern lineage through time. PMID:19364738

Comparison of the different approaches to generate holograms from data acquired with a Kinect sensor

NASA Astrophysics Data System (ADS)

Kang, Ji-Hoon; Leportier, Thibault; Ju, Byeong-Kwon; Song, Jin Dong; Lee, Kwang-Hoon; Park, Min-Chul

2017-05-01

Data of real scenes acquired in real-time with a Kinect sensor can be processed with different approaches to generate a hologram. 3D models can be generated from a point cloud or a mesh representation. The advantage of the point cloud approach is that computation process is well established since it involves only diffraction and propagation of point sources between parallel planes. On the other hand, the mesh representation enables to reduce the number of elements necessary to represent the object. Then, even though the computation time for the contribution of a single element increases compared to a simple point, the total computation time can be reduced significantly. However, the algorithm is more complex since propagation of elemental polygons between non-parallel planes should be implemented. Finally, since a depth map of the scene is acquired at the same time than the intensity image, a depth layer approach can also be adopted. This technique is appropriate for a fast computation since propagation of an optical wavefront from one plane to another can be handled efficiently with the fast Fourier transform. Fast computation with depth layer approach is convenient for real time applications, but point cloud method is more appropriate when high resolution is needed. In this study, since Kinect can be used to obtain both point cloud and depth map, we examine the different approaches that can be adopted for hologram computation and compare their performance.

A formational model for the polygonal terrains of Mars: Taking a crack at the genesis of the Martian polygons

NASA Technical Reports Server (NTRS)

Wenrich, M. L.; Christensen, P. R.

1993-01-01

The mechanism for the genesis of the polygonal terrains in Acidalia and Utopia Planitia has long been sought: however, no completely satisfying model was put forth that characterizes the evolution of these complexly patterned terrains. The polygons are roughly hexagonal but some are not entirely enclosed by fractures. These polygonal features range in widths from approximately 5 to 20 km. Several origins were proposed that describe the polygon borders as desiccation cracks, columnar jointing in a cooled lava, or frost-wedge features. These tension-induced cracking hypotheses were addressed by Pechmann, who convincingly disputes these mechanisms of formation based on scale magnitude difficulties and morphology. Pechmann suggests instead that the cracks delineating the 5-20-km-wide polygons on the northern plains of Mars are graben resulting from deep-seated, uniform, horizontal tension. The difficulty with this hypothesis is that no analogous polygonal forms are known to have originated by tectonism on Earth. McGill and Hills propose that the polygonal terrains on Mars resulted from either rapid desiccation of sediments or cooling of volcanics coupled with differential compaction of the material over a buried irregular topographic surface. They suggest that fracturing was enhanced over the areas of positive relief and was suppressed above the topographic lows. McGill and Hills suggest that the spacing of the topographic highs primarily controls the size of the Martian polygons and the physics of the shrinkage process is a secondary concern. Ray et. al. conducted a terrestrial study of patterned ground in periglacial areas of the U.S. to determine the process responsible for polygonal ground formation. They developed a model for polygon formation in which convection of seasonal melt water above a permafrost layer, driven by an unstable density stratification, differentially melts the permafrost interface, causing it to become undulatory.

Giant polygons and mounds in the lowlands of Mars: signatures of an ancient ocean?

PubMed

Oehler, Dorothy Z; Allen, Carlton C

2012-06-01

This paper presents the hypothesis that the well-known giant polygons and bright mounds of the martian lowlands may be related to a common process-a process of fluid expulsion that results from burial of fine-grained sediments beneath a body of water. Specifically, we hypothesize that giant polygons and mounds in Chryse and Acidalia Planitiae are analogous to kilometer-scale polygons and mud volcanoes in terrestrial, marine basins and that the co-occurrence of masses of these features in Chryse and Acidalia may be the signature of sedimentary processes in an ancient martian ocean. We base this hypothesis on recent data from both Earth and Mars. On Earth, 3-D seismic data illustrate kilometer-scale polygons that may be analogous to the giant polygons on Mars. The terrestrial polygons form in fine-grained sediments that have been deposited and buried in passive-margin, marine settings. These polygons are thought to result from compaction/dewatering, and they are commonly associated with fluid expulsion features, such as mud volcanoes. On Mars, in Chryse and Acidalia Planitiae, orbital data demonstrate that giant polygons and mounds have overlapping spatial distributions. There, each set of features occurs within a geological setting that is seemingly analogous to that of the terrestrial, kilometer-scale polygons (broad basin of deposition, predicted fine-grained sediments, and lack of significant horizontal stress). Regionally, the martian polygons and mounds both show a correlation to elevation, as if their formation were related to past water levels. Although these observations are based on older data with incomplete coverage, a similar correlation to elevation has been established in one local area studied in detail with newer higher-resolution data. Further mapping with the latest data sets should more clearly elucidate the relationship(s) of the polygons and mounds to elevation over the entire Chryse-Acidalia region and thereby provide more insight into this hypothesis.

Ice-Wedge Polygon Formation Impacts Permafrost Carbon Storage and Vulnerability to Top-Down Thaw in Arctic Coastal Plain Soils

NASA Astrophysics Data System (ADS)

Jastrow, J. D.; Matamala, R.; Ping, C. L.; Vugteveen, T. W.; Lederhouse, J. S.; Michaelson, G. J.; Mishra, U.

2017-12-01

Ice-wedge polygons are ubiquitous, patterned ground features throughout Arctic coastal plains and river deltas. The progressive expansion of ice wedges influences polygon development and strongly affects cryoturbation and soil formation. Thus, we hypothesized that polygon type impacts the distribution and composition of soil organic carbon (C) stocks across the landscape and that such information can improve estimates of permafrost C stocks vulnerable to active layer thickening and increased decomposition due to climatic change. We quantified the distribution of soil C across entire polygon profiles (2-m depth) for three developmental types - flat-centered (FCP), low-centered (LCP), and high-centered (HCP) polygons (3 replicates of each) - formed on glaciomarine sediments within and near the Barrow Environmental Observatory at the northern tip of Alaska. Active layer thickness averaged 45 cm and did not vary among polygon types. Similarly, active layer C stocks were unaffected by polygon type, but permafrost C stocks increased from FCPs to LCPs to HCPs despite greater ice volumes in HCPs. These differences were due to a greater presence of organic horizons in the upper permafrost of LCPs and, especially, HCPs. On average, C stocks in polygon interiors were double those of troughs, on a square meter basis. However, HCPs were physically smaller than LCPs and FCPs, which affected estimates of C stocks at the landscape scale. Accounting for the number of polygons per unit area and the proportional distribution of troughs versus interiors, we estimated permafrost C stocks (2-m depth) increased from 259 Mg C ha-1 in FCPs to 366 Mg C ha-1 in HCPs. Active layer C stocks did not differ among polygon types and averaged 328 Mg C ha-1. We used our detailed polygon profiles to investigate the impact of active layer deepening as projected by Earth system models under future climate scenarios. Because HCPs have a greater proportion of upper permafrost C stocks in organic horizons, permafrost C in areas dominated by this polygon type may be at greater risk for destabilization. Thus, accounting for geospatial distributions of ice-wedge polygon types and associated variations in C stocks and composition could improve observational estimates of regional C stocks and their vulnerability to changing climatic conditions.

Isometric deformations of planar quadrilaterals with constant index

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zaputryaeva, E S

We consider isometric deformations (motions) of polygons (so-called carpenter's rule problem) in the case of self-intersecting polygons with the additional condition that the index of the polygon is preserved by the motion. We provide general information about isometric deformations of planar polygons and give a complete solution of the carpenter's problem for quadrilaterals. Bibliography: 17 titles.

Programming in Polygon R&D: Explorations with a Spatial Language II

ERIC Educational Resources Information Center

Morey, Jim

2006-01-01

This paper introduces the language associated with a polygon microworld called Polygon R&D, which has the mathematical crispness of Logo and has the discreteness and simplicity of a Turing machine. In this microworld, polygons serve two purposes: as agents (similar to the turtles in Logo), and as data (landmarks in the plane). Programming the…

Random packing of regular polygons and star polygons on a flat two-dimensional surface.

PubMed

Cieśla, Michał; Barbasz, Jakub

2014-08-01

Random packing of unoriented regular polygons and star polygons on a two-dimensional flat continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine the saturated random packing ratio as well as its density autocorrelation function. Additionally, the kinetics of packing growth and available surface function are measured. In general, stars give lower packing ratios than polygons, but when the number of vertexes is large enough, both shapes approach disks and, therefore, properties of their packing reproduce already known results for disks.

Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation.

PubMed

Dione, Ibrahima; Deteix, Jean; Briffard, Thomas; Chamberland, Eric; Doyon, Nicolas

2016-01-01

In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer.

Areal Feature Matching Based on Similarity Using Critic Method

NASA Astrophysics Data System (ADS)

Kim, J.; Yu, K.

2015-10-01

In this paper, we propose an areal feature matching method that can be applied for many-to-many matching, which involves matching a simple entity with an aggregate of several polygons or two aggregates of several polygons with fewer user intervention. To this end, an affine transformation is applied to two datasets by using polygon pairs for which the building name is the same. Then, two datasets are overlaid with intersected polygon pairs that are selected as candidate matching pairs. If many polygons intersect at this time, we calculate the inclusion function between such polygons. When the value is more than 0.4, many of the polygons are aggregated as single polygons by using a convex hull. Finally, the shape similarity is calculated between the candidate pairs according to the linear sum of the weights computed in CRITIC method and the position similarity, shape ratio similarity, and overlap similarity. The candidate pairs for which the value of the shape similarity is more than 0.7 are determined as matching pairs. We applied the method to two geospatial datasets: the digital topographic map and the KAIS map in South Korea. As a result, the visual evaluation showed two polygons that had been well detected by using the proposed method. The statistical evaluation indicates that the proposed method is accurate when using our test dataset with a high F-measure of 0.91.

Tessellating the Sphere with Regular Polygons

ERIC Educational Resources Information Center

Soto-Johnson, Hortensia; Bechthold, Dawn

2004-01-01

Tessellations in the Euclidean plane and regular polygons that tessellate the sphere are reviewed. The regular polygons that can possibly tesellate the sphere are spherical triangles, squares and pentagons.

Calculating the Areas of Polygons with a Smartphone Light Sensor

ERIC Educational Resources Information Center

Kapucu, Serkan; Simsek, Mertkan; Öçal, Mehmet Fatih

2017-01-01

This study explores finding the areas of polygons with a smartphone light sensor. A square and an irregular pentagon were chosen as our polygons. During the activity, the LED light was placed at the vertices of our polygons, and the illuminance values of this LED light were detected by the smartphone light sensor. The smartphone was placed on a…

A physically based catchment partitioning method for hydrological analysis

NASA Astrophysics Data System (ADS)

Menduni, Giovanni; Riboni, Vittoria

2000-07-01

We propose a partitioning method for the topographic surface, which is particularly suitable for hydrological distributed modelling and shallow-landslide distributed modelling. The model provides variable mesh size and appears to be a natural evolution of contour-based digital terrain models. The proposed method allows the drainage network to be derived from the contour lines. The single channels are calculated via a search for the steepest downslope lines. Then, for each network node, the contributing area is determined by means of a search for both steepest upslope and downslope lines. This leads to the basin being partitioned into physically based finite elements delimited by irregular polygons. In particular, the distributed computation of local geomorphological parameters (i.e. aspect, average slope and elevation, main stream length, concentration time, etc.) can be performed easily for each single element. The contributing area system, together with the information on the distribution of geomorphological parameters provide a useful tool for distributed hydrological modelling and simulation of environmental processes such as erosion, sediment transport and shallow landslides.

From SFM to 3d Print: Automated Workflow Addressed to Practitioner Aimed at the Conservation and Restauration

NASA Astrophysics Data System (ADS)

Inzerillo, L.; Di Paola, F.

2017-08-01

In In the last years there has been an increasing use of digital techniques for conservation and restoration purposes. Among these, a very dominant rule is played by the use of digital photogrammetry packages (Agisoft Photoscan, 3D Zephir) which allow to obtain in few steps 3D textured models of real objects. Combined with digital documentation technologies digital fabrication technologies can be employed in a variety of ways to assist in heritage documentation, conservation and dissemination. This paper will give to practitioners an overview on the state of the art available technologies and a feasible workflow for optimizing point cloud and polygon mesh datasets for the purpose of fabrication using 3D printing. The goal is to give an important contribute to confer an automation aspect at the whole processing. We tried to individuate a workflow that should be applicable to several types of cases apart from small precautions. In our experimentation we used a DELTA WASP 2040 printer with PLA easyfil.

Three-dimensional head anthropometric analysis

NASA Astrophysics Data System (ADS)

Enciso, Reyes; Shaw, Alex M.; Neumann, Ulrich; Mah, James

2003-05-01

Currently, two-dimensional photographs are most commonly used to facilitate visualization, assessment and treatment of facial abnormalities in craniofacial care but are subject to errors because of perspective, projection, lack metric and 3-dimensional information. One can find in the literature a variety of methods to generate 3-dimensional facial images such as laser scans, stereo-photogrammetry, infrared imaging and even CT however each of these methods contain inherent limitations and as such no systems are in common clinical use. In this paper we will focus on development of indirect 3-dimensional landmark location and measurement of facial soft-tissue with light-based techniques. In this paper we will statistically evaluate and validate a current three-dimensional image-based face modeling technique using a plaster head model. We will also develop computer graphics tools for indirect anthropometric measurements in a three-dimensional head model (or polygonal mesh) including linear distances currently used in anthropometry. The measurements will be tested against a validated 3-dimensional digitizer (MicroScribe 3DX).

Martian Oceans: Old Debate - New Insights

NASA Technical Reports Server (NTRS)

Oehler, Dorothy Z.; Allen, Carlton C.

2014-01-01

The possibility of an ancient ocean in the northern lowlands of Mars has been discussed for decades [1-14], but the subject remains controversial [15-20]. Among the many unique features of the northern lowlands is the extensive development of "giant polygons" - polygonal landforms that range from 1 to 20 km across. The kilometer-scale size of these features distinguishes them from a variety of smaller polygons (usually < 250 m) on Mars that have been compared to terrestrial analogs such as ice-wedge and desiccation features. However, until recently, geologists were aware of no examples of polygons on Earth comparable in scale to the giant polygons of Mars, so there were no good analogs from which to draw interpretations. That picture has changed with 3D seismic data acquired by the petroleum industry in exploration of offshore basins. The new data reveal kilometer-scale polygonal features in more than 50 offshore basins on Earth]. These features provide a credible analog for the giant polygons of Mars.

Linking of uniform random polygons in confined spaces

NASA Astrophysics Data System (ADS)

Arsuaga, J.; Blackstone, T.; Diao, Y.; Karadayi, E.; Saito, M.

2007-03-01

In this paper, we study the topological entanglement of uniform random polygons in a confined space. We derive the formula for the mean squared linking number of such polygons. For a fixed simple closed curve in the confined space, we rigorously show that the linking probability between this curve and a uniform random polygon of n vertices is at least 1-O\\big(\\frac{1}{\\sqrt{n}}\\big) . Our numerical study also indicates that the linking probability between two uniform random polygons (in a confined space), of m and n vertices respectively, is bounded below by 1-O\\big(\\frac{1}{\\sqrt{mn}}\\big) . In particular, the linking probability between two uniform random polygons, both of n vertices, is bounded below by 1-O\\big(\\frac{1}{n}\\big) .

Grid generation in three dimensions by Poisson equations with control of cell size and skewness at boundary surfaces

NASA Technical Reports Server (NTRS)

Sorenson, R. L.; Steger, J. L.

1983-01-01

An algorithm for generating computational grids about arbitrary three-dimensional bodies is developed. The elliptic partial differential equation (PDE) approach developed by Steger and Sorenson and used in the NASA computer program GRAPE is extended from two to three dimensions. Forcing functions which are found automatically by the algorithm give the user the ability to control mesh cell size and skewness at boundary surfaces. This algorithm, as is typical of PDE grid generators, gives smooth grid lines and spacing in the interior of the grid. The method is applied to a rectilinear wind-tunnel case and to two body shapes in spherical coordinates.

Free stream capturing in fluid conservation law for moving coordinates in three dimensions

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

The free-stream capturing technique for both the finite-volume (FV) and finite-difference (FD) framework is summarized. For an arbitrary motion of the grid, the FV analysis shows that volumes swept by all six surfaces of the cell have to be computed correctly. This means that the free-stream capturing time-metric terms should be calculated not only from a surface vector of a cell at a single time level, but also from a volume swept by the cell surface in space and time. The FV free-stream capturing formulation is applicable to the FD formulation by proper translation from an FV cell to an FD mesh.

An Enriched Shell Element for Delamination Simulation in Composite Laminates

NASA Technical Reports Server (NTRS)

McElroy, Mark

2015-01-01

A formulation is presented for an enriched shell finite element capable of delamination simulation in composite laminates. The element uses an adaptive splitting approach for damage characterization that allows for straightforward low-fidelity model creation and a numerically efficient solution. The Floating Node Method is used in conjunction with the Virtual Crack Closure Technique to predict delamination growth and represent it discretely at an arbitrary ply interface. The enriched element is verified for Mode I delamination simulation using numerical benchmark data. After determining important mesh configuration guidelines for the vicinity of the delamination front in the model, a good correlation was found between the enriched shell element model results and the benchmark data set.

ms 2: A molecular simulation tool for thermodynamic properties, release 3.0

NASA Astrophysics Data System (ADS)

Rutkai, Gábor; Köster, Andreas; Guevara-Carrion, Gabriela; Janzen, Tatjana; Schappals, Michael; Glass, Colin W.; Bernreuther, Martin; Wafai, Amer; Stephan, Simon; Kohns, Maximilian; Reiser, Steffen; Deublein, Stephan; Horsch, Martin; Hasse, Hans; Vrabec, Jadran

2017-12-01

A new version release (3.0) of the molecular simulation tool ms 2 (Deublein et al., 2011; Glass et al. 2014) is presented. Version 3.0 of ms 2 features two additional ensembles, i.e. microcanonical (NVE) and isobaric-isoenthalpic (NpH), various Helmholtz energy derivatives in the NVE ensemble, thermodynamic integration as a method for calculating the chemical potential, the osmotic pressure for calculating the activity of solvents, the six Maxwell-Stefan diffusion coefficients of quaternary mixtures, statistics for sampling hydrogen bonds, smooth-particle mesh Ewald summation as well as the ability to carry out molecular dynamics runs for an arbitrary number of state points in a single program execution.

GPC: General Polygon Clipper library

NASA Astrophysics Data System (ADS)

Murta, Alan

2015-12-01

The University of Manchester GPC library is a flexible and highly robust polygon set operations library for use with C, C#, Delphi, Java, Perl, Python, Haskell, Lua, VB.Net and other applications. It supports difference, intersection, exclusive-or and union clip operations, and polygons may be comprised of multiple disjoint contours. Contour vertices may be given in any order - clockwise or anticlockwise, and contours may be convex, concave or self-intersecting, and may be nested (i.e. polygons may have holes). Output may take the form of either polygon contours or tristrips, and hole and external contours are differentiated in the result.

A digital map of the high center (HC) and low center (LC) polygon boundaries delineated from high resolution LiDAR data for Barrow, Alaska

DOE Data Explorer

Gangodagamage, Chandana; Wullschleger, Stan

2014-07-03

This dataset represent a map of the high center (HC) and low center (LC) polygon boundaries delineated from high resolution LiDAR data for the arctic coastal plain at Barrow, Alaska. The polygon troughs are considered as the surface expression of the ice-wedges. The troughs are in lower elevations than the interior polygon. The trough widths were initially identified from LiDAR data, and the boundary between two polygons assumed to be located along the lowest elevations on trough widths between them.

Center for Automatic Target Recognition Research. Delivery Order 0005: Image Georegistration, Camera Calibration, and Dismount Categorization in Support of DEBU from Layered Sensing

DTIC Science & Technology

2011-07-01

rendering of a subject using 316,691 polygon faces and 161,951 points. The small white dots on the surface of the subject are landmark points. The...Figure 17: CAESAR Data. The leftmost image is a color polygon rendering of a subject using 316,691 polygon faces and 161,951 points. The small white...polygon rendering of a subject using 316,691 polygon faces and 161,951 points. The small white dots on the surface of the subject are landmark points

GRAPE- TWO-DIMENSIONAL GRIDS ABOUT AIRFOILS AND OTHER SHAPES BY THE USE OF POISSON'S EQUATION

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1994-01-01

The ability to treat arbitrary boundary shapes is one of the most desirable characteristics of a method for generating grids, including those about airfoils. In a grid used for computing aerodynamic flow over an airfoil, or any other body shape, the surface of the body is usually treated as an inner boundary and often cannot be easily represented as an analytic function. The GRAPE computer program was developed to incorporate a method for generating two-dimensional finite-difference grids about airfoils and other shapes by the use of the Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including a limited number of sharp corners. The GRAPE program has been developed to be numerically stable and computationally fast. GRAPE can provide the aerodynamic analyst with an efficient and consistent means of grid generation. The GRAPE procedure generates a grid between an inner and an outer boundary by utilizing an iterative procedure to solve the Poisson differential equation subject to geometrical restraints. In this method, the inhomogeneous terms of the equation are automatically chosen such that two important effects are imposed on the grid. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. Along with the iterative solution to Poisson's equation, a technique of coarse-fine sequencing is employed to accelerate numerical convergence. GRAPE program control cards and input data are entered via the NAMELIST feature. Each variable has a default value such that user supplied data is kept to a minimum. Basic input data consists of the boundary specification, mesh point spacings on the boundaries, and mesh line angles at the boundaries. Output consists of a dataset containing the grid data and, if requested, a plot of the generated mesh. The GRAPE program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 135K (octal) of 60 bit words. For plotted output the commercially available DISSPLA graphics software package is required. The GRAPE program was developed in 1980.

Painting with polygons: a procedural watercolor engine.

PubMed

DiVerdi, Stephen; Krishnaswamy, Aravind; Měch, Radomír; Ito, Daichi

2013-05-01

Existing natural media painting simulations have produced high-quality results, but have required powerful compute hardware and have been limited to screen resolutions. Digital artists would like to be able to use watercolor-like painting tools, but at print resolutions and on lower end hardware such as laptops or even slates. We present a procedural algorithm for generating watercolor-like dynamic paint behaviors in a lightweight manner. Our goal is not to exactly duplicate watercolor painting, but to create a range of dynamic behaviors that allow users to achieve a similar style of process and result, while at the same time having a unique character of its own. Our stroke representation is vector based, allowing for rendering at arbitrary resolutions, and our procedural pigment advection algorithm is fast enough to support painting on slate devices. We demonstrate our technique in a commercially available slate application used by professional artists. Finally, we present a detailed analysis of the different vector-rendering technologies available.

Bias correction of bounded location errors in presence-only data

USGS Publications Warehouse

Hefley, Trevor J.; Brost, Brian M.; Hooten, Mevin B.

2017-01-01

Location error occurs when the true location is different than the reported location. Because habitat characteristics at the true location may be different than those at the reported location, ignoring location error may lead to unreliable inference concerning species–habitat relationships.We explain how a transformation known in the spatial statistics literature as a change of support (COS) can be used to correct for location errors when the true locations are points with unknown coordinates contained within arbitrary shaped polygons.We illustrate the flexibility of the COS by modelling the resource selection of Whooping Cranes (Grus americana) using citizen contributed records with locations that were reported with error. We also illustrate the COS with a simulation experiment.In our analysis of Whooping Crane resource selection, we found that location error can result in up to a five-fold change in coefficient estimates. Our simulation study shows that location error can result in coefficient estimates that have the wrong sign, but a COS can efficiently correct for the bias.

Distribution and Degradation State of Soil Organic Carbon Stocks in Ice Wedge Polygons of the Arctic Coastal Plain, Alaska

NASA Astrophysics Data System (ADS)

Jastrow, J. D.; Ping, C. L.; Deck, C. B.; Matamala, R.; Vugteveen, T. W.; Lederhouse, J. S.; Michaelson, G. J.

2016-12-01

Estimates of the amount of organic carbon (C) stored in permafrost-region soils and its susceptibility to mobilization with changing climate are improving but remain high, affecting the ability to reliably predict regional C-climate feedbacks. In lowland permafrost soils, much of the organic matter exists in a poorly degraded state and is often weakly associated with soil minerals due to the cold, wet environment and cryoturbation. Thus, the impacts of warming and permafrost thaw likely will depend, at least initially, on the past history of soil organic matter (SOM) degradation. Ice wedge polygons are ubiquitous, patterned ground features throughout Arctic coastal plain regions and are large enough (5-30 m across) that a better three-dimensional understanding of their C stocks and relative degradation state could improve geospatial upscaling of observational data and contribute benchmarks for constraining model parameters. We investigated the distribution and existing degradation state of SOM to a depth of 2 meters across three polygon types on the Arctic Coastal Plain of Alaska: flat-centered (FCP), low-centered (LCP), and high-centered (HCP) polygons, with each type replicated 3 times. To assess the relative degradation state of SOM, we used particle size fractionation to isolate fibric (coarse) from more degraded (fine) particulate organic matter and separated mineral-associated organic matter into silt- and clay-sized fractions. We found variations in the thickness and quality of surface organic layers for different polygon types. Below the active layer, organic-rich cryoturbated layers were located in the transition zone and fingered down into the upper permafrost. Soil organic C stocks varied across individual polygons and differed among polygon types, with HCPs generally having the largest C stocks. The relative degradation state of SOM also varied spatially and vertically within polygons and differed among polygon types. Our findings suggest that accounting for polygon-scale (wedge to center to wedge) and landscape-scale (polygon type) variations could help reduce the uncertainties in observational estimates of soil C stocks and their degradation state for areas dominated by ice wedge polygons.

Meter-scale thermal contraction crack polygons on the nucleus of comet 67P/Churyumov-Gerasimenko

NASA Astrophysics Data System (ADS)

Auger, A.-T.; Groussin, O.; Jorda, L.; El-Maarry, M. R.; Bouley, S.; Séjourné, A.; Gaskell, R.; Capanna, C.; Davidsson, B.; Marchi, S.; Höfner, S.; Lamy, P. L.; Sierks, H.; Barbieri, C.; Rodrigo, R.; Koschny, D.; Rickman, H.; Keller, H. U.; Agarwal, J.; A'Hearn, M. F.; Barucci, M. A.; Bertaux, J.-L.; Bertini, I.; Cremonese, G.; Da Deppo, V.; Debei, S.; De Cecco, M.; Fornasier, S.; Fulle, M.; Gutiérrez, P. J.; Güttler, C.; Hviid, S.; Ip, W.-H.; Knollenberg, J.; Kramm, J.-R.; Kührt, E.; Küppers, M.; Lara, L. M.; Lazzarin, M.; Lopez Moreno, J. J.; Marzari, F.; Massironi, M.; Michalik, H.; Naletto, G.; Oklay, N.; Pommerol, A.; Sabau, L.; Thomas, N.; Tubiana, C.; Vincent, J.-B.; Wenzel, K.-P.

2018-02-01

We report on the detection and characterization of more than 6300 polygons on the surface of the nucleus of comet 67P/Churyumov-Gerasimenko, using images acquired by the OSIRIS camera onboard Rosetta between August 2014 and March 2015. They are found in consolidated terrains and grouped in localized networks. They are present at all latitudes (from North to South) and longitudes (head, neck, and body), sometimes on pit walls or following lineaments. About 1.5% of the observed surface is covered by polygons. Polygons have an homogeneous size across the nucleus, with 90% of them in the size range 1 - 5 m and a mean size of 3.0 ± 1.4 m. They show different morphologies, depending on the width and depth of their trough. They are found in networks with 3- or 4-crack intersection nodes. The polygons observed on 67P are consistent with thermal contraction crack polygons formed by the diurnal or seasonal temperature variations in a hard (MPa) and consolidated sintered layer of water ice, located a few centimeters below the surface. Our thermal analysis shows an evolution of thermal contraction crack polygons according to the local thermal environment, with more evolved polygons (i.e. deeper and larger troughs) where the temperature and the diurnal and seasonal temperature range are the highest. Thermal contraction crack polygons are young surface morphologies that probably formed after the injection of 67P in the inner solar system, typically 100,000 years ago, and could be as young as a few orbital periods, following the decreasing of its perihelion distance in 1959 from 2.7 to 1.3 a.u. Meter scale thermal contraction crack polygons should be common features on the nucleus of Jupiter family comets.

South Polar Polygons

NASA Technical Reports Server (NTRS)

2004-01-01

4 March 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a spectacular suite of large and small polygons in the south polar region. On Earth, polygons such as these would be indicators of the presence of ground ice. Whether this is true for Mars remains to be determined, but it is interesting to note that these polygons do occur in a region identified by the Mars Odyssey Gamma Ray Spectrometer (GRS) team as a place with possible ground ice. The polygons are in an old impact crater located near 62.9oS, 281.4oW. This 1.5 meter (5 ft.) per pixel view covers an area 3 km (1.9 mi) wide and is illuminated by sunlight from the upper left. To see the smaller set of polygons, the reader must view the full-resolution image (click on picture, above).

Ares Vallis Polygons

NASA Image and Video Library

2002-12-04

The jumble of eroded ridges and mesas seen in this NASA Mars Odyssey image occurs within Ares Vallis, one of the largest catastrophic outflow channels on the planet. Floods raged through this channel, pouring out into the Chryse Basin to the north. Close inspection of the THEMIS image reveals polygonal shapes on the floor of the channel system. Polygonal terrain on Mars is fairly common although the variety of forms and scales of the polygons suggests multiple modes of origin. Those in Ares Vallis resemble giant desiccation polygons that form in soils on Earth when a moist layer at depth drys out. While polygons can form in icy soils (permafrost) and even lava flows, their presence in a channel thought to have been carved by flowing water is at least consistent with a mode of origin that involved liquid water. http://photojournal.jpl.nasa.gov/catalog/PIA04019

Nonlinear regimes on polygonal hydraulic jumps

NASA Astrophysics Data System (ADS)

Rojas, Nicolas

2016-11-01

This work extends previous leading and higher order results on the polygonal hydraulic jump in the framework of inertial lubrication theory. The rotation of steady polygonal jumps is observed in the transition from one wavenumber to the next one, induced by a change in height of an external obstacle near the outer edge. In a previous publication, the study of stationary polygons is considered under the assumption that the reference frame rotates with the polygons when the number of corners change, in order to preserve their orientation. In this research work I provide a Hamiltonian approach and the stability analysis of the nonlinear oscillator that describe the polygonal structures at the jump interface, in addition to a perturbation method that enables to explain, for instance, the diversity of patterns found in experiments. GRASP, Institute of Physics, University of Liege, Belgium.

Small-Scale Polygons and the History of Ground Ice on Mars

NASA Technical Reports Server (NTRS)

Mellon, Michael T.

2000-01-01

This research has laid a foundation for continued study of permafrost polygons on Mars using the models and understanding discussed here. Further study of polygonal patterns on Mars is proceeding (under new funding) which is expected to reveal more results about the origin of observed martian polygons and what information they contain regarding the recent history of tile martian climate and of water ice on Mars.

Surface Aesthetics and Analysis.

PubMed

Çakır, Barış; Öreroğlu, Ali Rıza; Daniel, Rollin K

2016-01-01

Surface aesthetics of an attractive nose result from certain lines, shadows, and highlights with specific proportions and breakpoints. Analysis emphasizes geometric polygons as aesthetic subunits. Evaluation of the complete nasal surface aesthetics is achieved using geometric polygons to define the existing deformity and aesthetic goals. The relationship between the dome triangles, interdomal triangle, facet polygons, and infralobular polygon are integrated to form the "diamond shape" light reflection on the nasal tip. The principles of geometric polygons allow the surgeon to analyze the deformities of the nose, define an operative plan to achieve specific goals, and select the appropriate operative technique. Copyright © 2016 Elsevier Inc. All rights reserved.

Sex differences in mental rotation with polygons of different complexity: Do men utilize holistic processes whereas women prefer piecemeal ones?

PubMed

Heil, Martin; Jansen-Osmann, Petra

2008-05-01

Sex differences in mental rotation were investigated as a function of stimulus complexity with a sample size of N = 72. Replicating earlier findings with polygons, mental rotation was faster for males than for females, and reaction time increased with more complex polygons. Additionally, sex differences increased for complex polygons. Most importantly, however, mental rotation speed decreased with increasing complexity for women but did not change for men. Thus, the sex effects reflect a difference in strategy, with women mentally rotating the polygons in an analytic, piecemeal fashion and men using a holistic mode of mental rotation.

Surface and Active Layer Pore Water Chemistry from Ice Wedge Polygons, Barrow, Alaska, 2013-2014

DOE Data Explorer

David E. Graham; Baohua Gu; Elizabeth M. Herndon; Stan D. Wullschleger; Ziming Yang; Liyuan Liang

2016-11-10

This data set reports the results of spatial surveys of aqueous geochemistry conducted at Intensive Site 1 of the Barrow Environmental Observatory in 2013 and 2014 (Herndon et al., 2015). Surface water and soil pore water samples were collected from multiple depths within the tundra active layer of different microtopographic features (troughs, ridges, center) of a low-centered polygon (area A), high-centered polygon (area B), flat-centered polygon (area C), and transitional polygon (area D). Reported analytes include dissolved organic and inorganic carbon, dissolved carbon dioxide and methane, major inorganic anions, and major and minor cations.

Hybrid computational phantoms representing the reference adult male and adult female: construction and applications for retrospective dosimetry.

PubMed

Hurtado, Jorge L; Lee, Choonsik; Lodwick, Daniel; Goede, Timothy; Williams, Jonathan L; Bolch, Wesley E

2012-03-01

Currently, two classes of computational phantoms have been developed for dosimetry calculation: (1) stylized (or mathematical) and (2) voxel (or tomographic) phantoms describing human anatomy through mathematical surface equations and 3D voxel matrices, respectively. Mathematical surface equations in stylized phantoms are flexible, but the resulting anatomy is not as realistic. Voxel phantoms display far better anatomical realism, but they are limited in terms of their ability to alter organ shape, position, and depth, as well as body posture. A new class of computational phantoms called hybrid phantoms takes advantage of the best features of stylized and voxel phantoms-flexibility and anatomical realism, respectively. In the current study, hybrid computational phantoms representing the adult male and female reference anatomy and anthropometry are presented. These phantoms serve as the starting framework for creating patient or worker sculpted whole-body phantoms for retrospective dose reconstruction. Contours of major organs and tissues were converted or segmented from computed tomography images of a 36-y-old Korean volunteer and a 25-y-old U.S. female patient, respectively, with supplemental high-resolution CT images of the cranium. Polygon mesh models for the major organs and tissues were reconstructed and imported into Rhinoceros™ for non-uniform rational B-spline (NURBS) surface modeling. The resulting NURBS/polygon mesh models representing body contour and internal anatomy were matched to anthropometric data and reference organ mass data provided by Centers for Disease Control and Prevention and International Commission on Radiation Protection, respectively. Finally, two hybrid adult male and female phantoms were completed where a total of eight anthropometric data categories were matched to standard values within 4% and organ volumes matched to ICRP data within 1% with the exception of total skin. The hybrid phantoms were voxelized from the NURBS phantoms at resolutions of 0.158 × 0.158 × 0.158 cm and 0.126 × 0.126 × 0.126 cm for the male and female, respectively. To highlight the flexibility of the hybrid phantoms, graphical displays are given of (1) underweight and overweight adult male phantoms, (2) a sitting position for the adult female phantom, and (3) extraction and higher-resolution voxelization of the small intestine for localized dosimetry of mucosal and stem cell layers. These phantoms are used to model radioactively contaminated individuals and to then assess time-dependent detector count rate thresholds corresponding to 50, 250, and 500 mSv effective dose, as might be needed during in-field radiological triage by first responders or first receivers.

Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence

NASA Technical Reports Server (NTRS)

Jameson, Antony

1994-01-01

The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.

Discrete crack growth analysis methodology for through cracks in pressurized fuselage structures

NASA Technical Reports Server (NTRS)

Potyondy, David O.; Wawrzynek, Paul A.; Ingraffea, Anthony R.

1994-01-01

A methodology for simulating the growth of long through cracks in the skin of pressurized aircraft fuselage structures is described. Crack trajectories are allowed to be arbitrary and are computed as part of the simulation. The interaction between the mechanical loads acting on the superstructure and the local structural response near the crack tips is accounted for by employing a hierarchical modeling strategy. The structural response for each cracked configuration is obtained using a geometrically nonlinear shell finite element analysis procedure. Four stress intensity factors, two for membrane behavior and two for bending using Kirchhoff plate theory, are computed using an extension of the modified crack closure integral method. Crack trajectories are determined by applying the maximum tangential stress criterion. Crack growth results in localized mesh deletion, and the deletion regions are remeshed automatically using a newly developed all-quadrilateral meshing algorithm. The effectiveness of the methodology and its applicability to performing practical analyses of realistic structures is demonstrated by simulating curvilinear crack growth in a fuselage panel that is representative of a typical narrow-body aircraft. The predicted crack trajectory and fatigue life compare well with measurements of these same quantities from a full-scale pressurized panel test.

Field Model: An Object-Oriented Data Model for Fields

NASA Technical Reports Server (NTRS)

Moran, Patrick J.

2001-01-01

We present an extensible, object-oriented data model designed for field data entitled Field Model (FM). FM objects can represent a wide variety of fields, including fields of arbitrary dimension and node type. FM can also handle time-series data. FM achieves generality through carefully selected topological primitives and through an implementation that leverages the potential of templated C++. FM supports fields where the nodes values are paired with any cell type. Thus FM can represent data where the field nodes are paired with the vertices ("vertex-centered" data), fields where the nodes are paired with the D-dimensional cells in R(sup D) (often called "cell-centered" data), as well as fields where nodes are paired with edges or other cell types. FM is designed to effectively handle very large data sets; in particular FM employs a demand-driven evaluation strategy that works especially well with large field data. Finally, the interfaces developed for FM have the potential to effectively abstract field data based on adaptive meshes. We present initial results with a triangular adaptive grid in R(sup 2) and discuss how the same design abstractions would work equally well with other adaptive-grid variations, including meshes in R(sup 3).

A resistive mesh phantom for assessing the performance of EIT systems.

PubMed

Gagnon, Hervé; Cousineau, Martin; Adler, Andy; Hartinger, Alzbeta E

2010-09-01

Assessing the performance of electrical impedance tomography (EIT) systems usually requires a phantom for validation, calibration, or comparison purposes. This paper describes a resistive mesh phantom to assess the performance of EIT systems while taking into account cabling stray effects similar to in vivo conditions. This phantom is built with 340 precision resistors on a printed circuit board representing a 2-D circular homogeneous medium. It also integrates equivalent electrical models of the Ag/AgCl electrode impedances. The parameters of the electrode models were fitted from impedance curves measured with an impedance analyzer. The technique used to build the phantom is general and applicable to phantoms of arbitrary shape and conductivity distribution. We describe three performance indicators that can be measured with our phantom for every measurement of an EIT data frame: SNR, accuracy, and modeling accuracy. These performance indicators were evaluated on our EIT system under different frame rates and applied current intensities. The performance indicators are dependent on frame rate, operating frequency, applied current intensity, measurement strategy, and intermodulation distortion when performing simultaneous measurements at several frequencies. These parameter values should, therefore, always be specified when reporting performance indicators to better appreciate their significance.

A model for the origin of Martian polygonal terrain

NASA Technical Reports Server (NTRS)

Mcgill, G. E.

1993-01-01

Extensive areas of the Martian northern plains in Utopia and Acidalia Planitiae are characterized by 'polygonal terrain.' Polygonal terrain consists of material cut by complex troughs defining a pattern resembling mudcracks, columnar joints, or frost-wedge polygons on the Earth. However, the Martian polygons are orders of magnitude larger than these potential Earth analogs, leading to severe mechanical difficulties for genetic models based on simple analogy arguments. Stratigraphic studies show that the polygonally fractured material in Utopia Planitia was deposited on a land surface with significant topography, including scattered knobs and mesas, fragments of ancient crater rims, and fresh younger craters. Sediments or volcanics deposited over topographically irregular surfaces can experience differential compaction producing drape folds. Bending stresses due to these drape folds would be superposed on the pervasive tensile stresses due to desiccation or cooling, such that the probability of fracturing is enhanced above buried topographic highs and suppressed above buried topographic lows. Thus it was proposed that the scale of the Martian polygons is controlled by the spacing of topographic highs on the buried surface rather than by the physics of the shrinkage process.

A Highly Parallelized Special-Purpose Computer for Many-Body Simulations with an Arbitrary Central Force: MD-GRAPE

NASA Astrophysics Data System (ADS)

Fukushige, Toshiyuki; Taiji, Makoto; Makino, Junichiro; Ebisuzaki, Toshikazu; Sugimoto, Daiichiro

1996-09-01

We have developed a parallel, pipelined special-purpose computer for N-body simulations, MD-GRAPE (for "GRAvity PipE"). In gravitational N- body simulations, almost all computing time is spent on the calculation of interactions between particles. GRAPE is specialized hardware to calculate these interactions. It is used with a general-purpose front-end computer that performs all calculations other than the force calculation. MD-GRAPE is the first parallel GRAPE that can calculate an arbitrary central force. A force different from a pure 1/r potential is necessary for N-body simulations with periodic boundary conditions using the Ewald or particle-particle/particle-mesh (P^3^M) method. MD-GRAPE accelerates the calculation of particle-particle force for these algorithms. An MD- GRAPE board has four MD chips and its peak performance is 4.2 GFLOPS. On an MD-GRAPE board, a cosmological N-body simulation takes 6O0(N/10^6^)^3/2^ s per step for the Ewald method, where N is the number of particles, and would take 24O(N/10^6^) s per step for the P^3^M method, in a uniform distribution of particles.

Fluid-Structure Interaction Simulation of Prosthetic Aortic Valves: Comparison between Immersed Boundary and Arbitrary Lagrangian-Eulerian Techniques for the Mesh Representation

PubMed Central

Iannaccone, Francesco; Degroote, Joris; Vierendeels, Jan; Segers, Patrick

2016-01-01

In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results. PMID:27128798

The Application of COMSOL Multiphysics Package on the Modelling of Complex 3-D Lithospheric Electrical Resistivity Structures - A Case Study from the Proterozoic Orogenic belt within the North China Craton

NASA Astrophysics Data System (ADS)

Guo, L.; Yin, Y.; Deng, M.; Guo, L.; Yan, J.

2017-12-01

At present, most magnetotelluric (MT) forward modelling and inversion codes are based on finite difference method. But its structured mesh gridding cannot be well adapted for the conditions with arbitrary topography or complex tectonic structures. By contrast, the finite element method is more accurate in calculating complex and irregular 3-D region and has lower requirement of function smoothness. However, the complexity of mesh gridding and limitation of computer capacity has been affecting its application. COMSOL Multiphysics is a cross-platform finite element analysis, solver and multiphysics full-coupling simulation software. It achieves highly accurate numerical simulations with high computational performance and outstanding multi-field bi-directional coupling analysis capability. In addition, its AC/DC and RF module can be used to easily calculate the electromagnetic responses of complex geological structures. Using the adaptive unstructured grid, the calculation is much faster. In order to improve the discretization technique of computing area, we use the combination of Matlab and COMSOL Multiphysics to establish a general procedure for calculating the MT responses for arbitrary resistivity models. The calculated responses include the surface electric and magnetic field components, impedance components, magnetic transfer functions and phase tensors. Then, the reliability of this procedure is certificated by 1-D, 2-D and 3-D and anisotropic forward modeling tests. Finally, we establish the 3-D lithospheric resistivity model for the Proterozoic Wutai-Hengshan Mts. within the North China Craton by fitting the real MT data collected there. The reliability of the model is also verified by induced vectors and phase tensors. Our model shows more details and better resolution, compared with the previously published 3-D model based on the finite difference method. In conclusion, COMSOL Multiphysics package is suitable for modeling the 3-D lithospheric resistivity structures under complex tectonic deformation backgrounds, which could be a good complement to the existing finite-difference inversion algorithms.

Planetary science: Pluto's polygons explained

NASA Astrophysics Data System (ADS)

Dombard, Andrew J.; O'Hara, Sean

2016-06-01

The Sputnik Planum basin of Pluto contains a sheet of nitrogen ice, the surface of which is divided into irregular polygons tens of kilometres across. Two studies reveal that vigorous convection causes these polygons. See Letters p.79 & 82

Lineament and polygon patterns on Europa

NASA Technical Reports Server (NTRS)

Pieri, D. C.

1981-01-01

A classification scheme is presented for the lineaments and associated polygonal patterns observed on the surface of Europa, and the frequency distribution of the polygons is discussed in terms of the stress-relief fracturing of the surface. The lineaments are divided on the basis of albedo, morphology, orientation and characteristic geometry into eight groups based on Voyager 2 images taken at a best resolution of 4 km. The lineaments in turn define a system of polygons varying in size from small reticulate patterns the limit of resolution to 1,000,000 sq km individuals. Preliminary analysis of polygon side frequency distributions reveals a class of polygons with statistics similar to those found in complex terrestrial terrains, particularly in areas of well-oriented stresses, a class with similar statistics around the antijovian point, and a class with a distribution similar to those seen in terrestrial tensional fracture patterns. Speculations concerning the processes giving rise to the lineament patterns are presented.

Small-scale martian polygonal terrain: Implications for liquid surface water

USGS Publications Warehouse

Seibert, N.M.; Kargel, J.S.

2001-01-01

Images from the Mars Orbiter Camera (MOC) through August 1999 were analyzed for the global distribution of small-scale polygonal terrain not clearly resolved in Viking Orbiter imagery. With very few exceptions, small-scale polygonal terrain occurs at middle to high latitudes of the northern and southern hemisphere in Hesperian-age geologic units. The largest concentration of this terrain occurs in the Utopia basin in close association with scalloped depressions (interpreted as thermokarst) and appears to represent an Amazonia event. The morphology and occurence of small polygonal terrain suggest they are either mud desiccation cracks or ice-wedge polygons. Because the small-scale polygons in Utopia and Argyre Planitiae are associated with other cold-climate permafrost or glacial features, an ice-wedge model is preferred for these areas. Both cracking mechanisms work most effectively in water- or ice-rich finegrained material and may imply the seasonal or episodic existence of liquid water at the surface.

BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices

NASA Astrophysics Data System (ADS)

Janse van Rensburg, E. J.; Rechnitzer, A.

2011-04-01

In this paper, the elementary moves of the BFACF-algorithm (Aragão de Carvalho and Caracciolo 1983 Phys. Rev. B 27 1635-45, Aragão de Carvalho and Caracciolo 1983 Nucl. Phys. B 215 209-48, Berg and Foester 1981 Phys. Lett. B 106 323-6) for lattice polygons are generalized to elementary moves of BFACF-style algorithms for lattice polygons in the body-centered (BCC) and face-centered (FCC) cubic lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC lattices and so expand a similar result for the cubic lattice (see Janse van Rensburg and Whittington (1991 J. Phys. A: Math. Gen. 24 5553-67)). Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC lattices.

The prediction of leaf area index from forest polygons decomposed through the integration of remote sensing, GIS, UNIX, and C

NASA Astrophysics Data System (ADS)

Wulder, M. A.

1998-03-01

Forest stand data are normally stored in a geographic information system (GIS) on the basis of areas of similar species combinations. Polygons are created based upon species assemblages and given labels relating the percentage of areal coverage by each significant species type within the specified area. As a result, estimation of leaf area index (LAI) from the digital numbers found within GIS-stored polygons lack accuracy as the predictive equations for LAI are normally developed for individual species, not species assemblages. A Landsat TM image was acquired to enable a classification which allows for the decomposition of forest-stand polygons into greater species detail. Knowledge of the actual internal composition of the stand polygons provides for computation of LAI values based upon the appropriate predictive equation resulting in higher accuracy of these estimates. To accomplish this goal it was necessary to extract, for each cover type in each polygon, descriptive values to represent the digital numbers located in that portion of the polygon. The classified image dictates the species composition of the various portions of the polygon and within these areas the raster pixel values are tabulated and averaged. Due to a lack of existing software tools to assess the raster values occurring within GIS polygons a combination of remote sensing, GIS, UNIX, and specifically coded C programs were necessary. Such tools are frequently used by the spatial analyst and indicate the complexity of what may appear to be a straight-forward spatial analysis problem.

Numerical investigations of microtopographic influence on the near surface thermal regime and thermokarst development in ice wedge polygons

NASA Astrophysics Data System (ADS)

Abolt, C.; Young, M.; Atchley, A. L.; Harp, D. R.

2017-12-01

Permafrost degradation in ice wedge polygon terrain has accelerated in the last three decades, resulting in drastic changes to tundra hydrology which may impact rates of soil organic carbon mobilization. The goal of this research is to determine to what extent the near surface thermal regime, and hence the vulnerability of the upper permafrost, may be controlled by surface topography in ice wedge polygons. The central hypothesis is that energy is preferentially transferred into the polygon subsurface in summer at low, wet zones (such as low-centered polygon centers and troughs), then released to the atmosphere in winter through elevated zones (such as rims) that are less insulated by snowpack. Disturbance to the approximate balance between these seasonal energy fluxes may help explain the onset and development of thermokarst. In this work, we present a numerical model of thermal hydrology in a low-centered polygon near Prudhoe Bay, Alaska, constructed within the Advanced Terrestrial Simulator, a state of the art code that couples a meteorologically driven surface energy balance with equations for surface and subsurface conservation of mass and energy. The model is calibrated against a year of daily ground temperature observations throughout the polygon and used to quantify meter-scale zonation in the subsurface thermal budget. The amount of relief in the rims and the trough of the simulated polygon is then manipulated, and simulations are repeated including a pulse of one warm year, to explore the extent to which topography may influence the response of permafrost to increased air temperatures. Results suggest that nearly 25% of energy entering the ground at the polygon center during summer may be released back to the atmosphere through the rims in winter, producing a modest effect on active layer thickness throughout the polygon. Simulated polygons with deeper, wetter troughs have only marginally thicker active layers than other polygons in average years, but are the most vulnerable to additional permafrost degradation during warm summers. The results confirm and expand upon current conceptual understanding of positive feedbacks during thermokarst development, and are compatible with historical observations indicating that ice wedge degradation tends to occur in discrete pulses, rather than as a gradual process.

Supramolecule-to-supramolecule transformations of coordination-driven self-assembled polygons.

PubMed

Zhao, Liang; Northrop, Brian H; Stang, Peter J

2008-09-10

Two types of supramolecular transformations, wherein a self-assembled Pt(II)-pyridyl metal-organic polygon is controllably converted into an alternative polygon, have been achieved through the reaction between cobalt carbonyl and the acetylene moiety of a dipyridyl donor ligand. A [6 + 6] hexagon is transformed into two [3 + 3] hexagons, and a triangle-square mixture is converted into [2 + 2] rhomboids. 1H and 31P NMR spectra are used to track the transformation process and evaluate the yield of new self-assembled polygons. Such transformed species are identified by electrospray ionization (ESI) mass spectrometry. This new kind of supramolecule-to-supramolecule transformations provides a viable means for constructing, and then converting, new self-assembled polygons.

Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

NASA Technical Reports Server (NTRS)

Vadyak, Joseph; Shrewsbury, George E.; Narramore, Jim C.; Montry, Gary; Holst, Terry; Kwak, Dochan (Technical Monitor)

1995-01-01

The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time, load balancing, and scalability will be provided.

Dynamic Rupture Benchmarking of the ADER-DG Method

NASA Astrophysics Data System (ADS)

Gabriel, Alice; Pelties, Christian

2013-04-01

We will verify the arbitrary high-order derivative Discontinuous Galerkin (ADER-DG) method in various test cases of the 'SCEC/USGS Dynamic Earthquake Rupture Code Verification Exercise' benchmark suite (Harris et al. 2009). The ADER-DG scheme is able to solve the spontaneous rupture problem with high-order accuracy in space and time on three-dimensional unstructured tetrahedral meshes. Strong mesh coarsening or refinement at areas of interest can be applied to keep the computational costs feasible. Moreover, the method does not generate spurious high-frequency contributions in the slip rate spectra and therefore does not require any artificial damping as demonstrated in previous presentations and publications (Pelties et al. 2010 and 2012). We will show that the mentioned features hold also for more advanced setups as e.g. a branching fault system, heterogeneous background stresses and bimaterial faults. The advanced geometrical flexibility combined with an enhanced accuracy will make the ADER-DG method a useful tool to study earthquake dynamics on complex fault systems in realistic rheologies. References: Harris, R.A., M. Barall, R. Archuleta, B. Aagaard, J.-P. Ampuero, H. Bhat, V. Cruz-Atienza, L. Dalguer, P. Dawson, S. Day, B. Duan, E. Dunham, G. Ely, Y. Kaneko, Y. Kase, N. Lapusta, Y. Liu, S. Ma, D. Oglesby, K. Olsen, A. Pitarka, S. Song, and E. Templeton, The SCEC/USGS Dynamic Earthquake Rupture Code Verification Exercise, Seismological Research Letters, vol. 80, no. 1, pages 119-126, 2009 Pelties, C., J. de la Puente, and M. Kaeser, Dynamic Rupture Modeling in Three Dimensions on Unstructured Meshes Using a Discontinuous Galerkin Method, AGU 2010 Fall Meeting, abstract #S21C-2068 Pelties, C., J. de la Puente, J.-P. Ampuero, G. Brietzke, and M. Kaeser, Three-Dimensional Dynamic Rupture Simulation with a High-order Discontinuous Galerkin Method on Unstructured Tetrahedral Meshes, JGR. - Solid Earth, VOL. 117, B02309, 2012

Dynamic Rupture Benchmarking of the ADER-DG Method

NASA Astrophysics Data System (ADS)

Pelties, C.; Gabriel, A.

2012-12-01

We will verify the arbitrary high-order derivative Discontinuous Galerkin (ADER-DG) method in various test cases of the 'SCEC/USGS Dynamic Earthquake Rupture Code Verification Exercise' benchmark suite (Harris et al. 2009). The ADER-DG scheme is able to solve the spontaneous rupture problem with high-order accuracy in space and time on three-dimensional unstructured tetrahedral meshes. Strong mesh coarsening or refinement at areas of interest can be applied to keep the computational costs feasible. Moreover, the method does not generate spurious high-frequency contributions in the slip rate spectra and therefore does not require any artificial damping as demonstrated in previous presentations and publications (Pelties et al. 2010 and 2012). We will show that the mentioned features hold also for more advanced setups as e.g. a branching fault system, heterogeneous background stresses and bimaterial faults. The advanced geometrical flexibility combined with an enhanced accuracy will make the ADER-DG method a useful tool to study earthquake dynamics on complex fault systems in realistic rheologies. References: Harris, R.A., M. Barall, R. Archuleta, B. Aagaard, J.-P. Ampuero, H. Bhat, V. Cruz-Atienza, L. Dalguer, P. Dawson, S. Day, B. Duan, E. Dunham, G. Ely, Y. Kaneko, Y. Kase, N. Lapusta, Y. Liu, S. Ma, D. Oglesby, K. Olsen, A. Pitarka, S. Song, and E. Templeton, The SCEC/USGS Dynamic Earthquake Rupture Code Verification Exercise, Seismological Research Letters, vol. 80, no. 1, pages 119-126, 2009 Pelties, C., J. de la Puente, and M. Kaeser, Dynamic Rupture Modeling in Three Dimensions on Unstructured Meshes Using a Discontinuous Galerkin Method, AGU 2010 Fall Meeting, abstract #S21C-2068 Pelties, C., J. de la Puente, J.-P. Ampuero, G. Brietzke, and M. Kaeser, Three-Dimensional Dynamic Rupture Simulation with a High-order Discontinuous Galerkin Method on Unstructured Tetrahedral Meshes, JGR. - Solid Earth, VOL. 117, B02309, 2012

The geometrical precision of virtual bone models derived from clinical computed tomography data for forensic anthropology.

PubMed

Colman, Kerri L; Dobbe, Johannes G G; Stull, Kyra E; Ruijter, Jan M; Oostra, Roelof-Jan; van Rijn, Rick R; van der Merwe, Alie E; de Boer, Hans H; Streekstra, Geert J

2017-07-01

Almost all European countries lack contemporary skeletal collections for the development and validation of forensic anthropological methods. Furthermore, legal, ethical and practical considerations hinder the development of skeletal collections. A virtual skeletal database derived from clinical computed tomography (CT) scans provides a potential solution. However, clinical CT scans are typically generated with varying settings. This study investigates the effects of image segmentation and varying imaging conditions on the precision of virtual modelled pelves. An adult human cadaver was scanned using varying imaging conditions, such as scanner type and standard patient scanning protocol, slice thickness and exposure level. The pelvis was segmented from the various CT images resulting in virtually modelled pelves. The precision of the virtual modelling was determined per polygon mesh point. The fraction of mesh points resulting in point-to-point distance variations of 2 mm or less (95% confidence interval (CI)) was reported. Colour mapping was used to visualise modelling variability. At almost all (>97%) locations across the pelvis, the point-to-point distance variation is less than 2 mm (CI = 95%). In >91% of the locations, the point-to-point distance variation was less than 1 mm (CI = 95%). This indicates that the geometric variability of the virtual pelvis as a result of segmentation and imaging conditions rarely exceeds the generally accepted linear error of 2 mm. Colour mapping shows that areas with large variability are predominantly joint surfaces. Therefore, results indicate that segmented bone elements from patient-derived CT scans are a sufficiently precise source for creating a virtual skeletal database.

Multi-dimensional multi-species modeling of transient electrodeposition in LIGA microfabrication.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Evans, Gregory Herbert; Chen, Ken Shuang

2004-06-01

This report documents the efforts and accomplishments of the LIGA electrodeposition modeling project which was headed by the ASCI Materials and Physics Modeling Program. A multi-dimensional framework based on GOMA was developed for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electro-chemical reactions on moving deposition surfaces. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation that explicitly describes the electrolyte potential was derived. The set of coupled, nonlinear equations governing species transport, electric potential, velocity, hydrodynamic pressure, and mesh motion were solved in GOMA, using themore » finite-element method and a fully-coupled implicit solution scheme via Newton's method. By treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and by repeatedly performing re-meshing with CUBIT and re-mapping with MAPVAR, the moving deposition surfaces were tracked explicitly from start of deposition until the trenches were filled with metal, thus enabling the computation of local current densities that potentially influence the microstructure and frictional/mechanical properties of the deposit. The multi-dimensional, multi-species, transient computational framework was demonstrated in case studies of two-dimensional nickel electrodeposition in single and multiple trenches, without and with bath stirring or forced flow. Effects of buoyancy-induced convection on deposition were also investigated. To further illustrate its utility, the framework was employed to simulate deposition in microscreen-based LIGA molds. Lastly, future needs for modeling LIGA electrodeposition are discussed.« less

Water Impact Test and Simulation of a Composite Energy Absorbing Fuselage Section

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Jackson, Karen E.; Sparks, Chad; Sareen, Ashish

2003-01-01

In March 2002, a 25-ft/s vertical drop test of a composite fuselage section was conducted onto water. The purpose of the test was to obtain experimental data characterizing the structural response of the fuselage section during water impact for comparison with two previous drop tests that were performed onto a rigid surface and soft soil. For the drop test, the fuselage section was configured with ten 100-lb. lead masses, five per side, that were attached to seat rails mounted to the floor. The fuselage section was raised to a height of 10-ft. and dropped vertically into a 15-ft. diameter pool filled to a depth of 3.5-ft. with water. Approximately 70 channels of data were collected during the drop test at a 10-kHz sampling rate. The test data were used to validate crash simulations of the water impact that were developed using the nonlinear, explicit transient dynamic codes, MSC.Dytran and LS-DYNA. The fuselage structure was modeled using shell and solid elements with a Lagrangian mesh, and the water was modeled with both Eulerian and Lagrangian techniques. The fluid-structure interactions were executed using the fast general coupling in MSC.Dytran and the Arbitrary Lagrange-Euler (ALE) coupling in LS-DYNA. Additionally, the smooth particle hydrodynamics (SPH) meshless Lagrangian technique was used in LS-DYNA to represent the fluid. The simulation results were correlated with the test data to validate the modeling approach. Additional simulation studies were performed to determine how changes in mesh density, mesh uniformity, fluid viscosity, and failure strain influence the test-analysis correlation.

ATHENA 3D: A finite element code for ultrasonic wave propagation

NASA Astrophysics Data System (ADS)

Rose, C.; Rupin, F.; Fouquet, T.; Chassignole, B.

2014-04-01

The understanding of wave propagation phenomena requires use of robust numerical models. 3D finite element (FE) models are generally prohibitively time consuming. However, advances in computing processor speed and memory allow them to be more and more competitive. In this context, EDF R&D developed the 3D version of the well-validated FE code ATHENA2D. The code is dedicated to the simulation of wave propagation in all kinds of elastic media and in particular, heterogeneous and anisotropic materials like welds. It is based on solving elastodynamic equations in the calculation zone expressed in terms of stress and particle velocities. The particularity of the code relies on the fact that the discretization of the calculation domain uses a Cartesian regular 3D mesh while the defect of complex geometry can be described using a separate (2D) mesh using the fictitious domains method. This allows combining the rapidity of regular meshes computation with the capability of modelling arbitrary shaped defects. Furthermore, the calculation domain is discretized with a quasi-explicit time evolution scheme. Thereby only local linear systems of small size have to be solved. The final step to reduce the computation time relies on the fact that ATHENA3D has been parallelized and adapted to the use of HPC resources. In this paper, the validation of the 3D FE model is discussed. A cross-validation of ATHENA 3D and CIVA is proposed for several inspection configurations. The performances in terms of calculation time are also presented in the cases of both local computer and computation cluster use.

Recent work on material interface reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mosso, S.J.; Swartz, B.K.

1997-12-31

For the last 15 years, many Eulerian codes have relied on a series of piecewise linear interface reconstruction algorithms developed by David Youngs. In a typical Youngs` method, the material interfaces were reconstructed based upon nearly cell values of volume fractions of each material. The interfaces were locally represented by linear segments in two dimensions and by pieces of planes in three dimensions. The first step in such reconstruction was to locally approximate an interface normal. In Youngs` 3D method, a local gradient of a cell-volume-fraction function was estimated and taken to be the local interface normal. A linear interfacemore » was moved perpendicular to the now known normal until the mass behind it matched the material volume fraction for the cell in question. But for distorted or nonorthogonal meshes, the gradient normal estimate didn`t accurately match that of linear material interfaces. Moreover, curved material interfaces were also poorly represented. The authors will present some recent work in the computation of more accurate interface normals, without necessarily increasing stencil size. Their estimate of the normal is made using an iterative process that, given mass fractions for nearby cells of known but arbitrary variable density, converges in 3 or 4 passes in practice (and quadratically--like Newton`s method--in principle). The method reproduces a linear interface in both orthogonal and nonorthogonal meshes. The local linear approximation is generally 2nd-order accurate, with a 1st-order accurate normal for curved interfaces in both two and three dimensional polyhedral meshes. Recent work demonstrating the interface reconstruction for curved surfaces will /be discussed.« less

MHD Simulation of the HIT-SI Experiment

NASA Astrophysics Data System (ADS)

Marklin, George

2003-10-01

The Helicity Injected Torus (HIT) experiment at the University of Washington has been reconfigured into a high beta spheromak with steady state AC current drive [1]. Helicity is injected by two half torus Reversed Field Pinches (RFP's) connected to the ends of the cylindrically symmetric flux conserver, rotated by 90 degrees from each other. The RFP's are driven with sinusoidally varying voltage and flux. Each side has its voltage and flux in phase, but is 90 degrees out of phase from the other side. The helicity injection rate, which is proportional to the voltage times the flux, goes like sin(wt)^2 on one side and cos(wt)^2 on the other, making the total injection rate constant in time. The complex multiply connected 3-dimensional geometry of this device make it difficult to simulate with existing codes that typically use a structured mesh. This poster will describe a new 3D MHD simulation code and a new 3D Taylor state code which both use an unstructured finite element mesh. The mesh is generated from a CAD-like description of an arbitrary arrangement of 3D geometrical objects. Taylor states in the HIT-SI geometry will be shown for different combinations of fluxes in the two injectors. MHD simulation results will be shown starting from a Taylor state with uniform density and temperature and continuing through several cycles of time dependent helicity injection. Field line tracing plots will show the quality of the flux surfaces at various stages in the injection cycle. [1] T. R. Jarboe, Fusion Technology, vol. 36, p. 85, 1999

Polygonal deformation bands in sandstone

NASA Astrophysics Data System (ADS)

Antonellini, Marco; Nella Mollema, Pauline

2017-04-01

We report for the first time the occurrence of polygonal faults in sandstone, which is compelling given that layer-bound polygonal fault systems have been observed so far only in fine-grained sediments such as clay and chalk. The polygonal faults are dm-wide zones of shear deformation bands that developed under shallow burial conditions in the lower portion of the Jurassic Entrada Fm (Utah, USA). The edges of the polygons are 1 to 5 meters long. The shear deformation bands are organized as conjugate faults along each edge of the polygon and form characteristic horst-like structures. The individual deformation bands have slip magnitudes ranging from a few mm to 1.5 cm; the cumulative average slip magnitude in a zone is up to 10 cm. The deformation bands heaves, in aggregate form, accommodate a small isotropic horizontal extension (strain < 0.005). The individual shear deformation bands show abutting T-junctions, veering, curving, and merging where they mechanically interact. Crosscutting relationships are rare. The interactions of the deformation bands are similar to those of mode I opening fractures. Density inversion, that takes place where under-compacted and over-pressurized layers (Carmel Fm) lay below normally compacted sediments (Entrada Sandstone), may be an important process for polygonal deformation bands formation. The gravitational sliding and soft sediment structures typically observed within the Carmel Fm support this hypothesis. Soft sediment deformation may induce polygonal faulting in the section of the Entrada Sandstone just above the Carmel Fm. The permeability of the polygonal deformation bands is approximately 10-14 to 10-13 m2, which is less than the permeability of the host, Entrada Sandstone (range 10-12 to 10-11 m2). The documented fault networks have important implications for evaluating the geometry of km-scale polygonal fault systems in the subsurface, top seal integrity, as well as constraining paleo-tectonic stress regimes.

Water polygons in high-resolution protein crystal structures.

PubMed

Lee, Jonas; Kim, Sung-Hou

2009-07-01

We have analyzed the interstitial water (ISW) structures in 1500 protein crystal structures deposited in the Protein Data Bank that have greater than 1.5 A resolution with less than 90% sequence similarity with each other. We observed varieties of polygonal water structures composed of three to eight water molecules. These polygons may represent the time- and space-averaged structures of "stable" water oligomers present in liquid water, and their presence as well as relative population may be relevant in understanding physical properties of liquid water at a given temperature. On an average, 13% of ISWs are localized enough to be visible by X-ray diffraction. Of those, averages of 78% are water molecules in the first water layer on the protein surface. Of the localized ISWs beyond the first layer, almost half of them form water polygons such as trigons, tetragons, as well as expected pentagons, hexagons, higher polygons, partial dodecahedrons, and disordered networks. Most of the octagons and nanogons are formed by fusion of smaller polygons. The trigons are most commonly observed. We suggest that our observation provides an experimental basis for including these water polygon structures in correlating and predicting various water properties in liquid state.

Water polygons in high-resolution protein crystal structures

PubMed Central

Lee, Jonas; Kim, Sung-Hou

2009-01-01

We have analyzed the interstitial water (ISW) structures in 1500 protein crystal structures deposited in the Protein Data Bank that have greater than 1.5 Å resolution with less than 90% sequence similarity with each other. We observed varieties of polygonal water structures composed of three to eight water molecules. These polygons may represent the time- and space-averaged structures of “stable” water oligomers present in liquid water, and their presence as well as relative population may be relevant in understanding physical properties of liquid water at a given temperature. On an average, 13% of ISWs are localized enough to be visible by X-ray diffraction. Of those, averages of 78% are water molecules in the first water layer on the protein surface. Of the localized ISWs beyond the first layer, almost half of them form water polygons such as trigons, tetragons, as well as expected pentagons, hexagons, higher polygons, partial dodecahedrons, and disordered networks. Most of the octagons and nanogons are formed by fusion of smaller polygons. The trigons are most commonly observed. We suggest that our observation provides an experimental basis for including these water polygon structures in correlating and predicting various water properties in liquid state. PMID:19551896

Aberdeen polygons: computer displays of physiological profiles for intensive care.

PubMed

Green, C A; Logie, R H; Gilhooly, K J; Ross, D G; Ronald, A

1996-03-01

The clinician in an intensive therapy unit is presented regularly with a range of information about the current physiological state of the patients under care. This information typically comes from a variety of sources and in a variety of formats. A more integrated form of display incorporating several physiological parameters may be helpful therefore. Three experiments are reported that explored the potential use of analogue, polygon diagrams to display physiological data from patients undergoing intensive therapy. Experiment 1 demonstrated that information can be extracted readily from such diagrams comprising 8- or 10-sided polygons, but with an advantage for simpler polygons and for information displayed at the top of the diagram. Experiment 2 showed that colour coding removed these biases for simpler polygons and the top of the diagram, together with speeding the processing time. Experiment 3 used polygons displaying patterns of physiological data that were consistent with typical conditions observed in the intensive care unit. It was found that physicians can readily learn to recognize these patterns and to diagnose both the nature and severity of the patient's physiological state. These polygon diagrams appear to have some considerable potential for use in providing on-line summary information of a patient's physiological state.

Technique for identifying, tracing, or tracking objects in image data

DOEpatents

Anderson, Robert J [Albuquerque, NM; Rothganger, Fredrick [Albuquerque, NM

2012-08-28

A technique for computer vision uses a polygon contour to trace an object. The technique includes rendering a polygon contour superimposed over a first frame of image data. The polygon contour is iteratively refined to more accurately trace the object within the first frame after each iteration. The refinement includes computing image energies along lengths of contour lines of the polygon contour and adjusting positions of the contour lines based at least in part on the image energies.

On the mean and variance of the writhe of random polygons.

PubMed

Portillo, J; Diao, Y; Scharein, R; Arsuaga, J; Vazquez, M

We here address two problems concerning the writhe of random polygons. First, we study the behavior of the mean writhe as a function length. Second, we study the variance of the writhe. Suppose that we are dealing with a set of random polygons with the same length and knot type, which could be the model of some circular DNA with the same topological property. In general, a simple way of detecting chirality of this knot type is to compute the mean writhe of the polygons; if the mean writhe is non-zero then the knot is chiral. How accurate is this method? For example, if for a specific knot type K the mean writhe decreased to zero as the length of the polygons increased, then this method would be limited in the case of long polygons. Furthermore, we conjecture that the sign of the mean writhe is a topological invariant of chiral knots. This sign appears to be the same as that of an "ideal" conformation of the knot. We provide numerical evidence to support these claims, and we propose a new nomenclature of knots based on the sign of their expected writhes. This nomenclature can be of particular interest to applied scientists. The second part of our study focuses on the variance of the writhe, a problem that has not received much attention in the past. In this case, we focused on the equilateral random polygons. We give numerical as well as analytical evidence to show that the variance of the writhe of equilateral random polygons (of length n ) behaves as a linear function of the length of the equilateral random polygon.

Isotopic insights into methane production, oxidation, and emissions in Arctic polygon tundra.

PubMed

Vaughn, Lydia J S; Conrad, Mark E; Bill, Markus; Torn, Margaret S

2016-10-01

Arctic wetlands are currently net sources of atmospheric CH4 . Due to their complex biogeochemical controls and high spatial and temporal variability, current net CH4 emissions and gross CH4 processes have been difficult to quantify, and their predicted responses to climate change remain uncertain. We investigated CH4 production, oxidation, and surface emissions in Arctic polygon tundra, across a wet-to-dry permafrost degradation gradient from low-centered (intact) to flat- and high-centered (degraded) polygons. From 3 microtopographic positions (polygon centers, rims, and troughs) along the permafrost degradation gradient, we measured surface CH4 and CO2 fluxes, concentrations and stable isotope compositions of CH4 and DIC at three depths in the soil, and soil moisture and temperature. More degraded sites had lower CH4 emissions, a different primary methanogenic pathway, and greater CH4 oxidation than did intact permafrost sites, to a greater degree than soil moisture or temperature could explain. Surface CH4 flux decreased from 64 nmol m(-2)  s(-1) in intact polygons to 7 nmol m(-2)  s(-1) in degraded polygons, and stable isotope signatures of CH4 and DIC showed that acetate cleavage dominated CH4 production in low-centered polygons, while CO2 reduction was the primary pathway in degraded polygons. We see evidence that differences in water flow and vegetation between intact and degraded polygons contributed to these observations. In contrast to many previous studies, these findings document a mechanism whereby permafrost degradation can lead to local decreases in tundra CH4 emissions. © 2016 John Wiley & Sons Ltd.

On the mean and variance of the writhe of random polygons

PubMed Central

Portillo, J.; Diao, Y.; Scharein, R.; Arsuaga, J.; Vazquez, M.

2013-01-01

We here address two problems concerning the writhe of random polygons. First, we study the behavior of the mean writhe as a function length. Second, we study the variance of the writhe. Suppose that we are dealing with a set of random polygons with the same length and knot type, which could be the model of some circular DNA with the same topological property. In general, a simple way of detecting chirality of this knot type is to compute the mean writhe of the polygons; if the mean writhe is non-zero then the knot is chiral. How accurate is this method? For example, if for a specific knot type K the mean writhe decreased to zero as the length of the polygons increased, then this method would be limited in the case of long polygons. Furthermore, we conjecture that the sign of the mean writhe is a topological invariant of chiral knots. This sign appears to be the same as that of an “ideal” conformation of the knot. We provide numerical evidence to support these claims, and we propose a new nomenclature of knots based on the sign of their expected writhes. This nomenclature can be of particular interest to applied scientists. The second part of our study focuses on the variance of the writhe, a problem that has not received much attention in the past. In this case, we focused on the equilateral random polygons. We give numerical as well as analytical evidence to show that the variance of the writhe of equilateral random polygons (of length n) behaves as a linear function of the length of the equilateral random polygon. PMID:25685182

An investigation into the mechanism of the polygonal wear of metro train wheels and its effect on the dynamic behaviour of a wheel/rail system

NASA Astrophysics Data System (ADS)

Jin, Xuesong; Wu, Lei; Fang, Jianying; Zhong, Shuoqiao; Ling, Liang

2012-12-01

This paper presents a detailed investigation conducted into the mechanism of the polygonal wear of metro train wheels through extensive experiments conducted at the sites. The purpose of the experimental investigation is to determine from where the resonant frequency that causes the polygonal wear of the metro train wheels originates. The experiments include the model tests of a vehicle and its parts and the tracks, the dynamic behaviour test of the vehicle in operation and the observation test of the polygonal wear development of the wheels. The tracks tested include the viaducts and the tunnel tracks. The structure model tests show that the average passing frequency of a polygonal wheel is approximately close to the first bending resonant frequency of the wheelset that is found by the wheelset model test and verified by the finite element analysis of the wheelset. Also, the dynamic behaviour test of the vehicle in operation indicates the main frequencies of the vertical acceleration vibration of the axle boxes, which are dominant in the vertical acceleration vibration of the axle boxes and close to the passing frequency of a polygonal wheel, which shows that the first bending resonant frequency of the wheelset is very exciting in the wheelset operation. The observation test of the polygonal wear development of the wheels indicates an increase in the rate of the polygonal wear of the wheels after their re-profiling. This paper also describes the dynamic models used for the metro vehicle coupled with the ballasted track and the slab track to analyse the effect of the polygonal wear of the wheels on the wheel/rail normal forces.

Computer program for calculating full potential transonic, quasi-three-dimensional flow through a rotating turbomachinery blade row

NASA Technical Reports Server (NTRS)

Farrell, C. A.

1982-01-01

A fast, reliable computer code is described for calculating the flow field about a cascade of arbitrary two dimensional airfoils. The method approximates the three dimensional flow in a turbomachinery blade row by correcting for stream tube convergence and radius change in the throughflow direction. A fully conservative solution of the full potential equation is combined with the finite volume technique on a body-fitted periodic mesh, with an artificial density imposed in the transonic region to insure stability and the capture of shock waves. The instructions required to set up and use the code are included. The name of the code is QSONIC. A numerical example is also given to illustrate the output of the program.

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits. Thesis

NASA Technical Reports Server (NTRS)

Oh, K. S.; Schutt-Aine, J.

1995-01-01

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Geometry effect on electrokinetic flow and ionic conductance in pH-regulated nanochannels

NASA Astrophysics Data System (ADS)

Sadeghi, Morteza; Saidi, Mohammad Hassan; Moosavi, Ali; Sadeghi, Arman

2017-12-01

Semi-analytical solutions are obtained for the electrical potential, electroosmotic velocity, ionic conductance, and surface physicochemical properties associated with long pH-regulated nanochannels of arbitrary but constant cross-sectional area. The effects of electric double layer overlap, multiple ionic species, and surface association/dissociation reactions are all taken into account, assuming low surface potentials. The method of analysis includes series solutions which the pertinent coefficients are obtained by applying the wall boundary conditions using either of the least-squares or point matching techniques. Although the procedure is general enough to be applied to almost any arbitrary cross section, nine nanogeometries including polygonal, trapezoidal, double-trapezoidal, rectangular, elliptical, semi-elliptical, isosceles triangular, rhombic, and isotropically etched profiles are selected for presentation. For the special case of an elliptic cross section, full analytical solutions are also obtained utilizing the Mathieu functions. We show that the geometrical configuration plays a key role in determination of the ionic conductance, surface charge density, electrical potential and velocity fields, and proton enhancement. In this respect, the net electric charge and convective ionic conductance are higher for channels of larger perimeter to area ratio, whereas the opposite is true for the average surface charge density and mean velocity; the geometry impact on the two latest ones, however, vanishes if the background salt concentration is high enough. Moreover, we demonstrate that considering a constant surface potential equal to the average charge-regulated potential provides sufficiently accurate results for smooth geometries such as an ellipse at medium-high aspect ratios but leads to significant errors for geometries having narrow corners such as a triangle.

High Latitude Polygons

NASA Technical Reports Server (NTRS)

2005-01-01

26 September 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows polygonal patterned ground on a south high-latitude plain. The outlines of the polygons, like the craters and hills in this region, are somewhat enhanced by the presence of bright frost left over from the previous winter. On Earth, polygons at high latitudes would usually be attributed to the seasonal freezing and thawing cycles of ground ice. The origin of similar polygons on Mars is less certain, but might also be an indicator of ground ice.

Location near: 75.3oS, 113.2oW Image width: width: 3 km (1.9 mi) Illumination from: upper left Season: Southern Spring

Supramolecule-to-Supramolecule Transformations of Coordination-Driven Self-Assembled Polygons

PubMed Central

Zhao, Liang; Northrop, Brian H.; Stang, Peter J.

2009-01-01

Two types of supramolecular transformations, wherein a self-assembled Pt(II)-pyridyl metal-organic polygon is controllably converted into an alternative polygon, have been achieved through the reaction between cobalt carbonyl and the acetylene moiety of a dipyridyl donor ligand. A [6+6] hexagon is transformed into two [3+3] hexagons and a triangle-square mixture is converted into [2+2] rhomboids. 1H and 31P NMR spectra are used to track the transformation process and evaluate the yield of new self-assembled polygons. Such transformed species are identified by electrospray ionization (ESI) mass spectrometry. This new kind of supramolecule-to-supramolecule transformations provides a viable means for constructing, and then converting, new self-assembled polygons. PMID:18702485

Average size of random polygons with fixed knot topology.

PubMed

Matsuda, Hiroshi; Yao, Akihisa; Tsukahara, Hiroshi; Deguchi, Tetsuo; Furuta, Ko; Inami, Takeo

2003-07-01

We have evaluated by numerical simulation the average size R(K) of random polygons of fixed knot topology K=,3(1),3(1) musical sharp 4(1), and we have confirmed the scaling law R(2)(K) approximately N(2nu(K)) for the number N of polygonal nodes in a wide range; N=100-2200. The best fit gives 2nu(K) approximately 1.11-1.16 with good fitting curves in the whole range of N. The estimate of 2nu(K) is consistent with the exponent of self-avoiding polygons. In a limited range of N (N greater, similar 600), however, we have another fit with 2nu(K) approximately 1.01-1.07, which is close to the exponent of random polygons.

Acid-Base Titration Curves of Soils from a Low-Centered Polygon, Barrow, Alaska, 2013

DOE Data Explorer

Jianqiu Zheng; David Graham

2017-12-05

This dataset provides pH titration data of soils from a low-centered polygon center. The soil core was collected in 2013 from a low-centered polygon center from the NGEE-Arctic Intensive Study Site 1, Barrow, Alaska.

CONNECTICUT GROUND WATER QUALITY CLASSIFICATIONS

EPA Science Inventory

This is a 1:24,000-scale datalayer of Ground Water Quality Classifications in Connecticut. It is a polygon Shapefile that includes polygons for GA, GAA, GAAs, GB, GC and other related ground water quality classes. Each polygon is assigned a ground water quality class, which is s...

Ice Wedge Polygon Bromide Tracer Experiment in Subsurface Flow, Barrow, Alaska, 2015-2016

DOE Data Explorer

Nathan Wales

2018-02-15

Time series of bromide tracer concentrations at several points within a low-centered polygon and a high-centered polygon. Concentration values were obtained from the analysis of water samples via ion chromatography with an accuracy of 0.01 mg/l.

Partial polygon pruning of hydrographic features in automated generalization

USGS Publications Warehouse

Stum, Alexander K.; Buttenfield, Barbara P.; Stanislawski, Larry V.

2017-01-01

This paper demonstrates a working method to automatically detect and prune portions of waterbody polygons to support creation of a multi-scale hydrographic database. Water features are known to be sensitive to scale change; and thus multiple representations are required to maintain visual and geographic logic at smaller scales. Partial pruning of polygonal features—such as long and sinuous reservoir arms, stream channels that are too narrow at the target scale, and islands that begin to coalesce—entails concurrent management of the length and width of polygonal features as well as integrating pruned polygons with other generalized point and linear hydrographic features to maintain stream network connectivity. The implementation follows data representation standards developed by the U.S. Geological Survey (USGS) for the National Hydrography Dataset (NHD). Portions of polygonal rivers, streams, and canals are automatically characterized for width, length, and connectivity. This paper describes an algorithm for automatic detection and subsequent processing, and shows results for a sample of NHD subbasins in different landscape conditions in the United States.

Exposed Ice in the Northern Mid-Latitudes of Mars

NASA Technical Reports Server (NTRS)

Allen, Carlton C.

2007-01-01

Ice-Rich Layer: Polygonal features with dimensions of approximately 100 meters, bounded by cracks, are commonly observed on the martian northern plains. These features are generally attributed to thermal cracking of ice-rich sediments, in direct analogy to polygons in terrestrial polar regions. We mapped polygons in the northern mid-latitudes (30 to 65 N) using MOC and HiRISE images. Polygons are scattered across the northern plains, with a particular concentration in western Utopia Planitia. This region largely overlaps the Late Amazonian Astapus Colles unit, characterized by polygonal terrain and nested pits consistent with periglacial and thermokarst origins. Bright and Dark Polygonal Cracks: An examination of all MOC images (1997 through 2003) covering the study area demonstrated that, at latitudes of 55 to 65 N, most of the imaged polygons show bright bounding cracks. We interpret these bright cracks as exposed ice. Between 40 and 55 N, most of the imaged polygons show dark bounding cracks. These are interpreted as polygons from which the exposed ice has been removed by sublimation. The long-term stability limit for exposed ice, even in deep cracks, apparently lies near 55 N. Bright and Dark Spots: Many HiRISE and MOC frames showing polygons in the northern plains also show small numbers of bright and dark spots, particularly in western Utopia Planitia. Many of the spots are closely associated with collapse features suggestive of thermokarst. The spots range from tens to approximately 100 meters in diameter. The bright spots are interpreted as exposed ice, due to their prevalence on terrain mapped as ice rich. The dark spots are interpreted as former bright spots, which have darkened as the exposed ice is lost by sublimation. The bright spots may be the martian equivalents of pingos, ice-cored mounds found in periglacial regions on Earth. Terrestrial pingos from which the ice core has melted often collapse to form depressions similar to the martian dark spots. Future Observations: The SHARAD radar should be able to confirm the presence and measure the depth of the interpreted ice-rich layer that forms the Astapus Colles unit. If this layer is confirmed it will strengthen the interpretation of bright polygon cracks and bright spots as exposed ice. HiRISE images of the northern plains are showing unprecedented details of the polygonal cracks. Future HiRISE images that include bright spots, compared to MOC images taken years earlier, will illustrate the temporal stability of the spots. The CRISM spectrometer, with multiple spectral bands and a spatial resolution around 20 meters, should allow mineralogical identification of the material exposed in the polygonal bounding cracks and in the bright spots.

Infrared thermography of the udder surface of dairy cattle: characteristics, methods, and correlation with rectal temperature.

PubMed

Metzner, Moritz; Sauter-Louis, Carola; Seemueller, Andrea; Petzl, Wolfram; Klee, Wolfgang

2014-01-01

Thermograms of the caudal udder surface were taken of five healthy cows before and after inoculation of Escherichia coli into the right hind quarter. Images in clinically normal udder quarters from cows without fever (CN) were compared with those post inoculation when cows had fever (⩾ 39.5°C) and showed elevation of somatic cell counts (⩾ 400,000 cells/mL) in the inoculated quarter (CM). Using graphic software tools, different geometric analysis tools (GATs: polygons, rectangles, lines) were set within the thermographic images. The following descriptive parameters (DPs) were employed: minimum value ('min'), maximum value ('max'), range ('max-min'), and arithmetic mean ('am'). Surface temperatures in group CN were between 34.1°C ('polygons'/'min') and 37.9°C ('polygons'/'max'), and in group CM between 34.5°C ('polygons'/'min') and 40.0°C ('polygons'/'max'). The greatest differences in the temperatures between CN and CM (2.06°C) were found in 'polygons' and 'rectangles' using 'max'. The smallest coefficient of variation in triplicate determinations was found in GAT 'polygons' with DP 'max' (Tmax) (0.15%), and the relationship to the rectal body temperature (Tr) could be described by Tr=5.68+0.874*Tmax. The results show that significant changes can be displayed best using the GAT 'polygons' and the DP 'max'. These methods should be considered for automated monitoring of udder health in dairy cows. Copyright © 2013 Elsevier Ltd. All rights reserved.

Experimental investigation into the mechanism of the polygonal wear of electric locomotive wheels

NASA Astrophysics Data System (ADS)

Tao, Gongquan; Wang, Linfeng; Wen, Zefeng; Guan, Qinghua; Jin, Xuesong

2018-06-01

Experiments were conducted at field sites to investigate the mechanism of the polygonal wear of electric locomotive wheels. The polygonal wear rule of electric locomotive wheels was obtained. Moreover, two on-track tests have been carried out to investigate the vibration characteristics of the electric locomotive's key components. The measurement results of wheels out-of-round show that most electric locomotive wheels exhibit polygonal wear. The main centre wavelength in the 1/3 octave bands is 200 mm and/or 160 mm. The test results of vibration characteristics indicate that the dominating frequency of the vertical acceleration measured on the axle box is approximately equal to the passing frequency of a polygonal wheel, and does not vary with the locomotive speed during the acceleration course. The wheelset modal analysis using the finite element method (FEM) indicates that the first bending resonant frequency of the wheelset is quite close to the main vibration frequency of the axle box. The FEM results are verified by the experimental modal analysis of the wheelset. Moreover, different plans were designed to verify whether the braking system and the locomotive's adhesion control have significant influence on the wheel polygon or not. The test results indicate that they are not responsible for the initiation of the wheel polygon. The first bending resonance of the wheelset is easy to be excited in the locomotive operation and it is the root cause of wheel polygon with centre wavelength of 200 mm in the 1/3 octave bands.

A Periglacial Analog for Landforms in Gale Crater, Mars

NASA Technical Reports Server (NTRS)

Oehler, Dorothy Z.

2013-01-01

Several features in a high thermal inertia (TI) unit at Gale crater can be interpreted within a periglacial framework. These features include polygonally fractured terrain (cf. ice-wedge polygons), circumferential patterns of polygonal fractures (cf. relict pingos with ice-wedge polygons on their surfaces), irregularly-shaped and clustered depressions (cf. remnants of collapsed pingos and ephemeral lakes), and a general hummocky topography (cf. thermokarst). This interpretation would imply a major history of water and ice in Gale crater, involving permafrost, freeze-thaw cycles, and perhaps ponded surface water.

Morphometric analysis of polygonal cracking patterns in desiccated starch slurries

NASA Astrophysics Data System (ADS)

Akiba, Yuri; Magome, Jun; Kobayashi, Hiroshi; Shima, Hiroyuki

2017-08-01

We investigate the geometry of two-dimensional polygonal cracking that forms on the air-exposed surface of dried starch slurries. Two different kinds of starches, made from potato and corn, exhibited distinguished crack evolution, and there were contrasting effects of slurry thickness on the probability distribution of the polygonal cell area. The experimental findings are believed to result from the difference in the shape and size of starch grains, which strongly influence the capillary transport of water and tensile stress field that drives the polygonal cracking.

Cholesteric microlenses and micromirrors in the beetle cuticle and in synthetic oligomer films: a comparative study

NASA Astrophysics Data System (ADS)

Agez, Gonzague; Bayon, Chloé; Mitov, Michel

2017-02-01

The polygonal texture in cholesteric liquid crystals consist in an array of contiguous polygonal cells. The optical response and the structure of polygonal texture are investigated in the cuticle of beetle Chrysina gloriosa and in synthetic oligomer films. In the insect carapace, the polygons are concave and behave as spherical micro-mirrors whereas they are convex and behave as diverging microlenses in synthetic films. The characteristics of light focusing (spot, donut or continuum background) are highly tunable with the wavelength and the polarization of the incident light.

Convex lattice polygons of fixed area with perimeter-dependent weights.

PubMed

Rajesh, R; Dhar, Deepak

2005-01-01

We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight tm to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s varies as s(-theta(conv))eK(t)square root(s) for large s and t less than a critical threshold tc, where K(t) is a t-dependent constant, and theta(conv) is a critical exponent which does not change with t. Using heuristic arguments, we find that theta(conv) is 1/4 for the square lattice, but -1/4 for the hexagonal lattice. The reason for this unexpected nonuniversality of theta(conv) is traced to existence of sharp corners in the asymptotic shape of these polygons.

Comic image understanding based on polygon detection

NASA Astrophysics Data System (ADS)

Li, Luyuan; Wang, Yongtao; Tang, Zhi; Liu, Dong

2013-01-01

Comic image understanding aims to automatically decompose scanned comic page images into storyboards and then identify the reading order of them, which is the key technique to produce digital comic documents that are suitable for reading on mobile devices. In this paper, we propose a novel comic image understanding method based on polygon detection. First, we segment a comic page images into storyboards by finding the polygonal enclosing box of each storyboard. Then, each storyboard can be represented by a polygon, and the reading order of them is determined by analyzing the relative geometric relationship between each pair of polygons. The proposed method is tested on 2000 comic images from ten printed comic series, and the experimental results demonstrate that it works well on different types of comic images.

Zernike-like systems in polygons and polygonal facets.

PubMed

Ferreira, Chelo; López, José L; Navarro, Rafael; Sinusía, Ester Pérez

2015-07-20

Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit disk. In [Opt. Lett.32, 74 (2007)10.1364/OL.32.000074OPLEDP0146-9592] we introduced a new Zernike basis for elliptic and annular optical apertures based on an appropriate diffeomorphism between the unit disk and the ellipse and the annulus. Here, we present a generalization of this Zernike basis for a variety of important optical apertures, paying special attention to polygons and the polygonal facets present in segmented mirror telescopes. On the contrary to ad hoc solutions, most of them based on the Gram-Smith orthonormalization method, here we consider a piecewise diffeomorphism that transforms the unit disk into the polygon under consideration. We use this mapping to define a Zernike-like orthonormal system over the polygon. We also consider ensembles of polygonal facets that are essential in the design of segmented mirror telescopes. This generalization, based on in-plane warping of the basis functions, provides a unique solution, and what is more important, it guarantees a reasonable level of invariance of the mathematical properties and the physical meaning of the initial basis functions. Both the general form and the explicit expressions for a typical example of telescope optical aperture are provided.

Vigorous convection as the explanation for Pluto's polygonal terrain.

PubMed

Trowbridge, A J; Melosh, H J; Steckloff, J K; Freed, A M

2016-06-02

Pluto's surface is surprisingly young and geologically active. One of its youngest terrains is the near-equatorial region informally named Sputnik Planum, which is a topographic basin filled by nitrogen (N2) ice mixed with minor amounts of CH4 and CO ices. Nearly the entire surface of the region is divided into irregular polygons about 20-30 kilometres in diameter, whose centres rise tens of metres above their sides. The edges of this region exhibit bulk flow features without polygons. Both thermal contraction and convection have been proposed to explain this terrain, but polygons formed from thermal contraction (analogous to ice-wedges or mud-crack networks) of N2 are inconsistent with the observations on Pluto of non-brittle deformation within the N2-ice sheet. Here we report a parameterized convection model to compute the Rayleigh number of the N2 ice and show that it is vigorously convecting, making Rayleigh-Bénard convection the most likely explanation for these polygons. The diameter of Sputnik Planum's polygons and the dimensions of the 'floating mountains' (the hills of of water ice along the edges of the polygons) suggest that its N2 ice is about ten kilometres thick. The estimated convection velocity of 1.5 centimetres a year indicates a surface age of only around a million years.

Evidence for an Ancient Periglacial Climate in Gale Crater, Mars

NASA Astrophysics Data System (ADS)

Fairén, A. G.; Oehler, D. Z.; Mangold, N.; Hallet, B.; Le Deit, L.; Williams, A.; Sletten, R. S.; Martínez-Frías, J.

2016-12-01

Decameter-scale polygons occur extensively in the lower Peace Vallis Fan of Gale crater, in the Bedded Fractured (BF) Unit, north of Yellowknife Bay (YKB) that was examined and drilled by the Curiosity rover. To gain insight into the origin of these polygons, we studied image data from the Context (CTX) and High Resolution Imaging Science Experiment (HiRISE) cameras on Mars Reconnaissance Orbiter and compared results to the geology of the fan. The polygons are 4 to 30 m across, square to rectangular, and defined by 0.5 to 4 m-wide linear troughs that probably reflect cm-wide, quasi-vertical fractures below the surface. Polygon networks are typically orthogonal systems, with occasional circularly organized patterns, hundreds of meters across. We evaluated multiple hypotheses for the origin of the polygons and concluded that thermal-contraction fracturing during cooling of ice-rich permafrost is most consistent with the sedimentary nature of the BF Unit, the morphology/geometry of the polygons, their restriction to the coarse-grained Gillespie Lake Member, and geologic context. Most of these polygons are confined to the Hesperian BF Unit and appear to be ancient, though individual polygon fractures may have been reactivated in more recent periods, perhaps due to stresses developed with exhumation or as the planet grew colder and drier. Some of the circular networks resemble ice-wedge polygons in thermokarst depressions and collapsed pingos, as seen in periglacial environments of the Arctic. An analog to collapsed pingos could be supported by modeling work of Andrews-Hanna et al. (2012, LPSC; 2012, 3rd Conf. Early Mars) suggesting that Gale was uniquely positioned for significant influx of ground water early its history. Also, results from Curiosity demonstrating limited chemical weathering and a past freshwater lake in YKB (Grotzinger et al., 2014, Science 343) would be consistent with an early periglacial setting. Our conclusions support an ancient, cold and wet periglacial landscape (Fairén et al., 2014, PSS 93-94) in this part of Gale - one with ice-wedge polygons, thermokarst features, ponded water, and possible ice-covered lakes and pingos in various stages of growth and decay (Oehler et al., 2016, Icarus 277).

Measured Two-Dimensional Ice-Wedge Polygon Thermal and Active Layer Dynamics

NASA Astrophysics Data System (ADS)

Cable, W.; Romanovsky, V. E.; Busey, R.

2016-12-01

Ice-wedge polygons are perhaps the most dominant permafrost related features in the arctic landscape. The microtopography of these features, that includes rims, troughs, and high and low polygon centers, alters the local hydrology. During winter, wind redistribution of snow leads to an increased snowpack depth in the low areas, while the slightly higher areas often have very thin snow cover, leading to differences across the landscape in vegetation communities and soil moisture between higher and lower areas. To investigate the effect of microtopographic caused variation in surface conditions on the ground thermal regime, we established temperature transects, composed of five vertical array thermistor probes (VATP), across four different development stages of ice-wedge polygons near Barrow, Alaska. Each VATP had 16 thermistors from the surface to a depth of 1.5 m, for a total of 80 temperature measurements per polygon. We found snow cover, timing and depth, and active layer soil moisture to be major controlling factors in the observed thermal regimes. In troughs and in the centers of low-centered polygons, the combined effect of typically saturated soils and increased snow accumulation resulted in the highest mean annual ground temperatures (MAGT) and latest freezeback dates. While the centers of high-centered polygons, with thinner snow cover and a dryer active layer, had the lowest MAGT, earliest freezeback dates, and shallowest active layer. Refreezing of the active layer initiated at nearly the same time for all locations and polygons however, we found large differences in the proportion of downward versus upward freezing and the length of time required to complete the refreezing process between polygon types and locations. Using our four polygon stages as a space for time substitution, we conclude that ice-wedge degradation resulting in surface subsidence and trough deepening can lead to overall drying of the active layer and increased skewedness of snow distribution. Which in turn leads to shallower active layers, earlier freezeback dates, and lower MAGT. We also find that the large variation in active layer dynamics (active layer depth, downward vs upward freezing, and freezeback date) are important considerations to understanding and scaling biological processes occurring in these landscapes.

Location memory for dots in polygons versus cities in regions: evaluating the category adjustment model.

PubMed

Friedman, Alinda; Montello, Daniel R; Burte, Heather

2012-09-01

We conducted 3 experiments to examine the category adjustment model (Huttenlocher, Hedges, & Duncan, 1991) in circumstances in which the category boundaries were irregular schematized polygons made from outlines of maps. For the first time, accuracy was tested when only perceptual and/or existing long-term memory information about identical locations was cued. Participants from Alberta, Canada and California received 1 of 3 conditions: dots-only, in which a dot appeared within the polygon, and after a 4-s dynamic mask the empty polygon appeared and the participant indicated where the dot had been; dots-and-names, in which participants were told that the first polygon represented Alberta/California and that each dot was in the correct location for the city whose name appeared outside the polygon; and names-only, in which there was no first polygon, and participants clicked on the city locations from extant memory alone. Location recall in the dots-only and dots-and-names conditions did not differ from each other and had small but significant directional errors that pointed away from the centroids of the polygons. In contrast, the names-only condition had large and significant directional errors that pointed toward the centroids. Experiments 2 and 3 eliminated the distribution of stimuli and overall screen position as causal factors. The data suggest that in the "classic" category adjustment paradigm, it is difficult to determine a priori when Bayesian cue combination is applicable, making Bayesian analysis less useful as a theoretical approach to location estimation. PsycINFO Database Record (c) 2012 APA, all rights reserved.

A simple algorithm for computing positively weighted straight skeletons of monotone polygons☆

PubMed Central

Biedl, Therese; Held, Martin; Huber, Stefan; Kaaser, Dominik; Palfrader, Peter

2015-01-01

We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlog⁡n) time and O(n) space, where n denotes the number of vertices of the polygon. PMID:25648376

WRIS: a resource information system for wildland management

Treesearch

Robert M. Russell; David A. Sharpnack; Elliot Amidon

1975-01-01

WRIS (Wildland Resource Information System) is a computer system for processing, storing, retrieving, updating, and displaying geographic data. The polygon, representing a land area boundary, forms the building block of WRIS. Polygons form a map. Maps are digitized manually or by automatic scanning. Computer programs can extract and produce polygon maps and can overlay...

Origin of the Polygons and Underground Structures in Western Utopia Planitia on Mars

NASA Technical Reports Server (NTRS)

Yoshikawa, K.

2002-01-01

The area of lower albedo (Hvm) has a higher density of polygonal patterns. These patterns potentially suggest that 1) the polygonal pattern is caused primarily by ground heaving and collapsing, 2) lower albedo materials had higher tensile strength. Additional information is contained in the original extended abstract.

Analysis of the Misconceptions of 7th Grade Students on Polygons and Specific Quadrilaterals

ERIC Educational Resources Information Center

Ozkan, Mustafa; Bal, Ayten Pinar

2017-01-01

Purpose: This study will find out student misconceptions about geometrical figures, particularly polygons and quadrilaterals. Thus, it will offer insights into teaching these concepts. The objective of this study, the question of "What are the misconceptions of seventh grade students on polygons and quadrilaterals?" constitutes the…

Measuring Historical Coastal Change using GIS and the Change Polygon Approach

USGS Publications Warehouse

Smith, M.J.; Cromley, R.G.

2012-01-01

This study compares two automated approaches, the transect-from-baseline technique and a new change polygon method, for quantifying historical coastal change over time. The study shows that the transect-from-baseline technique is complicated by choice of a proper baseline as well as generating transects that intersect with each other rather than with the nearest shoreline. The change polygon method captures the full spatial difference between the positions of the two shorelines and average coastal change is the defined as the ratio of the net area divided by the shoreline length. Although then change polygon method is sensitive to the definition and measurement of shoreline length, the results are more invariant to parameter changes than the transect-from-baseline method, suggesting that the change polygon technique may be a more robust coastal change method. ?? 2012 Blackwell Publishing Ltd.

Computation of Femoral Canine Morphometric Parameters in Three-Dimensional Geometrical Models.

PubMed

Savio, Gianpaolo; Baroni, Teresa; Concheri, Gianmaria; Baroni, Ermenegildo; Meneghello, Roberto; Longo, Federico; Isola, Maurizio

2016-11-01

To define and validate a method for the measurement of 3-dimensional (3D) morphometric parameters in polygonal mesh models of canine femora. Ex vivo/computerized model. Sixteen femora from 8 medium to large-breed canine cadavers (mean body weight 28.3 kg, mean age 5.3 years). Femora were measured with a 3D scanner, obtaining 3D meshes. A computer-aided design-based (CAD) software tool was purposely developed, which allowed automatic calculation of morphometric parameters on a mesh model. Anatomic and mechanical lateral proximal femoral angles (aLPFA and mLPFA), anatomic and mechanical lateral distal femoral angles (aLDFA and mLDFA), femoral neck angle (FNA), femoral torsion angle (FTA), and femoral varus angle (FVA) were measured in 3D space. Angles were also measured onto projected planes and radiographic images. Mean (SD) femoral angles (degrees) measured in 3D space were: aLPFA 115.2 (3.9), mLPFA 105.5 (4.2), aLDFA 88.6 (4.5), mLDFA 93.4 (3.9), FNA 129.6 (4.3), FTA 45 (4.5), and FVA -1.4 (4.5). Onto projection planes, aLPFA was 103.7 (5.9), mLPFA 98.4 (5.3), aLDFA 88.3 (5.5), mLDFA 93.6 (4.2), FNA 132.1 (3.5), FTA 19.1 (5.7), and FVA -1.7 (5.5). With radiographic imaging, aLPFA was 109.6 (5.9), mLPFA 105.3 (5.2), aLDFA 92.6 (3.8), mLDFA 96.9 (2.9), FNA 120.2 (8.0), FTA 30.2 (5.7), and FVA 2.6 (3.8). The proposed method gives reliable and consistent information about 3D bone conformation. Results are obtained automatically and depend only on femur morphology, avoiding any operator-related bias. Angles in 3D space are different from those measured with standard radiographic methods, mainly due to the different definition of femoral axes. © Copyright 2016 by The American College of Veterinary Surgeons.

SEM-microphotogrammetry, a new take on an old method for generating high-resolution 3D models from SEM images.

PubMed

Ball, A D; Job, P A; Walker, A E L

2017-08-01

The method we present here uses a scanning electron microscope programmed via macros to automatically capture dozens of images at suitable angles to generate accurate, detailed three-dimensional (3D) surface models with micron-scale resolution. We demonstrate that it is possible to use these Scanning Electron Microscope (SEM) images in conjunction with commercially available software originally developed for photogrammetry reconstructions from Digital Single Lens Reflex (DSLR) cameras and to reconstruct 3D models of the specimen. These 3D models can then be exported as polygon meshes and eventually 3D printed. This technique offers the potential to obtain data suitable to reconstruct very tiny features (e.g. diatoms, butterfly scales and mineral fabrics) at nanometre resolution. Ultimately, we foresee this as being a useful tool for better understanding spatial relationships at very high resolution. However, our motivation is also to use it to produce 3D models to be used in public outreach events and exhibitions, especially for the blind or partially sighted. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

Model for the architecture of caveolae based on a flexible, net-like assembly of Cavin1 and Caveolin discs

PubMed Central

Stoeber, Miriam; Schellenberger, Pascale; Siebert, C. Alistair; Leyrat, Cedric; Helenius, Ari

2016-01-01

Caveolae are invaginated plasma membrane domains involved in mechanosensing, signaling, endocytosis, and membrane homeostasis. Oligomers of membrane-embedded caveolins and peripherally attached cavins form the caveolar coat whose structure has remained elusive. Here, purified Cavin1 60S complexes were analyzed structurally in solution and after liposome reconstitution by electron cryotomography. Cavin1 adopted a flexible, net-like protein mesh able to form polyhedral lattices on phosphatidylserine-containing vesicles. Mutating the two coiled-coil domains in Cavin1 revealed that they mediate distinct assembly steps during 60S complex formation. The organization of the cavin coat corresponded to a polyhedral nano-net held together by coiled-coil segments. Positive residues around the C-terminal coiled-coil domain were required for membrane binding. Purified caveolin 8S oligomers assumed disc-shaped arrangements of sizes that are consistent with the discs occupying the faces in the caveolar polyhedra. Polygonal caveolar membrane profiles were revealed in tomograms of native caveolae inside cells. We propose a model with a regular dodecahedron as structural basis for the caveolae architecture. PMID:27834731

Polar Polygon Patterns

NASA Technical Reports Server (NTRS)

2003-01-01

MGS MOC Release No. MOC2-338, 22 April 2003

This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image was taken during southern spring, as the seasonal carbon dioxide frost cap was subliming away. Frost remaining in shallow cracks and depressions reveals a fantastic polygonal pattern. Similar polygons occur in the Earth's arctic and antarctic regions-on Earth such polygons are related to the freeze and thaw of ground ice. The picture covers an area about 3 km (about 1.9 mi) wide near 71.9oS, 11.1oW. Sunlight illuminates the scene from the left.

Integrating Carbon Flux Measurements with Hydrologic and Thermal Responses in a Low Centered Ice-Wedge Polygon near Prudhoe Bay, AK

NASA Astrophysics Data System (ADS)

Larson, T.; Young, M.; Caldwell, T. G.; Abolt, C.

2014-12-01

Substantial attention is being devoted to soil organic carbon (SOC) dynamics in Polar Regions, given the potential impacts of CO2 and methane (CH4) release into the atmosphere. In this study, which is part of a broader effort to quantify carbon loss pathways in patterned Arctic permafrost soils, CH4 and CO2 flux measurements were recorded from a site approximately 30 km south of Deadhorse, Alaska and 1 km west of the Dalton Highway. Samples were collected in late July, 2014 using six static flux chambers that were located within a single low-centered ice-wedge polygon. Three flux chambers were co-located (within a 1 m triangle of each other) near the center of the polygon and three were co-located (along a 1.5 m line) on the ridge adjacent to a trough. Soil in the center of the polygon was 100% water saturated, whereas water saturation measured on the ridge ranged between 25-50%. Depth to ice table was approximately 50 cm near the center of the polygon and 40 cm at the ridge. Temperature depth probes were installed within the center and ridge of the polygon. Nine gas measurements were collected from each chamber over a 24 h period, stored in helium-purged Exetainer vials, shipped to a laboratory, and analyzed using gas chromatography. Measured cumulative methane fluxes were linear over the 24 h period demonstrating constant methane production, but considerable spatial variability in flux was observed (0.1 to 4.7 mg hr-1 m-2 in polygon center, and 0.003 to 0.36 mg hr-1m-2 on polygon ridge). Shallow soil temperatures varied between 1.3 and 9.8oC in the center and 0.6 to 7.5oC in the rim of the polygon. Air temperatures varied between 1.3 and 4.6oC. CO2 fluxes were greater than methane fluxes and more consistent at each co-location; ranging from 21.7 to 36.6 mg hr-1 m-2 near the polygon centers and 3.5 to 29.1 mg hr-1 m-2 in the drier polygon ridge. Results are consistent with previous observations that methanogenesis is favored in a water saturated active layer. The independence of CH4 and CO2 fluxes suggests that different mechanisms may affect their formation and transport. Ongoing work on DOC and acetate concentrations may further elucidate the source of CH4 and CO2 flux. Results will be used to benchmark vertical SOC transport and active layer dynamics models, and then integrated into a Lidar-based geomorphic model for ice wedge polygon terrain.

Simulating Large-Scale Earthquake Dynamic Rupture Scenarios On Natural Fault Zones Using the ADER-DG Method

NASA Astrophysics Data System (ADS)

Gabriel, Alice; Pelties, Christian

2014-05-01

In this presentation we will demonstrate the benefits of using modern numerical methods to support physic-based ground motion modeling and research. For this purpose, we utilize SeisSol an arbitrary high-order derivative Discontinuous Galerkin (ADER-DG) scheme to solve the spontaneous rupture problem with high-order accuracy in space and time using three-dimensional unstructured tetrahedral meshes. We recently verified the method in various advanced test cases of the 'SCEC/USGS Dynamic Earthquake Rupture Code Verification Exercise' benchmark suite, including branching and dipping fault systems, heterogeneous background stresses, bi-material faults and rate-and-state friction constitutive formulations. Now, we study the dynamic rupture process using 3D meshes of fault systems constructed from geological and geophysical constraints, such as high-resolution topography, 3D velocity models and fault geometries. Our starting point is a large scale earthquake dynamic rupture scenario based on the 1994 Northridge blind thrust event in Southern California. Starting from this well documented and extensively studied event, we intend to understand the ground-motion, including the relevant high frequency content, generated from complex fault systems and its variation arising from various physical constraints. For example, our results imply that the Northridge fault geometry favors a pulse-like rupture behavior.

Jet simulations and gamma-ray burst afterglow jet breaks

NASA Astrophysics Data System (ADS)

van Eerten, H. J.; Meliani, Z.; Wijers, R. A. M. J.; Keppens, R.

2011-01-01

The conventional derivation of the gamma-ray burst afterglow jet break time uses only the blast wave fluid Lorentz factor and therefore leads to an achromatic break. We show that in general gamma-ray burst afterglow jet breaks are chromatic across the self-absorption break. Depending on circumstances, the radio jet break may be postponed significantly. Using high-accuracy adaptive mesh fluid simulations in one dimension, coupled to a detailed synchrotron radiation code, we demonstrate that this is true even for the standard fireball model and hard-edged jets. We confirm these effects with a simulation in two dimensions. The frequency dependence of the jet break is a result of the angle dependence of the emission, the changing optical depth in the self-absorbed regime and the shape of the synchrotron spectrum in general. In the optically thin case the conventional analysis systematically overestimates the jet break time, leading to inferred opening angles that are underestimated by a factor of ˜1.3 and explosion energies that are underestimated by a factor of ˜1.7, for explosions in a homogeneous environment. The methods presented in this paper can be applied to adaptive mesh simulations of arbitrary relativistic fluid flows. All analysis presented here makes the usual assumption of an on-axis observer.

Simulating Space Capsule Water Landing with Explicit Finite Element Method

NASA Technical Reports Server (NTRS)

Wang, John T.; Lyle, Karen H.

2007-01-01

A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.

Simulating Fragmentation and Fluid-Induced Fracture in Disordered Media Using Random Finite-Element Meshes

DOE PAGES

Bishop, Joseph E.; Martinez, Mario J.; Newell, Pania

2016-11-08

Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. In this paper, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipatedmore » during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Finally, applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.« less

Simulating Fragmentation and Fluid-Induced Fracture in Disordered Media Using Random Finite-Element Meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bishop, Joseph E.; Martinez, Mario J.; Newell, Pania

Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. In this paper, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipatedmore » during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Finally, applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.« less

GPU based contouring method on grid DEM data

NASA Astrophysics Data System (ADS)

Tan, Liheng; Wan, Gang; Li, Feng; Chen, Xiaohui; Du, Wenlong

2017-08-01

This paper presents a novel method to generate contour lines from grid DEM data based on the programmable GPU pipeline. The previous contouring approaches often use CPU to construct a finite element mesh from the raw DEM data, and then extract contour segments from the elements. They also need a tracing or sorting strategy to generate the final continuous contours. These approaches can be heavily CPU-costing and time-consuming. Meanwhile the generated contours would be unsmooth if the raw data is sparsely distributed. Unlike the CPU approaches, we employ the GPU's vertex shader to generate a triangular mesh with arbitrary user-defined density, in which the height of each vertex is calculated through a third-order Cardinal spline function. Then in the same frame, segments are extracted from the triangles by the geometry shader, and translated to the CPU-side with an internal order in the GPU's transform feedback stage. Finally we propose a "Grid Sorting" algorithm to achieve the continuous contour lines by travelling the segments only once. Our method makes use of multiple stages of GPU pipeline for computation, which can generate smooth contour lines, and is significantly faster than the previous CPU approaches. The algorithm can be easily implemented with OpenGL 3.3 API or higher on consumer-level PCs.

Wireless Sensor Networks - Node Localization for Various Industry Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Derr, Kurt; Manic, Milos

Fast, effective monitoring following airborne releases of toxic substances is critical to mitigate risks to threatened population areas. Wireless sensor nodes at fixed predetermined locations may monitor such airborne releases and provide early warnings to the public. A challenging algorithmic problem is determining the locations to place these sensor nodes while meeting several criteria: 1) provide complete coverage of the domain, and 2) create a topology with problem dependent node densities, while 3) minimizing the number of sensor nodes. This manuscript presents a novel approach to determining optimal sensor placement, Advancing Front mEsh generation with Constrained dElaunay Triangulation and Smoothingmore » (AFECETS) that addresses these criteria. A unique aspect of AFECETS is the ability to determine wireless sensor node locations for areas of high interest (hospitals, schools, high population density areas) that require higher density of nodes for monitoring environmental conditions, a feature that is difficult to find in other research work. The AFECETS algorithm was tested on several arbitrary shaped domains. AFECETS simulation results show that the algorithm 1) provides significant reduction in the number of nodes, in some cases over 40%, compared to an advancing front mesh generation algorithm, 2) maintains and improves optimal spacing between nodes, and 3) produces simulation run times suitable for real-time applications.« less

A consistent and conservative scheme for MHD flows with complex boundaries on an unstructured Cartesian adaptive system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Jie; Ni, Ming-Jiu, E-mail: mjni@ucas.ac.cn

2014-01-01

The numerical simulation of Magnetohydrodynamics (MHD) flows with complex boundaries has been a topic of great interest in the development of a fusion reactor blanket for the difficulty to accurately simulate the Hartmann layers and side layers along arbitrary geometries. An adaptive version of a consistent and conservative scheme has been developed for simulating the MHD flows. Besides, the present study forms the first attempt to apply the cut-cell approach for irregular wall-bounded MHD flows, which is more flexible and conveniently implemented under adaptive mesh refinement (AMR) technique. It employs a Volume-of-Fluid (VOF) approach to represent the fluid–conducting wall interfacemore » that makes it possible to solve the fluid–solid coupling magnetic problems, emphasizing at how electric field solver is implemented when conductivity is discontinuous in cut-cell. For the irregular cut-cells, the conservative interpolation technique is applied to calculate the Lorentz force at cell-center. On the other hand, it will be shown how consistent and conservative scheme is implemented on fine/coarse mesh boundaries when using AMR technique. Then, the applied numerical schemes are validated by five test simulations and excellent agreement was obtained for all the cases considered, simultaneously showed good consistency and conservative properties.« less

Wireless Sensor Networks - Node Localization for Various Industry Problems

DOE PAGES

Derr, Kurt; Manic, Milos

2015-06-01

Fast, effective monitoring following airborne releases of toxic substances is critical to mitigate risks to threatened population areas. Wireless sensor nodes at fixed predetermined locations may monitor such airborne releases and provide early warnings to the public. A challenging algorithmic problem is determining the locations to place these sensor nodes while meeting several criteria: 1) provide complete coverage of the domain, and 2) create a topology with problem dependent node densities, while 3) minimizing the number of sensor nodes. This manuscript presents a novel approach to determining optimal sensor placement, Advancing Front mEsh generation with Constrained dElaunay Triangulation and Smoothingmore » (AFECETS) that addresses these criteria. A unique aspect of AFECETS is the ability to determine wireless sensor node locations for areas of high interest (hospitals, schools, high population density areas) that require higher density of nodes for monitoring environmental conditions, a feature that is difficult to find in other research work. The AFECETS algorithm was tested on several arbitrary shaped domains. AFECETS simulation results show that the algorithm 1) provides significant reduction in the number of nodes, in some cases over 40%, compared to an advancing front mesh generation algorithm, 2) maintains and improves optimal spacing between nodes, and 3) produces simulation run times suitable for real-time applications.« less

Kinematics of polygonal fault systems: observations from the northern North Sea

NASA Astrophysics Data System (ADS)

Wrona, Thilo; Magee, Craig; Jackson, Christopher A.-L.; Huuse, Mads; Taylor, Kevin G.

2017-12-01

Layer-bound, low-displacement normal faults, arranged into a broadly polygonal pattern, are common in many sedimentary basins. Despite having constrained their gross geometry, we have a relatively poor understanding of the processes controlling the nucleation and growth (i.e. the kinematics) of polygonal fault systems. In this study we use high-resolution 3-D seismic reflection and borehole data from the northern North Sea to undertake a detailed kinematic analysis of faults forming part of a seismically well-imaged polygonal fault system hosted within the up to 1000 m thick, Early Palaeocene-to-Middle Miocene mudstones of the Hordaland Group. Growth strata and displacement-depth profiles indicate faulting commenced during the Eocene to early Oligocene, with reactivation possibly occurring in the late Oligocene to middle Miocene. Mapping the position of displacement maxima on 137 polygonal faults suggests that the majority (64%) nucleated in the lower 500 m of the Hordaland Group. The uniform distribution of polygonal fault strikes in the area indicates that nucleation and growth were not driven by gravity or far-field tectonic extension as has previously been suggested. Instead, fault growth was likely facilitated by low coefficients of residual friction on existing slip surfaces, and probably involved significant layer-parallel contraction (strains of 0.01-0.19) of the host strata. To summarize, our kinematic analysis provides new insights into the spatial and temporal evolution of polygonal fault systems.

The mere exposure effect for visual image.

PubMed

Inoue, Kazuya; Yagi, Yoshihiko; Sato, Nobuya

2018-02-01

Mere exposure effect refers to a phenomenon in which repeated stimuli are evaluated more positively than novel stimuli. We investigated whether this effect occurs for internally generated visual representations (i.e., visual images). In an exposure phase, a 5 × 5 dot array was presented, and a pair of dots corresponding to the neighboring vertices of an invisible polygon was sequentially flashed (in red), creating an invisible polygon. In Experiments 1, 2, and 4, participants visualized and memorized the shapes of invisible polygons based on different sequences of flashed dots, whereas in Experiment 3, participants only memorized positions of these dots. In a subsequent rating phase, participants visualized the shape of the invisible polygon from allocations of numerical characters on its vertices, and then rated their preference for invisible polygons (Experiments 1, 2, and 3). In contrast, in Experiment 4, participants rated the preference for visible polygons. Results showed that the mere exposure effect appeared only when participants visualized the shape of invisible polygons in both the exposure and rating phases (Experiments 1 and 2), suggesting that the mere exposure effect occurred for internalized visual images. This implies that the sensory inputs from repeated stimuli play a minor role in the mere exposure effect. Absence of the mere exposure effect in Experiment 4 suggests that the consistency of processing between exposure and rating phases plays an important role in the mere exposure effect.

Vigorous convection as the explanation for Pluto’s polygonal terrain

NASA Astrophysics Data System (ADS)

Trowbridge, A. J.; Melosh, H. J.; Steckloff, J. K.; Freed, A. M.

2016-06-01

Pluto’s surface is surprisingly young and geologically active. One of its youngest terrains is the near-equatorial region informally named Sputnik Planum, which is a topographic basin filled by nitrogen (N2) ice mixed with minor amounts of CH4 and CO ices. Nearly the entire surface of the region is divided into irregular polygons about 20-30 kilometres in diameter, whose centres rise tens of metres above their sides. The edges of this region exhibit bulk flow features without polygons. Both thermal contraction and convection have been proposed to explain this terrain, but polygons formed from thermal contraction (analogous to ice-wedges or mud-crack networks) of N2 are inconsistent with the observations on Pluto of non-brittle deformation within the N2-ice sheet. Here we report a parameterized convection model to compute the Rayleigh number of the N2 ice and show that it is vigorously convecting, making Rayleigh-Bénard convection the most likely explanation for these polygons. The diameter of Sputnik Planum’s polygons and the dimensions of the ‘floating mountains’ (the hills of of water ice along the edges of the polygons) suggest that its N2 ice is about ten kilometres thick. The estimated convection velocity of 1.5 centimetres a year indicates a surface age of only around a million years.

Tile Patterns with LOGO--Part III: Tile Patterns from Mult Tiles Using Logo.

ERIC Educational Resources Information Center

Clason, Robert G.

1991-01-01

A mult tile is a set of polygons each of which can be dissected into smaller polygons similar to the original set of polygons. Using a recursive LOGO method that requires solutions to various geometry and trigonometry problems, dissections of mult tiles are carried out repeatedly to produce tile patterns. (MDH)

Calculation of subsonic and supersonic steady and unsteady aerodynamic forces using velocity potential aerodynamic elements

NASA Technical Reports Server (NTRS)

Haviland, J. K.; Yoo, Y. S.

1976-01-01

Expressions for calculation of subsonic and supersonic, steady and unsteady aerodynamic forces are derived, using the concept of aerodynamic elements applied to the downwash velocity potential method. Aerodynamic elements can be of arbitrary out of plane polygon shape, although numerical calculations are restricted to rectangular elements, and to the steady state case in the supersonic examples. It is suggested that the use of conforming, in place of rectangular elements, would give better results. Agreement with results for subsonic oscillating T tails is fair, but results do not converge as the number of collocation points is increased. This appears to be due to the form of expression used in the calculations. The methods derived are expected to facilitate automated flutter analysis on the computer. In particular, the aerodynamic element concept is consistent with finite element methods already used for structural analysis. The method is universal for the complete Mach number range, and, finally, the calculations can be arranged so that they do not have to be repeated completely for every reduced frequency.

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

Determination of mean camber surfaces for wings having uniform chordwise loading and arbitrary spanwise loading in subsonic flow

NASA Technical Reports Server (NTRS)

Katzoff, S; Faison, M Frances; Dubose, Hugh C

1954-01-01

The field of a uniformly loaded wing in subsonic flow is discussed in terms of the acceleration potential. It is shown that, for the design of such wings, the slope of the mean camber surface at any point can be determined by a line integration around the wing boundary. By an additional line integration around the wing boundary, this method is extended to include the case where the local section lift coefficient varies with spanwise location (the chordwise loading at every section still remaining uniform). For the uniformly loaded wing of polygonal plan form, the integrations necessary to determine the local slope of the surface and the further integration of the slopes to determine the ordinate can be done analytically. An outline of these integrations and the resulting formulas are included. Calculated results are given for a sweptback wing with uniform chordwise loading and a highly tapered spanwise loading, a uniformly loaded delta wing, a uniformly loaded sweptback wing, and the same sweptback wing with uniform chordwise loading but elliptical span load distribution.

Underworld: What we set out to do, How far did we get, What did we Learn ? (Invited)

NASA Astrophysics Data System (ADS)

Moresi, L. N.

2013-12-01

Underworld was conceived as a tool for modelling 3D lithospheric deformation coupled with the underlying / surrounding mantle flow. The challenges involved were to find a method capable of representing the complicated, non-linear, history dependent rheology of the near surface as well as being able to model mantle convection, and, simultaneously, to be able to solve the numerical system efficiently. Underworld is a hybrid particle / mesh code reminiscent of the particle-in-cell techniques from the early 1960s. The Underworld team (*) was not the first to use this approach, nor the last, but the team does have considerable experience and much has been learned along the way. The use of a finite element method as the underlying "cell" in which the Lagrangian particles are embedded considerably reduces errors associated with mapping material properties to the cells. The particles are treated as moving quadrature points in computing the stiffness matrix integrals. The decoupling of deformation markers from computation points allows the use of structured meshes, efficient parallel decompositions, and simple-to-code geometric multigrid solution methods. For a 3D code such efficiencies are very important. The elegance of the method is that it can be completely described in a couple of sentences. However, there are some limitations: it is not obvious how to retain this elegance for unstructured or adaptive meshes, arbitrary element types are not sufficiently well integrated by the simple quadrature approach, and swarms of particles representing volumes are usually an inefficient representation of surfaces. This will be discussed ! (*) Although not formally constituted, my co-conspirators in this exercise are listed as the Underworld team and I will reveal their true identities on the day.

A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

DOE PAGES

Charest, Marc R.J.; Canfield, Thomas R.; Morgan, Nathaniel R.; ...

2015-03-11

High-order discretization methods offer the potential to reduce the computational cost associated with modeling compressible flows. However, it is difficult to obtain accurate high-order discretizations of conservation laws that do not produce spurious oscillations near discontinuities, especially on multi-dimensional unstructured meshes. A novel, high-order, central essentially non-oscillatory (CENO) finite-volume method that does not have these difficulties is proposed for tetrahedral meshes. The proposed unstructured method is vertex-based, which differs from existing cell-based CENO formulations, and uses a hybrid reconstruction procedure that switches between two different solution representations. It applies a high-order k-exact reconstruction in smooth regions and a limited linearmore » reconstruction when discontinuities are encountered. Both reconstructions use a single, central stencil for all variables, making the application of CENO to arbitrary unstructured meshes relatively straightforward. The new approach was applied to the conservation equations governing compressible flows and assessed in terms of accuracy and computational cost. For all problems considered, which included various function reconstructions and idealized flows, CENO demonstrated excellent reliability and robustness. Up to fifth-order accuracy was achieved in smooth regions and essentially non-oscillatory solutions were obtained near discontinuities. The high-order schemes were also more computationally efficient for high-accuracy solutions, i.e., they took less wall time than the lower-order schemes to achieve a desired level of error. In one particular case, it took a factor of 24 less wall-time to obtain a given level of error with the fourth-order CENO scheme than to obtain the same error with the second-order scheme.« less

Near-Surface Profiles of Water Stable Isotope Components and Indicated Transitional History of Ice-Wedge Polygons Near Barrow

NASA Astrophysics Data System (ADS)

Iwahana, G.; Wilson, C.; Newman, B. D.; Heikoop, J. M.; Busey, R.

2017-12-01

Wetlands associated with ice-wedge polygons are commonly distributed across the Arctic Coastal Plain of northern Alaska, a region underlain by continuous permafrost. Micro-topography of the ice-wedge polygons controls local hydrology, and the micro-topography could be altered due to factors such like surface vegetation, wetness, freeze-thaw cycles, and permafrost degradation/aggradation under climate change. Understanding status of the wetlands in the near future is important because it determines biogeochemical cycle, which drives release of greenhouse gases from the ground. However, transitional regime of the ice-wedge polygons under the changing climate is not fully understood. In this study, we analyzed geochemistry of water extracted from frozen soil cores sampled down to about 1m depth in 2014 March at NGEE-Arctic sites in the Barrow Environmental Observatory. The cores were sampled from troughs/rims/centers of five different low-centered or flat-centered polygons. The frozen cores are divided into 5-10cm cores for each location, thawed in sealed plastic bags, and then extracted water was stored in vials. Comparison between the profiles of geochemistry indicated connection of soil water in the active layer at different location in a polygon, while it revealed that distinctly different water has been stored in permafrost layer at troughs/rims/centers of some polygons. Profiles of volumetric water content (VWC) showed clear signals of freeze-up desiccation in the middle of saturated active layers as low VWC anomalies at most sampling points. Water in the active layer and near-surface permafrost was classified into four categories: ice wedge / fresh meteoric / transitional / highly fractionated water. The overall results suggested prolonged separation of water in the active layer at the center of low-centered polygons without lateral connection in water path in the past.

Structural characterization of the packings of granular regular polygons.

PubMed

Wang, Chuncheng; Dong, Kejun; Yu, Aibing

2015-12-01

By using a recently developed method for discrete modeling of nonspherical particles, we simulate the random packings of granular regular polygons with three to 11 edges under gravity. The effects of shape and friction on the packing structures are investigated by various structural parameters, including packing fraction, the radial distribution function, coordination number, Voronoi tessellation, and bond-orientational order. We find that packing fraction is generally higher for geometrically nonfrustrated regular polygons, and can be increased by the increase of edge number and decrease of friction. The changes of packing fraction are linked with those of the microstructures, such as the variations of the translational and orientational orders and local configurations. In particular, the free areas of Voronoi tessellations (which are related to local packing fractions) can be described by log-normal distributions for all polygons. The quantitative analyses establish a clearer picture for the packings of regular polygons.

Polygons near Lyot Crater

NASA Technical Reports Server (NTRS)

2003-01-01

MGS MOC Release No. MOC2-564, 4 December 2003

This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows patterned ground, arranged in the form of polygons, on the undulating plains associated with ejecta from the Lyot impact crater on the martian northern plains. This picture was acquired in October 2003 and shows that the polygon margins are ridges with large boulders--shown here as dark dots--on them. On Earth, polygon patterns like this are created in arctic and antarctic regions where there is ice in the ground. The seasonal and longer-term cycles of freezing and thawing of the ice-rich ground cause these features to form over time. Whether the same is true for Mars is unknown. The polygons are located near 54.6oN, 326.6oW. The image covers an area 3 km (1.9 mi) wide and is illuminated from the lower left.

FAST TRACK COMMUNICATION: The unusual asymptotics of three-sided prudent polygons

NASA Astrophysics Data System (ADS)

Beaton, Nicholas R.; Flajolet, Philippe; Guttmann, Anthony J.

2010-08-01

We have studied the area-generating function of prudent polygons on the square lattice. Exact solutions are obtained for the generating function of two-sided and three-sided prudent polygons, and a functional equation is found for four-sided prudent polygons. This is used to generate series coefficients in polynomial time, and these are analysed to determine the asymptotics numerically. A careful asymptotic analysis of the three-sided polygons produces a most surprising result. A transcendental critical exponent is found, and the leading amplitude is not quite a constant, but is a constant plus a small oscillatory component with an amplitude approximately 10-8 times that of the leading amplitude. This effect cannot be seen by any standard numerical analysis, but it may be present in other models. If so, it changes our whole view of the asymptotic behaviour of lattice models.

Microfracturing and fluid pathways in serpentinizing abyssal peridotites along the Southwest Indian Ridge (62°-65°E)

NASA Astrophysics Data System (ADS)

Rouméjon, S.; Cannat, M.; Agrinier, P.; Godard, M.; Andreani, M.

2013-12-01

At slow spreading ridges, axial detachment faults exhume mantle-derived peridotites. Their interaction with seawater-derived hydrothermal fluids causes serpentinization down to 2-3km from the fault, as inferred from seismic velocity models. It is commonly proposed that fractures allow penetration of seawater into the fault's footwall. At the microscopic scale, the hydration front progresses from a microfracture network toward the center of olivine relicts and forms the serpentine mesh texture. The origin of these microfractures is a matter of debate: tectonic, anisotropic thermal contraction of olivine during peridotite cooling or hierarchical fracturing of the olivine due to volume increase during serpentinization. In this presentation we use petrology and geochemistry to analyze the links between microfractures and serpentinization in a set of highly serpentinized peridotites dredged along the melt-starved easternmost part of the Southwest Indian Ridge (Smoothseafloor cruise). Our observations suggest that thermal contraction of olivine combines with tectonic stresses to fracture fresh peridotite in the brittle lithosphere. These ~60μm-spaced microfractures constitute the initial sample-scale permeability network for fluid penetration, onset of serpentinization and formation of additional hierarchical fractures. As serpentinization proceeds, the volume increase closes the least-developed planes and preferential pathways for fluid circulation become more distant, forming the 200-500μm-wide polygonal pattern typical of the serpentine mesh texture. In about 20% of the recovered samples the mesh serpentine is partially recrystallized forming rims next to later microfractures and serpentine veins. The spacing of these rims, and the limited proportion of affected samples suggest that the scales of the efficient permeability network in the serpentinites at this stage had increased to decimetric and greater scales. We use geochemical constrains to derive temperature conditions associated with this serpentinization history and to discuss the nature of serpentinizing fluids, based on a comparison with published work on serpentinites from the Mid-Atlantic Ridge. δ18O values decrease from 5.98‰ to 1.91‰, from mesh texture serpentine to the later recrystallized serpentines. These values probably correspond to temperatures on the order of 200-300°C and to a progressive equilibration with serpentinizing fluid values due to increasing water-rock ratios. Fluid-rock interactions produce serpentine minerals that are enriched in fluid-mobile elements (B, As, Sb, U, Cu) compared to primary minerals in the peridotites and present occasional Eu anomalies that may reflect variable redox conditions during serpentinization.

Verification of transport equations in a general purpose commercial CFD code.

NASA Astrophysics Data System (ADS)

Melot, Matthieu; Nennemann, Bernd; Deschênes, Claire

2016-11-01

In this paper, the Verification and Validation methodology is presented. This method aims to increase the reliability and the trust that can be placed into complex CFD simulations. The first step of this methodology, the code verification is presented in greater details. The CFD transport equations in steady state, transient and Arbitrary Eulerian Lagrangian (ALE, used for transient moving mesh) formulations in Ansys CFX are verified. It is shown that the expected spatial and temporal order of convergence are achieved for the steady state and the transient formulations. Unfortunately this is not completely the case for the ALE formulation. As for a lot of other commercial and in-house CFD codes, the temporal convergence of the velocity is limited to a first order where a second order would have been expected.

A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields. I - An extended DKT element for thick-plate bending analysis. II - An extended DKQ element for thick-plate bending analysis

NASA Astrophysics Data System (ADS)

Katili, Irwan

1993-06-01

A new three-node nine-degree-of-freedom triangular plate bending element is proposed which is valid for the analysis of both thick and thin plates. The element, called the discrete Kirchhoff-Mindlin triangle (DKMT), has a proper rank, passes the patch test for thin and thick plates in an arbitrary mesh, and is free of shear locking. As an extension of the DKMT element, a four-node element with 3 degrees of freedom per node is developed. The element, referred to as DKMQ (discrete Kirchhoff-Mindlin quadrilateral) is found to provide good results for both thin and thick plates without any compatibility problems.

On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

NASA Astrophysics Data System (ADS)

Hu, Zixi; Yao, Zhewei; Li, Jinglai

2017-03-01

Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

Surface tension models for a multi-material ALE code with AMR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Wangyi; Koniges, Alice; Gott, Kevin

A number of surface tension models have been implemented in a 3D multi-physics multi-material code, ALE–AMR, which combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR). ALE–AMR is unique in its ability to model hot radiating plasmas, cold fragmenting solids, and most recently, the deformation of molten material. The surface tension models implemented include a diffuse interface approach with special numerical techniques to remove parasitic flow and a height function approach in conjunction with a volume-fraction interface reconstruction package. These surface tension models are benchmarked with a variety of test problems. In conclusion, based on the results, themore » height function approach using volume fractions was chosen to simulate droplet dynamics associated with extreme ultraviolet (EUV) lithography.« less

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Greengard, Leslie F; Waag, Robert C

2010-02-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators

PubMed Central

Hesford, Andrew J.; Astheimer, Jeffrey P.; Greengard, Leslie F.; Waag, Robert C.

2010-01-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method. PMID:20136208

Surface tension models for a multi-material ALE code with AMR

DOE PAGES

Liu, Wangyi; Koniges, Alice; Gott, Kevin; ...

2017-06-01

A number of surface tension models have been implemented in a 3D multi-physics multi-material code, ALE–AMR, which combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR). ALE–AMR is unique in its ability to model hot radiating plasmas, cold fragmenting solids, and most recently, the deformation of molten material. The surface tension models implemented include a diffuse interface approach with special numerical techniques to remove parasitic flow and a height function approach in conjunction with a volume-fraction interface reconstruction package. These surface tension models are benchmarked with a variety of test problems. In conclusion, based on the results, themore » height function approach using volume fractions was chosen to simulate droplet dynamics associated with extreme ultraviolet (EUV) lithography.« less

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data.

PubMed

Suresh, Niraj; Stephens, Sean A; Adams, Lexor; Beck, Anthon N; McKinney, Adriana L; Varga, Tamas

2016-04-26

Plant roots play a critical role in plant-soil-microbe interactions that occur in the rhizosphere, as well as processes with important implications to climate change and crop management. Quantitative size information on roots in their native environment is invaluable for studying root growth and environmental processes involving plants. X-ray computed tomography (XCT) has been demonstrated to be an effective tool for in situ root scanning and analysis. We aimed to develop a costless and efficient tool that approximates the surface and volume of the root regardless of its shape from three-dimensional (3D) tomography data. The root structure of a Prairie dropseed (Sporobolus heterolepis) specimen was imaged using XCT. The root was reconstructed, and the primary root structure was extracted from the data using a combination of licensed and open-source software. An isosurface polygonal mesh was then created for ease of analysis. We have developed the standalone application imeshJ, generated in MATLAB(1), to calculate root volume and surface area from the mesh. The outputs of imeshJ are surface area (in mm(2)) and the volume (in mm(3)). The process, utilizing a unique combination of tools from imaging to quantitative root analysis, is described. A combination of XCT and open-source software proved to be a powerful combination to noninvasively image plant root samples, segment root data, and extract quantitative information from the 3D data. This methodology of processing 3D data should be applicable to other material/sample systems where there is connectivity between components of similar X-ray attenuation and difficulties arise with segmentation.

Finding the Maximal Area of Bounded Polygons in a Circle

ERIC Educational Resources Information Center

Rokach, Arie

2005-01-01

The article deals with the area of polygons that are inscribed in a given circle. Naturally, the following question arises: Among all n-polygons that are inscribed in a given circle, which one has the biggest area? Intuitively, it may be guessed that is suitable for secondary students, and without any use id calculus, but only using very…

ON THE THEORY AND PROCEDURE FOR CONSTRUCTING A MINIMAL-LENGTH, AREA-CONSERVING FREQUENCY POLYGON FROM GROUPED DATA.

ERIC Educational Resources Information Center

CASE, C. MARSTON

THIS PAPER IS CONCERNED WITH GRAPHIC PRESENTATION AND ANALYSIS OF GROUPED OBSERVATIONS. IT PRESENTS A METHOD AND SUPPORTING THEORY FOR THE CONSTRUCTION OF AN AREA-CONSERVING, MINIMAL LENGTH FREQUENCY POLYGON CORRESPONDING TO A GIVEN HISTOGRAM. TRADITIONALLY, THE CONCEPT OF A FREQUENCY POLYGON CORRESPONDING TO A GIVEN HISTOGRAM HAS REFERRED TO THAT…

Polygons on Crater Floor

NASA Technical Reports Server (NTRS)

2003-01-01

MGS MOC Release No. MOC2-357, 11 May 2003

This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) picture shows a pattern of polygons on the floor of a northern plains impact crater. These landforms are common on crater floors at high latitudes on Mars. Similar polygons occur in the arctic and antarctic regions of Earth, where they indicate the presence and freeze-thaw cycling of ground ice. Whether the polygons on Mars also indicate water ice in the ground is uncertain. The image is located in a crater at 64.8oN, 292.7oW. Sunlight illuminates the scene from the lower left.

Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons

PubMed Central

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2012-01-01

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π. PMID:24027379

Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2013-08-01

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.

A Polygon Model for Wireless Sensor Network Deployment with Directional Sensing Areas

PubMed Central

Wu, Chun-Hsien; Chung, Yeh-Ching

2009-01-01

The modeling of the sensing area of a sensor node is essential for the deployment algorithm of wireless sensor networks (WSNs). In this paper, a polygon model is proposed for the sensor node with directional sensing area. In addition, a WSN deployment algorithm is presented with topology control and scoring mechanisms to maintain network connectivity and improve sensing coverage rate. To evaluate the proposed polygon model and WSN deployment algorithm, a simulation is conducted. The simulation results show that the proposed polygon model outperforms the existed disk model and circular sector model in terms of the maximum sensing coverage rate. PMID:22303159

Mola Topography Supports Drape-Folding Models for Polygonal Terrain of Utopia Planitia, Mars

NASA Technical Reports Server (NTRS)

McGill, George E.; Buczkowski, D. L.

2002-01-01

One of the most important questions we ask about Mars is whether or not there have ever been large bodies of standing water on the surface. The polygonal terrains of Utopia and Acidalia Planitiae are located in the lowest parts of the northern lowlands, the most logical places for water to pond and sediments to accumulate. Showing that polygonal terrain is sedimentary in origin would represent strong evidence in favor of a northern ocean. A number of hypotheses for the origin of the giant martian polygons have been proposed, from the cooling of lava to frost wedging to the desiccation of wet sediments, but Pechman showed that none of these familiar processes could be scaled up to martian dimensions. Two models for polygon origin attempt to explain the scale of the martian polygons by postulating drape folding of a cover material, either sedimentary or volcanic, over an uneven, buried surface. The drape folding would produce bending stresses in the surface layers that increase the probability of Fracturing over drape anticlines and suppress the probability of fracturing over drape synclines. However, both models require an additional source of extensional strain to produce the total strain needed to produce the observed troughs.

Sampling large random knots in a confined space

NASA Astrophysics Data System (ADS)

Arsuaga, J.; Blackstone, T.; Diao, Y.; Hinson, K.; Karadayi, E.; Saito, M.

2007-09-01

DNA knots formed under extreme conditions of condensation, as in bacteriophage P4, are difficult to analyze experimentally and theoretically. In this paper, we propose to use the uniform random polygon model as a supplementary method to the existing methods for generating random knots in confinement. The uniform random polygon model allows us to sample knots with large crossing numbers and also to generate large diagrammatically prime knot diagrams. We show numerically that uniform random polygons sample knots with large minimum crossing numbers and certain complicated knot invariants (as those observed experimentally). We do this in terms of the knot determinants or colorings. Our numerical results suggest that the average determinant of a uniform random polygon of n vertices grows faster than O(e^{n^2}) . We also investigate the complexity of prime knot diagrams. We show rigorously that the probability that a randomly selected 2D uniform random polygon of n vertices is almost diagrammatically prime goes to 1 as n goes to infinity. Furthermore, the average number of crossings in such a diagram is at the order of O(n2). Therefore, the two-dimensional uniform random polygons offer an effective way in sampling large (prime) knots, which can be useful in various applications.

A finite-time exponent for random Ehrenfest gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moudgalya, Sanjay; Chandra, Sarthak; Jain, Sudhir R., E-mail: srjain@barc.gov.in

2015-10-15

We consider the motion of a system of free particles moving on a plane with regular hard polygonal scatterers arranged in a random manner. Calling this the Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a finite-time exponent to characterize its dynamics. As the number of sides of the polygon goes to infinity, when polygon tends to a circle, we recover the usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To obtain this result, we generalize the reflection law of a beam of rays incident on a polygonal scatterer in amore » way that the formula for the circular scatterer is recovered in the limit of infinite number of vertices. Thus, chaos emerges from pseudochaos in an appropriate limit. - Highlights: • We present a finite-time exponent for particles moving in a plane containing polygonal scatterers. • The exponent found recovers the Lyapunov exponent in the limit of the polygon becoming a circle. • Our findings unify pseudointegrable and chaotic scattering via a generalized collision rule. • Stretch and fold:shuffle and cut :: Lyapunov:finite-time exponent :: fluid:granular mixing.« less

The UF family of reference hybrid phantoms for computational radiation dosimetry

NASA Astrophysics Data System (ADS)

Lee, Choonsik; Lodwick, Daniel; Hurtado, Jorge; Pafundi, Deanna; Williams, Jonathan L.; Bolch, Wesley E.

2010-01-01

Computational human phantoms are computer models used to obtain dose distributions within the human body exposed to internal or external radiation sources. In addition, they are increasingly used to develop detector efficiencies for in vivo whole-body counters. Two classes of computational human phantoms have been widely utilized for dosimetry calculation: stylized and voxel phantoms that describe human anatomy through mathematical surface equations and 3D voxel matrices, respectively. Stylized phantoms are flexible in that changes to organ position and shape are possible given avoidance of region overlap, while voxel phantoms are typically fixed to a given patient anatomy, yet can be proportionally scaled to match individuals of larger or smaller stature, but of equivalent organ anatomy. Voxel phantoms provide much better anatomical realism as compared to stylized phantoms which are intrinsically limited by mathematical surface equations. To address the drawbacks of these phantoms, hybrid phantoms based on non-uniform rational B-spline (NURBS) surfaces have been introduced wherein anthropomorphic flexibility and anatomic realism are both preserved. Researchers at the University of Florida have introduced a series of hybrid phantoms representing the ICRP Publication 89 reference newborn, 15 year, and adult male and female. In this study, six additional phantoms are added to the UF family of hybrid phantoms—those of the reference 1 year, 5 year and 10 year child. Head and torso CT images of patients whose ages were close to the targeted ages were obtained under approved protocols. Major organs and tissues were segmented from these images using an image processing software, 3D-DOCTOR™. NURBS and polygon mesh surfaces were then used to model individual organs and tissues after importing the segmented organ models to the 3D NURBS modeling software, Rhinoceros™. The phantoms were matched to four reference datasets: (1) standard anthropometric data, (2) reference organ masses from ICRP Publication 89, (3) reference elemental compositions provided in ICRP 89 as well as ICRU Report 46, and (4) reference data on the alimentary tract organs given in ICRP Publications 89 and 100. Various adjustments and refinements to the organ systems of the previously described newborn, 15 year and adult phantoms are also presented. The UF series of hybrid phantoms retain the non-uniform scalability of stylized phantoms while maintaining the anatomical realism of patient-specific voxel phantoms with respect to organ shape, depth and inter-organ distance. While the final versions of these phantoms are in a voxelized format for radiation transport simulation, their primary format is given as NURBS and polygon mesh surfaces, thus permitting one to sculpt non-reference phantoms using the reference phantoms as an anatomic template.

Clusters in irregular areas and lattices.

PubMed

Wieczorek, William F; Delmerico, Alan M; Rogerson, Peter A; Wong, David W S

2012-01-01

Geographic areas of different sizes and shapes of polygons that represent counts or rate data are often encountered in social, economic, health, and other information. Often political or census boundaries are used to define these areas because the information is available only for those geographies. Therefore, these types of boundaries are frequently used to define neighborhoods in spatial analyses using geographic information systems and related approaches such as multilevel models. When point data can be geocoded, it is possible to examine the impact of polygon shape on spatial statistical properties, such as clustering. We utilized point data (alcohol outlets) to examine the issue of polygon shape and size on visualization and statistical properties. The point data were allocated to regular lattices (hexagons and squares) and census areas for zip-code tabulation areas and tracts. The number of units in the lattices was set to be similar to the number of tract and zip-code areas. A spatial clustering statistic and visualization were used to assess the impact of polygon shape for zip- and tract-sized units. Results showed substantial similarities and notable differences across shape and size. The specific circumstances of a spatial analysis that aggregates points to polygons will determine the size and shape of the areal units to be used. The irregular polygons of census units may reflect underlying characteristics that could be missed by large regular lattices. Future research to examine the potential for using a combination of irregular polygons and regular lattices would be useful.

Image segmentation by hierarchial agglomeration of polygons using ecological statistics

DOEpatents

Prasad, Lakshman; Swaminarayan, Sriram

2013-04-23

A method for rapid hierarchical image segmentation based on perceptually driven contour completion and scene statistics is disclosed. The method begins with an initial fine-scale segmentation of an image, such as obtained by perceptual completion of partial contours into polygonal regions using region-contour correspondences established by Delaunay triangulation of edge pixels as implemented in VISTA. The resulting polygons are analyzed with respect to their size and color/intensity distributions and the structural properties of their boundaries. Statistical estimates of granularity of size, similarity of color, texture, and saliency of intervening boundaries are computed and formulated into logical (Boolean) predicates. The combined satisfiability of these Boolean predicates by a pair of adjacent polygons at a given segmentation level qualifies them for merging into a larger polygon representing a coarser, larger-scale feature of the pixel image and collectively obtains the next level of polygonal segments in a hierarchy of fine-to-coarse segmentations. The iterative application of this process precipitates textured regions as polygons with highly convolved boundaries and helps distinguish them from objects which typically have more regular boundaries. The method yields a multiscale decomposition of an image into constituent features that enjoy a hierarchical relationship with features at finer and coarser scales. This provides a traversable graph structure from which feature content and context in terms of other features can be derived, aiding in automated image understanding tasks. The method disclosed is highly efficient and can be used to decompose and analyze large images.

Content-aware automatic cropping for consumer photos

NASA Astrophysics Data System (ADS)

Tang, Hao; Tretter, Daniel; Lin, Qian

2013-03-01

Consumer photos are typically authored once, but need to be retargeted for reuse in various situations. These include printing a photo on different size paper, changing the size and aspect ratio of an embedded photo to accommodate the dynamic content layout of web pages or documents, adapting a large photo for browsing on small displays such as mobile phone screens, and improving the aesthetic quality of a photo that was badly composed at the capture time. In this paper, we propose a novel, effective, and comprehensive content-aware automatic cropping (hereafter referred to as "autocrop") method for consumer photos to achieve the above purposes. Our autocrop method combines the state-of-the-art context-aware saliency detection algorithm, which aims to infer the likely intent of the photographer, and the "branch-and-bound" efficient subwindow search optimization technique, which seeks to locate the globally optimal cropping rectangle in a fast manner. Unlike most current autocrop methods, which can only crop a photo into an arbitrary rectangle, our autocrop method can automatically crop a photo into either a rectangle of arbitrary dimensions or a rectangle of the desired aspect ratio specified by the user. The aggressiveness of the cropping operation may be either automatically determined by the method or manually indicated by the user with ease. In addition, our autocrop method is extended to support the cropping of a photo into non-rectangular shapes such as polygons of any number of sides. It may also be potentially extended to return multiple cropping suggestions, which will enable the creation of new photos to enrich the original photo collections. Our experimental results show that the proposed autocrop method in this paper can generate high-quality crops for consumer photos of various types.

Self-assembly of a constitutional dynamic library of Cu(II) coordination polygons and reversible sorting by crystallization.

PubMed

Rancan, Marzio; Tessarolo, Jacopo; Zanonato, Pier Luigi; Seraglia, Roberta; Quici, Silvio; Armelao, Lidia

2013-06-07

A small coordination constitutional dynamic library (CDL) is self-assembled from Cu(2+) ions and the ortho bis-(3-acetylacetone)benzene ligand. Two coordination polygons, a rhomboid and a triangle, establish a dynamic equilibrium. Quantitative sorting of the rhomboidal polygon is reversibly obtained by crystallization. Thermodynamic and kinetic aspects ruling the CDL system have been elucidated.

The Effect of Inquiry-Based Explorations in a Dynamic Geometry Environment on Sixth Grade Students' Achievements in Polygons

ERIC Educational Resources Information Center

Erbas, Ayhan Kursat; Yenmez, Arzu Aydogan

2011-01-01

The purpose of this study was to investigate the effects of using a dynamic geometry environment (DGE) together with inquiry-based explorations on the sixth grade students' achievements in polygons and congruency and similarity of polygons. Two groups of sixth grade students were selected for this study: an experimental group composed of 66…

Frosty Polygons

NASA Technical Reports Server (NTRS)

2004-01-01

16 January 2004 Looking somewhat like a roadmap, this 3 km (1.9 mi) wide view of a cratered plain in the martian south polar region shows a plethora of cracks that form polygonal patterns. This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image is located near 78.9oS, 357.3oW. Polygons such as these, where they are found on Earth, would be indicators of the presence of subsurface ice. Whether the same is true for Mars is uncertain. What is certain is that modern, seasonal frost on the surface enhances the appearance of the polygons as the frost persists longer in the cracks than on adjacent plains. This southern springtime image is illuminated by sunlight from the upper left.

Secondary Emission Calorimeter Sensor Development

NASA Astrophysics Data System (ADS)

Winn, David R.; Onel, Yasar

2012-12-01

In a Secondary Emission electron(SEe) detector module, Secondary Emission electrons (SEe) are generated from an SE surface/cathode, when charged hadronic or electromagnetic particles, particularly shower particles, penetrate an SE sampling module placed between absorber materials (Fe, Cu, Pb, W etc) in calorimeters. The SE cathode is a thin (10-50 nm thick) film (simple metal-oxides, or other higher yield materials) on the surface of a metal plate, which serves as the entrance “window” to a compact vacuum vessel (metal or metal-ceramic); this SE film cathode is analogous to a photocathode, and the SEe are similar to p.e., which are then amplified by dynodes, also is in a PMT. SE sensor modules can make use of electrochemically etched/machined or laser-cut metal mesh dynode sheets, as large as ~30 cm square, to amplify the Secondary Emission Electrons (SEe), much like those that compact metal mesh or mesh dynode PMT's use to amplify p.e.'s. The construction requirements easier than a PMT, since the entire final assembly can be done in air; there are no critical controlled thin film depositions, cesiation or other oxygen-excluded processes or other required vacuum activation, and consequently bake-out can be a refractory temperatures; the module is sealed by normal vacuum techniques (welding or brazing or other high temperature joinings), with a simple final heated vacuum pump-out and tip-off. The modules envisioned are compact, high gain, high speed, exceptionally radiation damage resistant, rugged, and cost effective, and can be fabricated in arbitrary tileable shapes. The SE sensor module anodes can be segmented transversely to sizes appropriate to reconstruct electromagnetic cores with high precision. The GEANT4 and existing calorimeter data estimated calorimeter response performance is between 35-50 Secondary Emission electrons per GeV, in a 1 cm thick Cu absorber calorimeter, with a gain per SEe > 105 per SEe, and an e/pi<1.2. The calorimeter pulse width is estimated to be <15 ns. With fine mesh sampling only (no thick absorbers) the resolution is ~25 MeV at 1 GeV.

Self-Assembly of Flux-Closure Polygons from Magnetite Nanocubes.

PubMed

Szyndler, Megan W; Corn, Robert M

2012-09-06

Well-defined nanoscale flux-closure polygons (nanogons) have been fabricated on hydrophilic surfaces from the face-to-face self-assembly of magnetite nanocubes. Uniform ferrimagnetic magnetite nanocubes (∼86 nm) were synthesized and characterized with a combination of electron microscopy, diffraction, and magnetization measurements. The nanocubes were subsequently cast onto hydrophilic substrates, wherein the cubes lined up face-to-face and formed a variety of polygons due to magnetostatic and hydrophobic interactions. The generated surfaces consist primarily of three- and four-sided nanogons; polygons ranging from two to six sides were also observed. Further examination of the nanogons showed that the constraints of the face-to-face assembly of nanocubes often led to bowed sides, strained cube geometries, and mismatches at the acute angle vertices. Additionally, extra nanocubes were often present at the vertices, suggesting the presence of external magnetostatic fields at the polygon corners. These nanogons are inimitable nanoscale magnetic structures with potential applications in the areas of magnetic memory storage and high-frequency magnetics.

Total curvature and total torsion of knotted random polygons in confinement

NASA Astrophysics Data System (ADS)

Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta

2018-04-01

Knots in nature are typically confined spatially. The confinement affects the possible configurations, which in turn affects the spectrum of possible knot types as well as the geometry of the configurations within each knot type. The goal of this paper is to determine how confinement, length, and knotting affect the total curvature and total torsion of random polygons. Previously published papers have investigated these effects in the unconstrained case. In particular, we analyze how the total curvature and total torsion are affected by (1) varying the length of polygons within a fixed confinement radius and (2) varying the confinement radius of polygons with a fixed length. We also compare the total curvature and total torsion of groups of knots with similar complexity (measured as crossing number). While some of our results fall in line with what has been observed in the studies of the unconfined random polygons, a few surprising results emerge from our study, showing some properties that are unique due to the effect of knotting in confinement.

Statistical and hydrodynamic properties of double-ring polymers with a fixed linking number between twin rings.

PubMed

Uehara, Erica; Deguchi, Tetsuo

2014-01-28

For a double-ring polymer in solution we evaluate the mean-square radius of gyration and the diffusion coefficient through simulation of off-lattice self-avoiding double polygons consisting of cylindrical segments with radius rex of unit length. Here, a self-avoiding double polygon consists of twin self-avoiding polygons which are connected by a cylindrical segment. We show numerically that several statistical and dynamical properties of double-ring polymers in solution depend on the linking number of the constituent twin ring polymers. The ratio of the mean-square radius of gyration of self-avoiding double polygons with zero linking number to that of no topological constraint is larger than 1, in particular, when the radius of cylindrical segments rex is small. However, the ratio is almost constant with respect to the number of vertices, N, and does not depend on N. The large-N behavior of topological swelling is thus quite different from the case of knotted random polygons.

Knot probability of polygons subjected to a force: a Monte Carlo study

NASA Astrophysics Data System (ADS)

Janse van Rensburg, E. J.; Orlandini, E.; Tesi, M. C.; Whittington, S. G.

2008-01-01

We use Monte Carlo methods to study the knot probability of lattice polygons on the cubic lattice in the presence of an external force f. The force is coupled to the span of the polygons along a lattice direction, say the z-direction. If the force is negative polygons are squeezed (the compressive regime), while positive forces tend to stretch the polygons along the z-direction (the tensile regime). For sufficiently large positive forces we verify that the Pincus scaling law in the force-extension curve holds. At a fixed number of edges n the knot probability is a decreasing function of the force. For a fixed force the knot probability approaches unity as 1 - exp(-α0(f)n + o(n)), where α0(f) is positive and a decreasing function of f. We also examine the average of the absolute value of the writhe and we verify the square root growth law (known for f = 0) for all values of f.

Point-in-convex polygon and point-in-convex polyhedron algorithms with O(1) complexity using space subdivision

NASA Astrophysics Data System (ADS)

Skala, Vaclav

2016-06-01

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In the case of convex polygon in E2 a simple Point-in-Polygon test is of the O(N) complexity and the optimal algorithm is of O(log N) computational complexity. In the E3 case, the complexity is O(N) even for the convex polyhedron as no ordering is defined. New Point-in-Convex Polygon and Point-in-Convex Polyhedron algorithms are presented based on space subdivision in the preprocessing stage resulting to O(1) run-time complexity. The presented approach is simple to implement. Due to the principle of duality, dual problems, e.g. line-convex polygon, line clipping, can be solved in a similarly.

Polygonal shaft hole rotor

DOEpatents

Hussey, John H.; Rose, John Scott; Meystrik, Jeffrey J.; White, Kent Lee

2001-01-23

A laminated rotor for an induction motor has a plurality of ferro-magnetic laminations mounted axially on a rotor shaft. Each of the plurality of laminations has a central aperture in the shape of a polygon with sides of equal length. The laminations are alternatingly rotated 180.degree. from one another so that the straight sides of the polygon shaped apertures are misaligned. As a circular rotor shaft is press fit into a stack of laminations, the point of maximum interference occurs at the midpoints of the sides of the polygon (i.e., at the smallest radius of the central apertures of the laminations). Because the laminates are alternatingly rotated, the laminate material at the points of maximum interference yields relatively easily into the vertices (i.e., the greatest radius of the central aperture) of the polygonal central aperture of the next lamination as the shaft is inserted into the stack of laminations. Because of this yielding process, the amount of force required to insert the shaft is reduced, and a tighter fit is achieved.

Generating equilateral random polygons in confinement

NASA Astrophysics Data System (ADS)

Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U.

2011-10-01

One challenging problem in biology is to understand the mechanism of DNA packing in a confined volume such as a cell. It is known that confined circular DNA is often knotted and hence the topology of the extracted (and relaxed) circular DNA can be used as a probe of the DNA packing mechanism. However, in order to properly estimate the topological properties of the confined circular DNA structures using mathematical models, it is necessary to generate large ensembles of simulated closed chains (i.e. polygons) of equal edge lengths that are confined in a volume such as a sphere of certain fixed radius. Finding efficient algorithms that properly sample the space of such confined equilateral random polygons is a difficult problem. In this paper, we propose a method that generates confined equilateral random polygons based on their probability distribution. This method requires the creation of a large database initially. However, once the database has been created, a confined equilateral random polygon of length n can be generated in linear time in terms of n. The errors introduced by the method can be controlled and reduced by the refinement of the database. Furthermore, our numerical simulations indicate that these errors are unbiased and tend to cancel each other in a long polygon.

Polygonal Craters on Dwarf-Planet Ceres

NASA Astrophysics Data System (ADS)

Otto, K. A.; Jaumann, R.; Krohn, K.; Buczkowski, D. L.; von der Gathen, I.; Kersten, E.; Mest, S. C.; Preusker, F.; Roatsch, T.; Schenk, P. M.; Schröder, S.; Schulzeck, F.; Scully, J. E. C.; Stepahn, K.; Wagner, R.; Williams, D. A.; Raymond, C. A.; Russell, C. T.

2015-10-01

With approximately 950 km diameter and a mass of #1/3 of the total mass of the asteroid belt, (1) Ceres is the largest and most massive object in the Main Asteroid Belt. As an intact proto-planet, Ceres is key to understanding the origin and evolution of the terrestrialplanets [1]. In particular, the role of water during planet formation is of interest, because the differentiated dwarf-planet is thought to possess a water rich mantle overlying a rocky core [2]. The Dawn space craft arrived at Ceres in March this year after completing its mission at (4) Vesta. At Ceres, the on-board Framing Camera (FC) collected image data which revealed a large variety of impact crater morphologies including polygonal craters (Figure 1). Polygonal craters show straight rim sections aligned to form an angular shape. They are commonly associated with fractures in the target material. Simple polygonal craters develop during the excavation stage when the excavation flow propagates faster along preexisting fractures [3, 5]. Complex polygonal craters adopt their shape during the modification stage when slumping along fractures is favoured [3]. Polygonal craters are known from a variety of planetary bodies including Earth [e.g. 4], the Moon [e.g. 5], Mars [e.g. 6], Mercury [e.g. 7], Venus [e.g. 8] and outer Solar System icy satellites [e.g. 9].

Methods for rapidly processing angular masks of next-generation galaxy surveys

NASA Astrophysics Data System (ADS)

Swanson, M. E. C.; Tegmark, Max; Hamilton, Andrew J. S.; Hill, J. Colin

2008-07-01

As galaxy surveys become larger and more complex, keeping track of the completeness, magnitude limit and other survey parameters as a function of direction on the sky becomes an increasingly challenging computational task. For example, typical angular masks of the Sloan Digital Sky Survey contain about N = 300000 distinct spherical polygons. Managing masks with such large numbers of polygons becomes intractably slow, particularly for tasks that run in time with a naive algorithm, such as finding which polygons overlap each other. Here we present a `divide-and-conquer' solution to this challenge: we first split the angular mask into pre-defined regions called `pixels', such that each polygon is in only one pixel, and then perform further computations, such as checking for overlap, on the polygons within each pixel separately. This reduces tasks to , and also reduces the important task of determining in which polygon(s) a point on the sky lies from to , resulting in significant computational speedup. Additionally, we present a method to efficiently convert any angular mask to and from the popular HEALPIX format. This method can be generically applied to convert to and from any desired spherical pixelization. We have implemented these techniques in a new version of the MANGLE software package, which is freely available at http://space.mit.edu/home/tegmark/mangle/, along with complete documentation and example applications. These new methods should prove quite useful to the astronomical community, and since MANGLE is a generic tool for managing angular masks on a sphere, it has the potential to benefit terrestrial mapmaking applications as well.

The polygonal model: A simple representation of biomolecules as a tool for teaching metabolism.

PubMed

Bonafe, Carlos Francisco Sampaio; Bispo, Jose Ailton Conceição; de Jesus, Marcelo Bispo

2018-01-01

Metabolism involves numerous reactions and organic compounds that the student must master to understand adequately the processes involved. Part of biochemical learning should include some knowledge of the structure of biomolecules, although the acquisition of such knowledge can be time-consuming and may require significant effort from the student. In this report, we describe the "polygonal model" as a new means of graphically representing biomolecules. This model is based on the use of geometric figures such as open triangles, squares, and circles to represent hydroxyl, carbonyl, and carboxyl groups, respectively. The usefulness of the polygonal model was assessed by undergraduate students in a classroom activity that consisted of "transforming" molecules from Fischer models to polygonal models and vice and versa. The survey was applied to 135 undergraduate Biology and Nursing students. Students found the model easy to use and we noted that it allowed identification of students' misconceptions in basic concepts of organic chemistry, such as in stereochemistry and organic groups that could then be corrected. The students considered the polygonal model easier and faster for representing molecules than Fischer representations, without loss of information. These findings indicate that the polygonal model can facilitate the teaching of metabolism when the structures of biomolecules are discussed. Overall, the polygonal model promoted contact with chemical structures, e.g. through drawing activities, and encouraged student-student dialog, thereby facilitating biochemical learning. © 2017 by The International Union of Biochemistry and Molecular Biology, 46(1):66-75, 2018. © 2017 The International Union of Biochemistry and Molecular Biology.

Stoichiometric control of multiple different tectons in coordination-driven self-assembly: preparation of fused metallacyclic polygons.

PubMed

Lee, Junseong; Ghosh, Koushik; Stang, Peter J

2009-09-02

We present a general strategy for the synthesis of stable, multicomponent fused polygon complexes in which coordination-driven self-assembly allows for single supramolecular species to be formed from multicomponent self-assembly and the shape of the obtained polygons can be controlled simply by changing the ratio of individual components. The compounds have been characterized by multinuclear NMR spectroscopy and electrospray ionization mass spectrometry.