Finite element solution of lubrication problems

NASA Technical Reports Server (NTRS)

Reddi, M. M.

1971-01-01

A variational formulation of the transient lubrication problem is presented and the corresponding finite element equations derived for three and six point triangles, and, four and eight point quadrilaterals. Test solutions for a one dimensional slider bearing used in validating the computer program are given. Utility of the method is demonstrated by a solution of the shrouded step bearing.

Electromagnetic synchronisation of clocks with finite separation in a rotating system

NASA Astrophysics Data System (ADS)

Cohen, J. M.; Moses, H. E.; Rosenblum, A.

1984-11-01

For clocks on the vertices of a triangle, it is shown that clock synchronisation using electromagnetic signals between finitely spaced clocks in a rotating frame leads to the same synchronization error as a closely spaced band of clocks along the same light path. In addition, the above result is generalized to n equally spaced clocks.

Available pressure amplitude of linear compressor based on phasor triangle model

NASA Astrophysics Data System (ADS)

Duan, C. X.; Jiang, X.; Zhi, X. Q.; You, X. K.; Qiu, L. M.

2017-12-01

The linear compressor for cryocoolers possess the advantages of long-life operation, high efficiency, low vibration and compact structure. It is significant to study the match mechanisms between the compressor and the cold finger, which determines the working efficiency of the cryocooler. However, the output characteristics of linear compressor are complicated since it is affected by many interacting parameters. The existing matching methods are simplified and mainly focus on the compressor efficiency and output acoustic power, while neglecting the important output parameter of pressure amplitude. In this study, a phasor triangle model basing on analyzing the forces of the piston is proposed. It can be used to predict not only the output acoustic power, the efficiency, but also the pressure amplitude of the linear compressor. Calculated results agree well with the measurement results of the experiment. By this phasor triangle model, the theoretical maximum output pressure amplitude of the linear compressor can be calculated simply based on a known charging pressure and operating frequency. Compared with the mechanical and electrical model of the linear compressor, the new model can provide an intuitionistic understanding on the match mechanism with faster computational process. The model can also explain the experimental phenomenon of the proportional relationship between the output pressure amplitude and the piston displacement in experiments. By further model analysis, such phenomenon is confirmed as an expression of the unmatched design of the compressor. The phasor triangle model may provide an alternative method for the compressor design and matching with the cold finger.

Construction of optimal 3-node plate bending triangles by templates

NASA Astrophysics Data System (ADS)

Felippa, C. A.; Militello, C.

A finite element template is a parametrized algebraic form that reduces to specific finite elements by setting numerical values to the free parameters. The present study concerns Kirchhoff Plate-Bending Triangles (KPT) with 3 nodes and 9 degrees of freedom. A 37-parameter template is constructed using the Assumed Natural Deviatoric Strain (ANDES). Specialization of this template includes well known elements such as DKT and HCT. The question addressed here is: can these parameters be selected to produce high performance elements? The study is carried out by staged application of constraints on the free parameters. The first stage produces element families satisfying invariance and aspect ratio insensitivity conditions. Application of energy balance constraints produces specific elements. The performance of such elements in benchmark tests is presently under study.

Explicit formulation of an anisotropic Allman/DKT 3-node thin triangular flat shell elements

NASA Astrophysics Data System (ADS)

Ertas, A.; Krafcik, J. T.; Ekwaro-Osire, S.

A simple, explicit formulation of the stiffness matrix for an anisotropic, 3-node, thin triangular, flat shell element in global coordinates is presented. An Allman triangle is used for membrane stiffness. The membrane stiffness matrix is explicitly derived by applying an Allman transformation to a Felippa 6-node linear strain triangle (LST). Bending stiffness is incorporated by the use of a discrete Kirchhoff triangle (DKT) bending triangle. Stiffness terms resulting from anisotropic membrane-bending coupling are included by integrating, in area coordinates, membrane and bending strain-displacement matrices.

YORP torques with 1D thermal model

NASA Astrophysics Data System (ADS)

Breiter, S.; Bartczak, P.; Czekaj, M.

2010-11-01

A numerical model of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect for objects defined in terms of a triangular mesh is described. The algorithm requires that each surface triangle can be handled independently, which implies the use of a 1D thermal model. Insolation of each triangle is determined by an optimized ray-triangle intersection search. Surface temperature is modelled with a spectral approach; imposing a quasi-periodic solution we replace heat conduction equation by the Helmholtz equation. Non-linear boundary conditions are handled by an iterative, fast Fourier transform based solver. The results resolve the question of the YORP effect in rotation rate independence on conductivity within the non-linear 1D thermal model regardless of the accuracy issues and homogeneity assumptions. A seasonal YORP effect in attitude is revealed for objects moving on elliptic orbits when a non-linear thermal model is used.

[Establishment of a 3D finite element model of human skull using MSCT images and mimics software].

PubMed

Huang, Ping; Li, Zheng-dong; Shao, Yu; Zou, Dong-hua; Liu, Ning-guo; Li, Li; Chen, Yuan-yuan; Wan, Lei; Chen, Yi-jiu

2011-02-01

To establish a human 3D finite element skull model, and to explore its value in biomechanics analysis. The cadaveric head was scanned and then 3D skull model was created using Mimics software based on 2D CT axial images. The 3D skull model was optimized by preprocessor along with creation of the surface and volume meshes. The stress changes, after the head was struck by an object or the head hit the ground directly, were analyzed using ANSYS software. The original 3D skull model showed a large number of triangles with a poor quality and high similarity with the real head, while the optimized model showed high quality surface and volume meshes with a small number of triangles comparatively. The model could show the local and global stress changes effectively. The human 3D skull model can be established using MSCT and Mimics software and provides a good finite element model for biomechanics analysis. This model may also provide a base for the study of head stress changes following different forces.

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.

Some constructions on total labelling of m triangles

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

Voon, Chen Huey, E-mail: chenhv@utar.edu.my; Hui, Liew How, E-mail: liewhh@utar.edu.my; How, Yim Kheng, E-mail: tidusyimhome@hotmail.com

2016-06-02

Let mK{sub 3} = (V{sub m}, E{sub m}) be a finite disconnected graph consisting of m disjoint triangles K{sub 3}, where V{sub m} is the set of vertices, E{sub m} is the set of edges and both V{sub m} and E{sub m} are of the same size 3m. A total labelling of mK{sub 3} is a function f which maps the elements in V{sub m} and E{sub m} to positive integer values, i.e. f : V{sub m} ∪ E{sub m} → {1, 2, 3,···}. Let c be a positive integer. A triangle is said have a c-Erdősian triangle labelling ifmore » it is a total labelling f : V{sub m} ∪ E{sub m} → {c, c + 1, ···, c + 6m − 1} such that f (x) + f (y) = f (xy) for any x, y ∈ V{sub m} and an edge xy ∈ E{sub m} joining them. In order to find all the c-Erdősian triangle labelling, a straightforward is to use the exhaustive search. However, the exhaustive search is only able to find c-Erdősian triangle labelling for m ≤ 5 due to combinatorial explosion. By studying the constant sum of vertex labels, we propose a strong permutation approach, which allows us to generate a certain classes of c-Erdősian triangle labelling up until m = 8.« less

Finite element method for calculating spectral and optical characteristics of axially symmetric quantum dots

NASA Astrophysics Data System (ADS)

Gusev, A. A.; Chuluunbaatar, O.; Vinitsky, S. I.; Derbov, V. L.; Hai, L. L.; Kazaryan, E. M.; Sarkisyan, H. A.

2018-04-01

We present new calculation schemes using high-order finite element method implemented on unstructured grids with triangle elements for solving boundary-value problems that describe axially symmetric quantum dots. The efficiency of the algorithms and software is demonstrated by benchmark calculations of the energy spectrum, the envelope eigenfunctions of electron, hole and exciton states, and the direct interband light absorption in conical and spheroidal impenetrable quantum dots.

Continuously differentiable PIC shape functions for triangular meshes

DOE PAGES

Barnes, D. C.

2018-03-21

In this study, a new class of continuously-differentiable shape functions is developed and applied to two-dimensional electrostatic PIC simulation on an unstructured simplex (triangle) mesh. It is shown that troublesome aliasing instabilities are avoided for cold plasma simulation in which the Debye length is as small as 0.01 cell sizes. These new shape functions satisfy all requirements for PIC particle shape. They are non-negative, have compact support, and partition unity. They are given explicitly by cubic expressions in the usual triangle logical (areal) coordinates. The shape functions are not finite elements because their structure depends on the topology of themore » mesh, in particular, the number of triangles neighboring each mesh vertex. Nevertheless, they may be useful as approximations to solution of other problems in which continuity of derivatives is required or desired.« less

Continuously differentiable PIC shape functions for triangular meshes

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

Barnes, D. C.

In this study, a new class of continuously-differentiable shape functions is developed and applied to two-dimensional electrostatic PIC simulation on an unstructured simplex (triangle) mesh. It is shown that troublesome aliasing instabilities are avoided for cold plasma simulation in which the Debye length is as small as 0.01 cell sizes. These new shape functions satisfy all requirements for PIC particle shape. They are non-negative, have compact support, and partition unity. They are given explicitly by cubic expressions in the usual triangle logical (areal) coordinates. The shape functions are not finite elements because their structure depends on the topology of themore » mesh, in particular, the number of triangles neighboring each mesh vertex. Nevertheless, they may be useful as approximations to solution of other problems in which continuity of derivatives is required or desired.« less

Grouper: A Compact, Streamable Triangle Mesh Data Structure.

PubMed

Luffel, Mark; Gurung, Topraj; Lindstrom, Peter; Rossignac, Jarek

2013-05-08

We present Grouper: an all-in-one compact file format, random-access data structure, and streamable representation for large triangle meshes. Similarly to the recently published SQuad representation, Grouper represents the geometry and connectivity of a mesh by grouping vertices and triangles into fixed-size records, most of which store two adjacent triangles and a shared vertex. Unlike SQuad, however, Grouper interleaves geometry with connectivity and uses a new connectivity representation to ensure that vertices and triangles can be stored in a coherent order that enables memory-efficient sequential stream processing. We present a linear-time construction algorithm that allows streaming out Grouper meshes using a small memory footprint while preserving the initial ordering of vertices. As part of this construction, we show how the problem of assigning vertices and triangles to groups reduces to a well-known NP-hard optimization problem, and present a simple yet effective heuristic solution that performs well in practice. Our array-based Grouper representation also doubles as a triangle mesh data structure that allows direct access to vertices and triangles. Storing only about two integer references per triangle, Grouper answers both incidence and adjacency queries in amortized constant time. Our compact representation enables data-parallel processing on multicore computers, instant partitioning and fast transmission for distributed processing, as well as efficient out-of-core access.

Damage-control laparoscopic partial cholecystectomy with an endoscopic linear stapler.

PubMed

Özçınar, Beyza; Memişoğlu, Ecem; Gök, Ali Fuat Kaan; Ağcaoğlu, Orhan; Yanar, Fatih; İlhan, Mehmet; Yanar, Hakan Teoman; Günay, Kayıhan

2017-01-01

Several damage-control procedures have been described in the literature in case of severe Calot's triangle inflammation and fibrosis. In this report, we describe patients who underwent laparoscopic partial cholecystectomy using an endoscopic linear stapler. Five patients with acute cholecystitis underwent laparoscopic partial cholecystectomy in our clinic between January - December 2011. All patients had severe fibrosis and inflammation of Calot's triangle. The anterior and posterior walls of the gallbladder were totally resected if possible. The gallbladder was transected at its neck or Hartmann's pouch, leaving a remnant gallbladder pouch behind. Five patients had laparoscopic partial cholecystectomy with an endoscopic linear stapler. The main symptom of all patients on admission to the emergency room was abdominal pain. The mean time for the surgical procedure was 140 minutes (range, 120-180 minutes). Inflammation and fibrosis of Calot's triangle was detected in all patients during surgery and a phlegmonous gallbladder was detected in one patient. Surgical drains were used in all patients and no biliary leakage was detected. Remnant common bile duct calculi were detected in one patient and this patient underwent endoscopic retrograde cholangiopancreatography one month after surgery. When a reliable view of Calot's triangle cannot be obtained due to severe inflammation and fibrosis during laparoscopy, laparoscopic partial cholecystectomy seems to be a safe and feasible alternative to open surgery with an acceptable morbidity rate.

Three-Dimensional Viscous Flow Analysis for Moving Bodies Past Fixed Structures

DTIC Science & Technology

1988-05-13

BELLEVUE, WA 98n)05 Research Triangle Park, UC 27709-2211 6Sý. NAME Of FUNDING I PONSORING O Ib. C’FFICE SYMBOL 9 . PROCUREMENT INSTRUMENT IPENTIFICATION...34 otheor sditico Grs IMa ý; pl S- Three- Dimvensio:.iýal Viscrous Flow Analysis for Moving Bodies Past Fixed Structures Fina.11Report, Kelton M. Peery and...Recommendations 40 List of Figures 1 Finite-Volume Mesh ......... ......................... 8 2 Finite-Volume Cell ....... ............................ 9 3

Elementary properties of triangle in normed spaces

NASA Astrophysics Data System (ADS)

Triana, Deri; Yunus, Mahmud

2018-03-01

Based on concepts of trigonometric on plane, In this paper we generalized those concept in normed spaces. About the orthogonality concept between two vectors already well known, we are interested to develop elementary properties of triangle, especially the properties of its angle. We propose a non-linear (Wilson) functional to define an angle and explore its properties.

Effect of large deformation and surface stiffening on the transmission of a line load on a neo-Hookean half space.

PubMed

Wu, Haibin; Liu, Zezhou; Jagota, Anand; Hui, Chung-Yuen

2018-03-07

A line force acting on a soft elastic solid, say due to the surface tension of a liquid drop, can cause significant deformation and the formation of a kink close to the point of force application. Analysis based on linearized elasticity theory shows that sufficiently close to its point of application, the force is borne entirely by the surface stress, not by the elasticity of the substrate; this local balance of three forces is called Neumann's triangle. However, it is not difficult to imagine realistic properties for which this force balance cannot be satisfied. For example, if the line force corresponds to surface tension of water, the numerical values of (unstretched) solid-vapor and solid-liquid surface stresses can easily be such that their sum is insufficient to balance the applied force. In such cases conventional (or naïve) Neumann's triangle of surface forces must break down. Here we study how force balance is rescued from the breakdown of naïve Neumann's triangle by a combination of (a) large hyperelastic deformations of the underlying bulk solid, and (b) increase in surface stress due to surface elasticity (surface stiffening). For a surface with constant surface stress (no surface stiffening), we show that the linearized theory remains accurate if the applied force is less than about 1.3 times the solid surface stress. For a surface in which the surface stress increases linearly with the surface stretch, we find that the Neumann's triangle construction works well as long as we replace the constant surface stress in the naïve Neumann triangle by the actual surface stress underneath the line load.

LR: Compact connectivity representation for triangle meshes

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

Gurung, T; Luffel, M; Lindstrom, P

2011-01-28

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

Morphometric study of the triangle of Petit in human fetuses.

PubMed

Grzonkowska, Magdalena; Badura, Mateusz; Baumgart, Mariusz; Wiczołek, Anna; Lisiecki, Jakub; Biernacki, Maciej; Szpinda, Michał

2018-02-01

The inferior lumbar triangle of Petit is bounded by the iliac crest, lateral border of the latissimus dorsi and the medial border of the external oblique. In the present study, we aimed to quantitatively examine the base, sides, area, and interior angles of the inferior lumbar triangle in the human fetus so as to provide their growth dynamics. Using anatomical dissection, digital image analysis (NIS-Elements AR 3.0), and statistics (Student's t-test, regression analysis), we measured the base, 2 sides, area and interior angles of Petit's triangle in 35 fetuses of both sexes (16 male, 19 female) aged 14-24 weeks. Neither sex nor laterality differences were found. All the parameters studied increased commensurately with age. The linear functions were computed as follows: y = -0.427 + 0.302 × age for base, y = 1.386 + 0.278 × age for medial side, y = 0.871 + 0.323 × age for lateral side, and y = -13.230 + 1.590 × age for area of the Petit triangle. In terms of geometry, Petit triangle reveals neither male-female nor right-left differences. An increase in both lengths and area of the inferior lumbar triangle follows proportionately. The Petit triangle is an acute one in the human fetus.

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

3D Higher Order Modeling in the BEM/FEM Hybrid Formulation

NASA Technical Reports Server (NTRS)

Fink, P. W.; Wilton, D. R.

2000-01-01

Higher order divergence- and curl-conforming bases have been shown to provide significant benefits, in both convergence rate and accuracy, in the 2D hybrid finite element/boundary element formulation (P. Fink and D. Wilton, National Radio Science Meeting, Boulder, CO, Jan. 2000). A critical issue in achieving the potential for accuracy of the approach is the accurate evaluation of all matrix elements. These involve products of high order polynomials and, in some instances, singular Green's functions. In the 2D formulation, the use of a generalized Gaussian quadrature method was found to greatly facilitate the computation and to improve the accuracy of the boundary integral equation self-terms. In this paper, a 3D, hybrid electric field formulation employing higher order bases and higher order elements is presented. The improvements in convergence rate and accuracy, compared to those resulting from lower order modeling, are established. Techniques developed to facilitate the computation of the boundary integral self-terms are also shown to improve the accuracy of these terms. Finally, simple preconditioning techniques are used in conjunction with iterative solution procedures to solve the resulting linear system efficiently. In order to handle the boundary integral singularities in the 3D formulation, the parent element- either a triangle or rectangle-is subdivided into a set of sub-triangles with a common vertex at the singularity. The contribution to the integral from each of the sub-triangles is computed using the Duffy transformation to remove the singularity. This method is shown to greatly facilitate t'pe self-term computation when the bases are of higher order. In addition, the sub-triangles can be further divided to achieve near arbitrary accuracy in the self-term computation. An efficient method for subdividing the parent element is presented. The accuracy obtained using higher order bases is compared to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained using higher order bases are compared to those obtained with lower order bases for selected sample

Sandia Unstructured Triangle Tabular Interpolation Package v 0.1 beta

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

2013-09-24

The software interpolates tabular data, such as for equations of state, provided on an unstructured triangular grid. In particular, interpolation occurs in a two dimensional space by looking up the triangle in which the desired evaluation point resides and then performing a linear interpolation over the n-tuples associated with the nodes of the chosen triangle. The interface to the interpolation routines allows for automated conversion of units from those tabulated to the desired output units. when multiple tables are included in a data file, new tables may be generated by on-the-fly mixing of the provided tables

Airy pulse shaping using time-dependent power-law potentials

NASA Astrophysics Data System (ADS)

Han, Tianwen; Chen, Hao; Qin, Chengzhi; Li, Wenwan; Wang, Bing; Lu, Peixiang

2018-06-01

We investigate the temporal and spectral evolutions of finite-energy Airy pulses in the presence of power-law optical potentials. The potentials are generated by the time-dependent pumped light, which propagates together with the Airy pulses in a highly nonlinear optical fiber. We show that the intrinsic acceleration of Airy pulses can be modified by an external force that stems from a linear potential, and hence unidirectional frequency shift can be realized. When a triangle potential is employed, the pulse will exhibit self-splitting both in temporal and spectral domains. Additionally, as a parabolic potential is utilized, both the temporal waveform and frequency spectrum of the Airy pulse will exchange alternately between the Airy and Gaussian profiles. By using higher-order power-law potentials, we also realize both revival and antirevival effects for the Airy pulses. The study may find wide applications in pulse reshaping and spectral-temporal imaging for both optical communication and signal processing.

Grouper: a compact, streamable triangle mesh data structure.

PubMed

Luffel, Mark; Gurung, Topraj; Lindstrom, Peter; Rossignac, Jarek

2014-01-01

We present Grouper: an all-in-one compact file format, random-access data structure, and streamable representation for large triangle meshes. Similarly to the recently published SQuad representation, Grouper represents the geometry and connectivity of a mesh by grouping vertices and triangles into fixed-size records, most of which store two adjacent triangles and a shared vertex. Unlike SQuad, however, Grouper interleaves geometry with connectivity and uses a new connectivity representation to ensure that vertices and triangles can be stored in a coherent order that enables memory-efficient sequential stream processing. We present a linear-time construction algorithm that allows streaming out Grouper meshes using a small memory footprint while preserving the initial ordering of vertices. As a part of this construction, we show how the problem of assigning vertices and triangles to groups reduces to a well-known NP-hard optimization problem, and present a simple yet effective heuristic solution that performs well in practice. Our array-based Grouper representation also doubles as a triangle mesh data structure that allows direct access to vertices and triangles. Storing only about two integer references per triangle--i.e., less than the three vertex references stored with each triangle in a conventional indexed mesh format--Grouper answers both incidence and adjacency queries in amortized constant time. Our compact representation enables data-parallel processing on multicore computers, instant partitioning and fast transmission for distributed processing, as well as efficient out-of-core access. We demonstrate the versatility and performance benefits of Grouper using a suite of example meshes and processing kernels.

Grouper: A Compact, Streamable Triangle Mesh Data Structure

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

Luffel, Mark; Gurung, Topraj; Lindstrom, Peter

2014-01-01

Here, we present Grouper: an all-in-one compact file format, random-access data structure, and streamable representation for large triangle meshes. Similarly to the recently published SQuad representation, Grouper represents the geometry and connectivity of a mesh by grouping vertices and triangles into fixed-size records, most of which store two adjacent triangles and a shared vertex. Unlike SQuad, however, Grouper interleaves geometry with connectivity and uses a new connectivity representation to ensure that vertices and triangles can be stored in a coherent order that enables memory-efficient sequential stream processing. We also present a linear-time construction algorithm that allows streaming out Grouper meshesmore » using a small memory footprint while preserving the initial ordering of vertices. In this construction, we show how the problem of assigning vertices and triangles to groups reduces to a well-known NP-hard optimization problem, and present a simple yet effective heuristic solution that performs well in practice. Our array-based Grouper representation also doubles as a triangle mesh data structure that allows direct access to vertices and triangles. Storing only about two integer references per triangle-i.e., less than the three vertex references stored with each triangle in a conventional indexed mesh format-Grouper answers both incidence and adjacency queries in amortized constant time. Our compact representation enables data-parallel processing on multicore computers, instant partitioning and fast transmission for distributed processing, as well as efficient out-of-core access. We demonstrate the versatility and performance benefits of Grouper using a suite of example meshes and processing kernels.« less

Level statistics of a noncompact cosmological billiard

NASA Astrophysics Data System (ADS)

Csordas, Andras; Graham, Robert; Szepfalusy, Peter

1991-08-01

A noncompact chaotic billiard on a two-dimensional space of constant negative curvature, the infinite equilateral triangle describing anisotropy oscillations in the very early universe, is studied quantum-mechanically. A Weyl formula with a logarithmic correction term is derived for the smoothed number of states function. For one symmetry class of the eigenfunctions, the level spacing distribution, the spectral rigidity Delta3, and the Sigma2 statistics are determined numerically using the finite matrix approximation. Systematic deviations are found both from the Gaussian orthogonal ensemble (GOE) and the Poissonian ensemble. However, good agreement with the GOE is found if the fundamental triangle is deformed in such a way that it no longer tiles the space.

Transactions of the Army Conference on Applied Mathematics and Computing (10th) Held at West Point, New York on 16-19 Jun 92

DTIC Science & Technology

1993-03-01

1600 Break 1600 - 1700 General Session IV - Thayer Hall, Room 342 Chairperson: David W. Hislop , U.S. Army Research Office, Research Triangle Park...dynamics studies conducted in the 1950’s and 1960’% using finite difference and finite element methods, and in the 1970’s and 1980 ’s using Green’s...1966. [13] L. C. Young. Lectures on the Calculus of Variations and Optimal Control. Chelsa, 1980 . 68 Kinetically Driven Elastic Phase Boundary Motion

Comparison of effects of different screw materials in the triangle fixation of femoral neck fractures.

PubMed

Gok, Kadir; Inal, Sermet; Gok, Arif; Gulbandilar, Eyyup

2017-05-01

In this study, biomechanical behaviors of three different screw materials (stainless steel, titanium and cobalt-chromium) have analyzed to fix with triangle fixation under axial loading in femoral neck fracture and which material is best has been investigated. Point cloud obtained after scanning the human femoral model with the three dimensional (3D) scanner and this point cloud has been converted to 3D femoral model by Geomagic Studio software. Femoral neck fracture was modeled by SolidWorks software for only triangle configuration and computer-aided numerical analyses of three different materials have been carried out by AnsysWorkbench finite element analysis (FEA) software. The loading, boundary conditions and material properties have prepared for FEA and Von-Misses stress values on upper and lower proximity of the femur and screws have been calculated. At the end of numerical analyses, the best advantageous screw material has calculated as titanium because it creates minimum stress at the upper and lower proximity of the fracture line.

Fuchsian triangle groups and Grothendieck dessins. Variations on a theme of Belyi

NASA Astrophysics Data System (ADS)

Cohen, Paula Beazley; Itzykson, Claude; Wolfart, Jürgen

1994-07-01

According to a theorem of Belyi, a smooth projective algebraic curve is defined over a number field if and only if there exists a non-constant element of its function field ramified only over 0, 1 and . The existence of such a Belyi function is equivalent to that of a representation of the curve as a possibly compactified quotient space of the Poincaré upper half plane by a subgroup of finite index in a Fuchsian triangle group. On the other hand, Fuchsian triangle groups arise in many contexts, such as in the theory of hypergeometric functions and certain triangular billiard problems, which would appear at first sight to have no relation to the Galois problems that motivated the above discovery of Belyi. In this note we review several results related to Belyi's theorem and we develop certain aspects giving examples. For preliminary accounts, see the preprint [Wo1], the conference proceedings article [BauItz] and the Comptes Rendus note [CoWo2].

IS THE DOSE-RESPONSE LINEAR OR NONLINEAR FOR GENOTOXIC EFFECTS?

EPA Science Inventory

IS THE DOSE-RESPONSE LINEAR OR NONLINEAR FOR GENOTOXIC EFFECTS?
Preston, RJ. Environmental Carcinogenesis Division, NHEERL, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711

For considerations of cancer risk assessment from exposure to environmenta...

Boolean Operations with Prism Algebraic Patches

PubMed Central

Bajaj, Chandrajit; Paoluzzi, Alberto; Portuesi, Simone; Lei, Na; Zhao, Wenqi

2009-01-01

In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches). This approach uses a linear polyhedron as a first approximation of both the arguments and the result. On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C1-continuous prism algebraic patch (prism A-patch) that interpolates the three triangle vertices, with given normal vectors. The boundary representation only stores the vertices of the initial triangulation and their external vertex normals. In order to represent also flat and/or sharp local features, the corresponding normal-per-face and/or normal-per-edge may be also given, respectively. The topology is described by storing, for each curved triangle, the two triples of pointers to incident vertices and to adjacent triangles. For each triangle, a scaffolding prism is built, produced by its extreme vertices and normals, which provides a containment volume for the curved interpolating A-patch. When looking for the result of a regularized Boolean operation, the 0-set of a tri-variate polynomial within each such prism is generated, and intersected with the analogous 0-sets of the other curved polyhedron, when two prisms have non-empty intersection. The intersection curves of the boundaries are traced and used to decompose each boundary into the 3 standard classes of subpatches, denoted in, out and on. While tracing the intersection curves, the locally refined triangulation of intersecting patches is produced, and added to the boundary representation. PMID:21516262

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

Nguyen, Khoi T.; Lilly, Michael P.; Nielsen, Erik

We report Pauli blockade in a multielectron silicon metal–oxide–semiconductor double quantum dot with an integrated charge sensor. The current is rectified up to a blockade energy of 0.18 ± 0.03 meV. The blockade energy is analogous to singlet–triplet splitting in a two electron double quantum dot. Built-in imbalances of tunnel rates in the MOS DQD obfuscate some edges of the bias triangles. A method to extract the bias triangles is described, and a numeric rate-equation simulation is used to understand the effect of tunneling imbalances and finite temperature on charge stability (honeycomb) diagram, in particular the identification of missing andmore » shifting edges. A bound on relaxation time of the triplet-like state is also obtained from this measurement.« less

Highly Compact Circulators in Square-Lattice Photonic Crystal Waveguides

PubMed Central

Jin, Xin; Ouyang, Zhengbiao; Wang, Qiong; Lin, Mi; Wen, Guohua; Wang, Jingjing

2014-01-01

We propose, demonstrate and investigate highly compact circulators with ultra-low insertion loss in square-lattice- square-rod-photonic-crystal waveguides. Only a single magneto- optical square rod is required to be inserted into the cross center of waveguides, making the structure very compact and ultra efficient. The square rods around the center defect rod are replaced by several right-angled-triangle rods, reducing the insertion loss further and promoting the isolations as well. By choosing a linear-dispersion region and considering the mode patterns in the square magneto-optical rod, the operating mechanism of the circulator is analyzed. By applying the finite-element method together with the Nelder-Mead optimization method, an extremely low insertion loss of 0.02 dB for the transmitted wave and ultra high isolation of 46 dB∼48 dB for the isolated port are obtained. The idea presented can be applied to build circulators in different wavebands, e.g., microwave or Tera-Hertz. PMID:25415417

Highly compact circulators in square-lattice photonic crystal waveguides.

PubMed

Jin, Xin; Ouyang, Zhengbiao; Wang, Qiong; Lin, Mi; Wen, Guohua; Wang, Jingjing

2014-01-01

We propose, demonstrate and investigate highly compact circulators with ultra-low insertion loss in square-lattice- square-rod-photonic-crystal waveguides. Only a single magneto- optical square rod is required to be inserted into the cross center of waveguides, making the structure very compact and ultra efficient. The square rods around the center defect rod are replaced by several right-angled-triangle rods, reducing the insertion loss further and promoting the isolations as well. By choosing a linear-dispersion region and considering the mode patterns in the square magneto-optical rod, the operating mechanism of the circulator is analyzed. By applying the finite-element method together with the Nelder-Mead optimization method, an extremely low insertion loss of 0.02 dB for the transmitted wave and ultra high isolation of 46 dB∼48 dB for the isolated port are obtained. The idea presented can be applied to build circulators in different wavebands, e.g., microwave or Tera-Hertz.

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

Schnack, D.D.; Lottati, I.; Mikic, Z.

The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.

Parameterized Finite Element Modeling and Buckling Analysis of Six Typical Composite Grid Cylindrical Shells

NASA Astrophysics Data System (ADS)

Lai, Changliang; Wang, Junbiao; Liu, Chuang

2014-10-01

Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.

Computer Classification of Triangles and Quadrilaterals--A Challenging Application

ERIC Educational Resources Information Center

Dennis, J. Richard

1978-01-01

Two computer exercises involving the classification of geometric figures are given. The mathematics required is relatively simple but comes from several areas--synthetic geometry, analytic geometry, and linear algebra. (MN)

Descriptive anatomy of the interscalene triangle and the costoclavicular space and their relationship to thoracic outlet syndrome: a study of 60 cadavers.

PubMed

Dahlstrom, Kelly A; Olinger, Anthony B

2012-06-01

Thoracic outlet syndrome classically results from constrictions in 1 or more of 3 specific anatomical locations: the interscalene triangle, costoclavicular space, and coracopectoral tunnel. Magnetic resonance and computed tomographic imaging studies suggest that, of the 3 potential locations for constriction, the costoclavicular space is the most susceptible to compression. This study of human cadavers aims to expand on the descriptive anatomy of the interscalene triangle and associated costoclavicular space. The interscalene angle, interscalene triangle base, and costoclavicular space were measured on 120 sides of embalmed human cadavers. Linear distances and angles were measured using a caliper and protractor, respectively. The data were analyzed by calculating the mean, range, and standard deviation. The range for the interscalene base was 0 to 21.0 mm with a mean of 10.7 mm. For the interscalene angle, the range was 4° to 22° with a mean of 11.3°. Measurements for the costoclavicular space ranged from 6 to 30.9 mm with a mean of 13.5 mm. No significant differences were observed between left and right interscalene triangles or costoclavicular spaces; furthermore, there were no differences between the sexes concerning these 2 locations. Copyright © 2012 National University of Health Sciences. Published by Mosby, Inc. All rights reserved.

Mössbauer spectra linearity improvement by sine velocity waveform followed by linearization process

NASA Astrophysics Data System (ADS)

Kohout, Pavel; Frank, Tomas; Pechousek, Jiri; Kouril, Lukas

2018-05-01

This note reports the development of a new method for linearizing the Mössbauer spectra recorded with a sine drive velocity signal. Mössbauer spectra linearity is a critical parameter to determine Mössbauer spectrometer accuracy. Measuring spectra with a sine velocity axis and consecutive linearization increases the linearity of spectra in a wider frequency range of a drive signal, as generally harmonic movement is natural for velocity transducers. The obtained data demonstrate that linearized sine spectra have lower nonlinearity and line width parameters in comparison with those measured using a traditional triangle velocity signal.

A Refined Cauchy-Schwarz Inequality

ERIC Educational Resources Information Center

Mercer, Peter R.

2007-01-01

The author presents a refinement of the Cauchy-Schwarz inequality. He shows his computations in which refinements of the triangle inequality and its reverse inequality are obtained for nonzero x and y in a normed linear space.

The L sub 1 finite element method for pure convection problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1991-01-01

The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

A Spectral Element Discretisation on Unstructured Triangle / Tetrahedral Meshes for Elastodynamics

NASA Astrophysics Data System (ADS)

May, Dave A.; Gabriel, Alice-A.

2017-04-01

The spectral element method (SEM) defined over quadrilateral and hexahedral element geometries has proven to be a fast, accurate and scalable approach to study wave propagation phenomena. In the context of regional scale seismology and or simulations incorporating finite earthquake sources, the geometric restrictions associated with hexahedral elements can limit the applicability of the classical quad./hex. SEM. Here we describe a continuous Galerkin spectral element discretisation defined over unstructured meshes composed of triangles (2D), or tetrahedra (3D). The method uses a stable, nodal basis constructed from PKD polynomials and thus retains the spectral accuracy and low dispersive properties of the classical SEM, in addition to the geometric versatility provided by unstructured simplex meshes. For the particular basis and quadrature rule we have adopted, the discretisation results in a mass matrix which is not diagonal, thereby mandating linear solvers be utilised. To that end, we have developed efficient solvers and preconditioners which are robust with respect to the polynomial order (p), and possess high arithmetic intensity. Furthermore, we also consider using implicit time integrators, together with a p-multigrid preconditioner to circumvent the CFL condition. Implicit time integrators become particularly relevant when considering solving problems on poor quality meshes, or meshes containing elements with a widely varying range of length scales - both of which frequently arise when meshing non-trivial geometries. We demonstrate the applicability of the new method by examining a number of two- and three-dimensional wave propagation scenarios. These scenarios serve to characterise the accuracy and cost of the new method. Lastly, we will assess the potential benefits of using implicit time integrators for regional scale wave propagation simulations.

Localised surface plasmon-like resonance generated by microwave electromagnetic waves in pipe defects

NASA Astrophysics Data System (ADS)

Alobaidi, Wissam M.; Nima, Zeid A.; Sandgren, Eric

2018-01-01

Localised surface plasmon (LSP)-like resonance phenomena were simulated in COMSOL Multiphysics™, and the electric field enhancement was evaluated in eight pipe defects using the microwave band from 1.80 to 3.00 GHz and analysed by finite element analysis (FEA). The simulation was carried out, in each defect case, on a pipe that has 762 mm length and 152.4 mm inner diameter, and 12.7 mm pipe wall thickness. Defects were positioned in the middle of the pipe and were named as follows; SD: Square Defect, FCD: fillet corner defect, FD: fillet defect, HCD: half circle defect, TCD: triangle corner defect, TD: triangle defect, ZD: zigzag defect, GD: gear defect. The LSP electric field, and scattering parametric (S21, and S11) waves were evaluated in all cases and found to be strongly dependent on the size and the shape of the defect rather than the pipe and or the medium materials.

Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory

DTIC Science & Technology

2016-05-12

valued times series from a sample. (A practical algorithm to compute the estimator is a work in progress.) Third, finitely-valued spatial processes...ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 mathematical statistics; time series ; Markov chains; random...proved. Second, a statistical method is developed to estimate the memory depth of discrete- time and continuously-valued times series from a sample. (A

Construction of a Holliday Junction in Small Circular DNA Molecules for Stable Motifs and Two-Dimensional Lattices.

PubMed

Guo, Xin; Wang, Xue-Mei; Wei, Shuai; Xiao, Shou-Jun

2018-04-12

Design rules for DNA nanotechnology have been mostly learnt from using linear single-stranded (ss) DNA as the source material. For example, the core structure of a typical DAO (double crossover, antiparallel, odd half-turns) tile for assembling 2D lattices is constructed from only two linear ss-oligonucleotide scaffold strands, similar to two ropes making a square knot. Herein, a new type of coupled DAO (cDAO) tile and 2D lattices of small circular ss-oligonucleotides as scaffold strands and linear ss-oligonucleotides as staple strands are reported. A cDAO tile of cDAO-c64nt (c64nt: circular 64 nucleotides), shaped as a solid parallelogram, is constructed with a Holliday junction (HJ) at the center and two HJs at both poles of a c64nt; similarly, cDAO-c84nt, shaped as a crossed quadrilateral composed of two congruent triangles, is formed with a HJ at the center and four three-way junctions at the corners of a c84nt. Perfect 2D lattices were assembled from cDAO tiles: infinite nanostructures of nanoribbons, nanotubes, and nanorings, and finite nanostructures. The structural relationship between the visible lattices imaged by AFM and the corresponding invisible secondary and tertiary molecular structures of HJs, inclination angle of hydrogen bonds against the double-helix axis, and the chirality of the tile can be interpreted very well. This work could shed new light on DNA nanotechnology with unique circular tiles. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Linear Characteristic Spatial Quadrature for Discrete Ordinates Neutral Particle Transport on Arbitrary Triangles

DTIC Science & Technology

1993-06-01

1•) + ) •,(v)(•,L) = ()(Q)+ sEXT (F). (4) The scalar flux, 0, is related to the angular flux, W, by (F)= f (dQ Vh) (5) and the particle current, J...J," v,p’) u +at(U, v) w(u, U, p’)= as(u, v) O(u, v) + SEXT (uv)] (92) 0 Ul,(V) I Assuming the area of the triangle is sufficiently small that cross...M + SEXT () (98) Wvn and WoUT are angular flux averages along the input and output edges, respectively, and are defined by WD Iv = f- ds. V(s.v) (99

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...linear systems with Brownian motion or a discrete time linear system with a white Gaussian noise and costs 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 stochastic optimal control, fractional Brownian motion , stochastic

On the photo-gravitational restricted four-body problem with variable mass

NASA Astrophysics Data System (ADS)

Mittal, Amit; Agarwal, Rajiv; Suraj, Md Sanam; Arora, Monika

2018-05-01

This paper deals with the photo-gravitational restricted four-body problem (PR4BP) with variable mass. Following the procedure given by Gascheau (C. R. 16:393-394, 1843) and Routh (Proc. Lond. Math. Soc. 6:86-97, 1875), the conditions of linear stability of Lagrange triangle solution in the PR4BP are determined. The three radiating primaries having masses m1, m2 and m3 in an equilateral triangle with m2=m3 will be stable as long as they satisfy the linear stability condition of the Lagrangian triangle solution. We have derived the equations of motion of the mentioned problem and observed that there exist eight libration points for a fixed value of parameters γ (m at time t/m at initial time, 0<γ≤1 ), α (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0≤α≤2.2), the mass parameter μ=0.005 and radiation parameters qi, (0< qi≤1, i=1, 2, 3). All the libration points are non-collinear if q2≠ q3. It has been observed that the collinear and out-of-plane libration points also exist for q2=q3. In all the cases, each libration point is found to be unstable. Further, zero velocity curves (ZVCs) and Newton-Raphson basins of attraction are also discussed.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations. Part 1; Viscous Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Nielsen, Eric J.; Nishikawa, Hiroaki; White, Jeffery A.

2009-01-01

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and efficiency are studied for six nominally second-order accurate schemes: a node-centered scheme, cell-centered node-averaging schemes with and without clipping, and cell-centered schemes with unweighted, weighted, and approximately mapped least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Results from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The second class of tests are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes are less accurate, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to the complexity of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping of the surface anisotropy or modifying the scheme stencil to reflect the direction of strong coupling.

MODFLOW–USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.; Niswonger, Richard G.; Ibaraki, Motomu; Hughes, Joseph D.

2013-01-01

A new version of MODFLOW, called MODFLOW–USG (for UnStructured Grid), was developed to support a wide variety of structured and unstructured grid types, including nested grids and grids based on prismatic triangles, rectangles, hexagons, and other cell shapes. Flexibility in grid design can be used to focus resolution along rivers and around wells, for example, or to subdiscretize individual layers to better represent hydrostratigraphic units. MODFLOW–USG is based on an underlying control volume finite difference (CVFD) formulation in which a cell can be connected to an arbitrary number of adjacent cells. To improve accuracy of the CVFD formulation for irregular grid-cell geometries or nested grids, a generalized Ghost Node Correction (GNC) Package was developed, which uses interpolated heads in the flow calculation between adjacent connected cells. MODFLOW–USG includes a Groundwater Flow (GWF) Process, based on the GWF Process in MODFLOW–2005, as well as a new Connected Linear Network (CLN) Process to simulate the effects of multi-node wells, karst conduits, and tile drains, for example. The CLN Process is tightly coupled with the GWF Process in that the equations from both processes are formulated into one matrix equation and solved simultaneously. This robustness results from using an unstructured grid with unstructured matrix storage and solution schemes. MODFLOW–USG also contains an optional Newton-Raphson formulation, based on the formulation in MODFLOW–NWT, for improving solution convergence and avoiding problems with the drying and rewetting of cells. Because the existing MODFLOW solvers were developed for structured and symmetric matrices, they were replaced with a new Sparse Matrix Solver (SMS) Package developed specifically for MODFLOW–USG. The SMS Package provides several methods for resolving nonlinearities and multiple symmetric and asymmetric linear solution schemes to solve the matrix arising from the flow equations and the Newton-Raphson formulation, respectively.

Performance of an anisotropic Allman/DKT 3-node thin triangular flat shell element

NASA Astrophysics Data System (ADS)

Ertas, A.; Krafcik, J. T.; Ekwaro-Osire, S.

1992-05-01

A simple, explicit formulation of the stiffness matrix for an anisotropic, 3-node, thin triangular flat shell element in global coordinates is presented. An Allman triangle (AT) is used for membrane stiffness. The membrane stiffness matrix is explicitly derived by applying an Allman transformation to a Felippa 6-node linear strain triangle (LST). Bending stiffness is incorporated by the use of a discrete Kirchhoff triangle (DKT) bending element. Stiffness terms resulting from anisotropic membrane-bending coupling are included by integrating, in area coordinates, the membrane and bending strain-displacement matrices. Using the aforementioned approach, the objective of this study is to develop and test the performance of a practical 3-node flat shell element that could be used in plate problems with unsymmetrically stacked composite laminates. The performance of the latter element is tested on plates of varying aspect ratios. The developed 3-node shell element should simplify the programming task and have the potential of reducing the computational time.

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2000-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Three-dimension finite-element analyses of multiple electrodes bipolar RF global endometrial ablation

NASA Astrophysics Data System (ADS)

Hu, Tao; Panhao, Tang; Xiao, Jiahua

2015-03-01

Radio-frequency ablation (RFA) is a minimally invasive surgical procedure to thermally ablate the targeted diseased tissue. There have been many finite-element method (FEM) studies of cardiac and hepatic RFA, but hardly find any FEM study on endometrial ablation for abnormal uterine bleeding. In this paper, a FEM model was generated to analyze the temperature distribution of bipolar RF global endometrial ablation with three pairs of bipolar electrodes placed at the perimeter of the uterine cavity. COMSOL was utilized to calculate the RF electric fields and temperature fields by numerically solving the bioheat equation in the triangle uterine cavity range. The 55°C isothermal surfaces show the shape of the ablation dimensions (depth and width), which reasonably matched the experimental results.

The von Mises stress distribution on the surface of UHMWPE with texture-shaped variation in the presence of normal load and dry sliding contact

NASA Astrophysics Data System (ADS)

Lestari, W. D.; Jamari, J.; Bayuseno, A. P.

2017-04-01

The texture shapes play a key role in the tribological performance of the surface material. This paper presents a study on the use of the 3D finite element method for surface stress analysis on the different texture shape under load and dry sliding contact. The five texture-shaped model was investigated in this work, namely square, circle, ellipse, triangle, and chevron. The result shown that the square shape has the highest value of von Mises resultant stress under static load. In contrast, the dry sliding contact on the triangle shape provided the highest von Mises stress distribution. The lowest value of von Mises stress can be found in the texture pattern of circle, square, and chevron under influence of load for 17 N, 30 N, and 50 N, respectively. Those texture patterns applied to surface of Ultra High Molecular Weight Polyethylene (UHMWPE) may have a strong effect on the reduction of wear rate and enhance tribological performance.

Solution of an eigenvalue problem for the Laplace operator on a spherical surface. M.S. Thesis - Maryland Univ.

NASA Technical Reports Server (NTRS)

Walden, H.

1974-01-01

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

A Modeling Approach for Burn Scar Assessment Using Natural Features and Elastic Property

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

Tsap, L V; Zhang, Y; Goldgof, D B

2004-04-02

A modeling approach is presented for quantitative burn scar assessment. Emphases are given to: (1) constructing a finite element model from natural image features with an adaptive mesh, and (2) quantifying the Young's modulus of scars using the finite element model and the regularization method. A set of natural point features is extracted from the images of burn patients. A Delaunay triangle mesh is then generated that adapts to the point features. A 3D finite element model is built on top of the mesh with the aid of range images providing the depth information. The Young's modulus of scars ismore » quantified with a simplified regularization functional, assuming that the knowledge of scar's geometry is available. The consistency between the Relative Elasticity Index and the physician's rating based on the Vancouver Scale (a relative scale used to rate burn scars) indicates that the proposed modeling approach has high potentials for image-based quantitative burn scar assessment.« less

Estimation of aortic valve leaflets from 3D CT images using local shape dictionaries and linear coding

NASA Astrophysics Data System (ADS)

Liang, Liang; Martin, Caitlin; Wang, Qian; Sun, Wei; Duncan, James

2016-03-01

Aortic valve (AV) disease is a significant cause of morbidity and mortality. The preferred treatment modality for severe AV disease is surgical resection and replacement of the native valve with either a mechanical or tissue prosthetic. In order to develop effective and long-lasting treatment methods, computational analyses, e.g., structural finite element (FE) and computational fluid dynamic simulations, are very effective for studying valve biomechanics. These computational analyses are based on mesh models of the aortic valve, which are usually constructed from 3D CT images though many hours of manual annotation, and therefore an automatic valve shape reconstruction method is desired. In this paper, we present a method for estimating the aortic valve shape from 3D cardiac CT images, which is represented by triangle meshes. We propose a pipeline for aortic valve shape estimation which includes novel algorithms for building local shape dictionaries and for building landmark detectors and curve detectors using local shape dictionaries. The method is evaluated on real patient image dataset using a leave-one-out approach and achieves an average accuracy of 0.69 mm. The work will facilitate automatic patient-specific computational modeling of the aortic valve.

Linear CCD attitude measurement system based on the identification of the auxiliary array CCD

NASA Astrophysics Data System (ADS)

Hu, Yinghui; Yuan, Feng; Li, Kai; Wang, Yan

2015-10-01

Object to the high precision flying target attitude measurement issues of a large space and large field of view, comparing existing measurement methods, the idea is proposed of using two array CCD to assist in identifying the three linear CCD with multi-cooperative target attitude measurement system, and to address the existing nonlinear system errors and calibration parameters and more problems with nine linear CCD spectroscopic test system of too complicated constraints among camera position caused by excessive. The mathematical model of binocular vision and three linear CCD test system are established, co-spot composition triangle utilize three red LED position light, three points' coordinates are given in advance by Cooperate Measuring Machine, the red LED in the composition of the three sides of a triangle adds three blue LED light points as an auxiliary, so that array CCD is easier to identify three red LED light points, and linear CCD camera is installed of a red filter to filter out the blue LED light points while reducing stray light. Using array CCD to measure the spot, identifying and calculating the spatial coordinates solutions of red LED light points, while utilizing linear CCD to measure three red LED spot for solving linear CCD test system, which can be drawn from 27 solution. Measured with array CCD coordinates auxiliary linear CCD has achieved spot identification, and has solved the difficult problems of multi-objective linear CCD identification. Unique combination of linear CCD imaging features, linear CCD special cylindrical lens system is developed using telecentric optical design, the energy center of the spot position in the depth range of convergence in the direction is perpendicular to the optical axis of the small changes ensuring highprecision image quality, and the entire test system improves spatial object attitude measurement speed and precision.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

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

A new 3D method for measuring cranio-facial relationships with cone beam computed tomography (CBCT)

PubMed Central

Cibrián, Rosa; Gandia, Jose L.; Paredes, Vanessa

2013-01-01

Objectives: CBCT systems, with their high precision 3D reconstructions, 1:1 images and accuracy in locating cephalometric landmarks, allows us to evaluate measurements from craniofacial structures, so enabling us to replace the anthropometric methods or bidimensional methods used until now. The aims are to analyse cranio-facial relationships in a sample of patients who had previously undergone a CBCT and create a new 3D cephalometric method for assessing and measuring patients. Study Design: 90 patients who had a CBCT (i-Cat®) as a diagnostic register were selected. 12 cephalometric landmarks on the three spatial planes (X,Y,Z) were defined and 21 linear measurements were established. Using these measurements, 7 triangles were described and analysed. With the sides of the triangles: (CdR-Me-CdL); (FzR-Me-FzL); (GoR-N-GoL); and the Gl-Me distance, the ratios between them were analysed. In addition, 4 triangles in the mandible were measured (body: GoR-DB-Me and GoL-DB-Me and ramus: KrR-CdR-GoR and KrL-CdL-GoL). Results: When analyzing the sides of the CdR-Me-CdL triangle, it was found that the 69.33% of the patients could be considered symmetric. Regarding the ratios between the sides of the following triangles: CdR-Me-CdL, FzR-Me-FzL, GoR-N-GoL and the Gl-Me distance, it was found that almost all ratios were close to 1:1 except between the CdR-CdL side with respect the rest of the sides. With regard to the ratios of the 4 triangles of the mandible, it was found that the most symmetrical relationships were those corresponding to the sides of the body of the mandible and the most asymmetrical ones were those corresponding to the base of such triangles. Conclusions: A new method for assessing cranio-facial relationshps using CBCT has been established. It could be used for diverse purposes including diagnosis and treatment planning. Key words:Craniofacial relationship, CBCT, 3D cephalometry. PMID:23524427

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

Extension to linear dynamics for hybrid stress finite element formulation based on additional displacements

NASA Astrophysics Data System (ADS)

Sumihara, K.

Based upon legitimate variational principles, one microscopic-macroscopic finite element formulation for linear dynamics is presented by Hybrid Stress Finite Element Method. The microscopic application of Geometric Perturbation introduced by Pian and the introduction of infinitesimal limit core element (Baby Element) have been consistently combined according to the flexible and inherent interpretation of the legitimate variational principles initially originated by Pian and Tong. The conceptual development based upon Hybrid Finite Element Method is extended to linear dynamics with the introduction of physically meaningful higher modes.

A contact algorithm for shell problems via Delaunay-based meshing of the contact domain

NASA Astrophysics Data System (ADS)

Kamran, K.; Rossi, R.; Oñate, E.

2013-07-01

The simulation of the contact within shells, with all of its different facets, represents still an open challenge in Computational Mechanics. Despite the effort spent in the development of techniques for the simulation of general contact problems, an all-seasons algorithm applicable to complex shell contact problems is yet to be developed. This work focuses on the solution of the contact between thin shells by using a technique derived from the particle finite element method together with a rotation-free shell triangle. The key concept is to define a discretization of the contact domain (CD) by constructing a finite element mesh of four-noded tetrahedra that describes the potential contact volume. The problem is completed by using an assumed-strain approach to define an elastic contact strain over the CD.

Experimental Non-Violation of the Bell Inequality

NASA Astrophysics Data System (ADS)

Palmer, Tim

2018-05-01

A finite non-classical framework for physical theory is described which challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the universe as a deterministic locally causal system evolving on a measure-zero fractal-like geometry $I_U$ in cosmological state space. Consistent with the assumed primacy of $I_U$, and $p$-adic number theory, a non-Euclidean (and hence non-classical) metric $g_p$ is defined on cosmological state space, where $p$ is a large but finite Pythagorean prime. Using number-theoretic properties of spherical triangles, the inequalities violated experimentally are shown to be $g_p$-distant from the CHSH inequality, whose violation would rule out local realism. This result fails in the singular limit $p=\\infty$, at which $g_p$ is Euclidean. Broader implications are discussed.

Grid Effect on Spherical Shallow Water Jets Using Continuous and Discontinuous Galerkin Methods

DTIC Science & Technology

2013-01-01

The high-order Legendre -Gauss-Lobatto (LGL) points are added to the linear grid by projecting the linear elements onto the auxiliary gnomonic space...mapping, the triangles are subdivided into smaller ones by a Lagrange polynomial of order nI . The number of quadrilateral elements and grid points of...of the acceleration of gravity and the vertical height of the fluid), ν∇2 is the artificial viscosity term of viscous coefficient ν = 1× 105 m2 s−1

Ultrametric properties of the attractor spaces for random iterated linear function systems

NASA Astrophysics Data System (ADS)

Buchovets, A. G.; Moskalev, P. V.

2018-03-01

We investigate attractors of random iterated linear function systems as independent spaces embedded in the ordinary Euclidean space. The introduction on the set of attractor points of a metric that satisfies the strengthened triangle inequality makes this space ultrametric. Then inherent in ultrametric spaces the properties of disconnectedness and hierarchical self-similarity make it possible to define an attractor as a fractal. We note that a rigorous proof of these properties in the case of an ordinary Euclidean space is very difficult.

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Comparative Evaluation of Stress Distribution in Experimentally Designed Nickel-titanium Rotary Files with Varying Cross Sections: A Finite Element Analysis.

PubMed

Basheer Ahamed, Shadir Bughari; Vanajassun, Purushothaman Pranav; Rajkumar, Kothandaraman; Mahalaxmi, Sekar

2018-04-01

Single cross-sectional nickel-titanium (NiTi) rotary instruments during continuous rotations are subjected to constant and variable stresses depending on the canal anatomy. This study was intended to create 2 new experimental, theoretic single-file designs with combinations of triple U (TU), triangle (TR), and convex triangle (CT) cross sections and to compare their bending stresses in simulated root canals with a single cross-sectional instrument using finite element analysis. A 3-dimensional model of the simulated root canal with 45° curvature and NiTi files with 5 cross-sectional designs were created using Pro/ENGINEER Wildfire 4.0 software (PTC Inc, Needham, MA) and ANSYS software (version 17; ANSYS, Inc, Canonsburg, PA) for finite element analysis. The NiTi files of 3 groups had single cross-sectional shapes of CT, TR, and TU designs, and 2 experimental groups had a CT, TR, and TU (CTU) design and a TU, TR, and CT (UTC) design. The file was rotated in simulated root canals to analyze the bending stress, and the von Mises stress value for every file was recorded in MPa. Statistical analysis was performed using the Kruskal-Wallis test and the Bonferroni-adjusted Mann-Whitney test for multiple pair-wise comparison with a P value <.05 (95 %). The maximum bending stress of the rotary file was observed in the apical third of the CT design, whereas comparatively less stress was recorded in the CTU design. The TU and TR designs showed a similar stress pattern at the curvature, whereas the UTC design showed greater stress in the apical and middle thirds of the file in curved canals. All the file designs showed a statistically significant difference. The CTU designed instruments showed the least bending stress on a 45° angulated simulated root canal when compared with all the other tested designs. Copyright © 2017 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

NASA Astrophysics Data System (ADS)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators

NASA Technical Reports Server (NTRS)

Taleghani, Barmac K.; Campbell, Joel F.

1999-01-01

A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.

Rank-based methods for modeling dependence between loss triangles.

PubMed

Côté, Marie-Pier; Genest, Christian; Abdallah, Anas

2016-01-01

In order to determine the risk capital for their aggregate portfolio, property and casualty insurance companies must fit a multivariate model to the loss triangle data relating to each of their lines of business. As an inadequate choice of dependence structure may have an undesirable effect on reserve estimation, a two-stage inference strategy is proposed in this paper to assist with model selection and validation. Generalized linear models are first fitted to the margins. Standardized residuals from these models are then linked through a copula selected and validated using rank-based methods. The approach is illustrated with data from six lines of business of a large Canadian insurance company for which two hierarchical dependence models are considered, i.e., a fully nested Archimedean copula structure and a copula-based risk aggregation model.

A semi-implicit finite element method for viscous lipid membranes

NASA Astrophysics Data System (ADS)

Rodrigues, Diego S.; Ausas, Roberto F.; Mut, Fernando; Buscaglia, Gustavo C.

2015-10-01

A finite element formulation to approximate the behavior of lipid membranes is proposed. The mathematical model incorporates tangential viscous stresses and bending elastic forces, together with the inextensibility constraint and the enclosed volume constraint. The membrane is discretized by a surface mesh made up of planar triangles, over which a mixed formulation (velocity-curvature) is built based on the viscous bilinear form (Boussinesq-Scriven operator) and the Laplace-Beltrami identity relating position and curvature. A semi-implicit approach is then used to discretize in time, with piecewise linear interpolants for all variables. Two stabilization terms are needed: The first one stabilizes the inextensibility constraint by a pressure-gradient-projection scheme (Codina and Blasco (1997) [33]), the second couples curvature and velocity to improve temporal stability, as proposed by Bänsch (2001) [36]. The volume constraint is handled by a Lagrange multiplier (which turns out to be the internal pressure), and an analogous strategy is used to filter out rigid-body motions. The nodal positions are updated in a Lagrangian manner according to the velocity solution at each time step. An automatic remeshing strategy maintains suitable refinement and mesh quality throughout the simulation. Numerical experiments show the convergent and robust behavior of the proposed method. Stability limits are obtained from numerous relaxation tests, and convergence with mesh refinement is confirmed both in the relaxation transient and in the final equilibrium shape. Virtual tweezing experiments are also reported, computing the dependence of the deformed membrane shape with the tweezing velocity (a purely dynamical effect). For sufficiently high velocities, a tether develops which shows good agreement, both in its final radius and in its transient behavior, with available analytical solutions. Finally, simulation results of a membrane subject to the simultaneous action of six tweezers illustrate the robustness of the method.

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

On Viviani's Theorem and Its Extensions

ERIC Educational Resources Information Center

Abboud, Elias

2010-01-01

Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Nielsen, Eric J.; Nishikawa, Hiroaki; White, Jeffery A.

2010-01-01

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes - a node-averaging scheme and two schemes with nearest-neighbor and adaptive compact stencils for least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Tests from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The tests of the second class are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes may degenerate on mixed grids, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to that of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping based on a distance function commonly available in practical schemes or modifying the scheme stencil to reflect the direction of strong coupling. The major conclusion is that accuracies of the node centered and the best cell-centered schemes are comparable at equivalent number of degrees of freedom.

The use of Galerkin finite-element methods to solve mass-transport equations

USGS Publications Warehouse

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Electronic structure and optical properties of triangular GaAs/AlGaAs quantum dots: Exciton and impurity states

NASA Astrophysics Data System (ADS)

Tiutiunnyk, A.; Akimov, V.; Tulupenko, V.; Mora-Ramos, M. E.; Kasapoglu, E.; Ungan, F.; Sökmen, I.; Morales, A. L.; Duque, C. A.

2016-03-01

Electronic structure and optical properties in equilateral triangular GaAs/Al0.3Ga0.7As quantum dots are studied extensively. The effects of donor and acceptor impurity atoms positioned in the orthocenter of the triangle, as well as of the external DC electric field are taken into account. Binding energies of the impurity, exciton energies, interband photoluminescence peak positions as well as linear and non-linear optical properties in THz range caused by transitions between excitonic states are calculated and discussed.

Narayanaswamy's 1971 aging theory and material time

NASA Astrophysics Data System (ADS)

Dyre, Jeppe C.

2015-09-01

The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy's phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely, the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance. One of these is the "unique-triangles property" according to which any three points on the system's path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibrium time-autocorrelation functions, which extends to aging a previously proposed framework for such functions in equilibrium [J. C. Dyre, e-print arXiv:cond-mat/9712222 (1997)].

A robust fingerprint matching algorithm based on compatibility of star structures

NASA Astrophysics Data System (ADS)

Cao, Jia; Feng, Jufu

2009-10-01

In fingerprint verification or identification systems, most minutiae-based matching algorithms suffered from the problems of non-linear distortion and missing or faking minutiae. Local structures such as triangle or k-nearest structure are widely used to reduce the impact of non-linear distortion, but are suffered from missing and faking minutiae. In our proposed method, star structure is used to present local structure. A star structure contains various number of minutiae, thus, it is more robust with missing and faking minutiae. Our method consists of four steps: 1) Constructing star structures at minutia level; 2) Computing similarity score for each structure pair, and eliminating impostor matched pairs which have the low scores. As it is generally assumed that there is only linear distortion in local area, the similarity is defined by rotation and shifting. 3) Voting for remained matched pairs according to the compatibility between them, and eliminating impostor matched pairs which gain few votes. The concept of compatibility is first introduced by Yansong Feng [4], the original definition is only based on triangles. We define the compatibility for star structures to adjust to our proposed algorithm. 4) Computing the matching score, based on the number of matched structures and their voting scores. The score also reflects the fact that, it should get higher score if minutiae match in more intensive areas. Experiments evaluated on FVC 2004 show both effectiveness and efficiency of our methods.

Mathematical Theories of Interaction with Oracles

DTIC Science & Technology

2013-10-01

have made a lasting impact on my mathematical perspective. I am grateful for the wonderful and stimulating discussion I had with Alan Frieze on...Otherwise, by Theorem 7.1, with probability at least 1−ε/2, we have ‖πθ⋆ −πθ̂(t−1)θ⋆‖ ≤ R(t−1, ε/2). On this event, ifR (t−1, ε/2) ≤ ε/8, then by a triangle... impact on how much benefit we gain from transfer learning when we are faced with only a finite sequence of learning problems. As such, it is certainly

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Optical coating on a corrugated surface to align the polarization of an unpolarized wave without loss

NASA Astrophysics Data System (ADS)

Jen, Yi Jun

2017-12-01

A multilayer comprising birefringent thin films is devised to present to function as a polarization beam splitter and waveplate simultaneously. By arranging such a multilayer on a right triangle-shaped corrugated surface, a polarizer is realized to align the randomly oscillating electric field of an unpolarized wave into a linear polarized wave without loss.

Testing the consistency of three-point halo clustering in Fourier and configuration space

NASA Astrophysics Data System (ADS)

Hoffmann, K.; Gaztañaga, E.; Scoccimarro, R.; Crocce, M.

2018-05-01

We compare reduced three-point correlations Q of matter, haloes (as proxies for galaxies) and their cross-correlations, measured in a total simulated volume of ˜100 (h-1 Gpc)3, to predictions from leading order perturbation theory on a large range of scales in configuration space. Predictions for haloes are based on the non-local bias model, employing linear (b1) and non-linear (c2, g2) bias parameters, which have been constrained previously from the bispectrum in Fourier space. We also study predictions from two other bias models, one local (g2 = 0) and one in which c2 and g2 are determined by b1 via approximately universal relations. Overall, measurements and predictions agree when Q is derived for triangles with (r1r2r3)1/3 ≳60 h-1 Mpc, where r1 - 3 are the sizes of the triangle legs. Predictions for Qmatter, based on the linear power spectrum, show significant deviations from the measurements at the BAO scale (given our small measurement errors), which strongly decrease when adding a damping term or using the non-linear power spectrum, as expected. Predictions for Qhalo agree best with measurements at large scales when considering non-local contributions. The universal bias model works well for haloes and might therefore be also useful for tightening constraints on b1 from Q in galaxy surveys. Such constraints are independent of the amplitude of matter density fluctuation (σ8) and hence break the degeneracy between b1 and σ8, present in galaxy two-point correlations.

Quantiles for Finite Mixtures of Normal Distributions

ERIC Educational Resources Information Center

Rahman, Mezbahur; Rahman, Rumanur; Pearson, Larry M.

2006-01-01

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

A novel recurrent neural network with finite-time convergence for linear programming.

PubMed

Liu, Qingshan; Cao, Jinde; Chen, Guanrong

2010-11-01

In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.

Convex set and linear mixing model

NASA Technical Reports Server (NTRS)

Xu, P.; Greeley, R.

1993-01-01

A major goal of optical remote sensing is to determine surface compositions of the earth and other planetary objects. For assessment of composition, single pixels in multi-spectral images usually record a mixture of the signals from various materials within the corresponding surface area. In this report, we introduce a closed and bounded convex set as a mathematical model for linear mixing. This model has a clear geometric implication because the closed and bounded convex set is a natural generalization of a triangle in n-space. The endmembers are extreme points of the convex set. Every point in the convex closure of the endmembers is a linear mixture of those endmembers, which is exactly how linear mixing is defined. With this model, some general criteria for selecting endmembers could be described. This model can lead to a better understanding of linear mixing models.

Global Dynamic Modeling of Space-Geodetic Data

NASA Technical Reports Server (NTRS)

Bird, Peter

1995-01-01

The proposal had outlined a year for program conversion, a year for testing and debugging, and two years for numerical experiments. We kept to that schedule. In first (partial) year, author designed a finite element for isostatic thin-shell deformation on a sphere, derived all of its algebraic and stiffness properties, and embedded it in a new finite element code which derives its basic solution strategy (and some critical subroutines) from earlier flat-Earth codes. Also designed and programmed a new fault element to represent faults along plate boundaries. Wrote a preliminary version of a spherical graphics program for the display of output. Tested this new code for accuracy on individual model plates. Made estimates of the computer-time/cost efficiency of the code for whole-earth grids, which were reasonable. Finally, converted an interactive graphical grid-designer program from Cartesian to spherical geometry to permit the beginning of serious modeling. For reasons of cost efficiency, models are isostatic, and do not consider the local effects of unsupported loads or bending stresses. The requirements are: (1) ability to represent rigid rotation on a sphere; (2) ability to represent a spatially uniform strain-rate tensor in the limit of small elements; and (3) continuity of velocity across all element boundaries. Author designed a 3-node triangle shell element which has two different sets of basis functions to represent (vector) velocity and all other (scalar) variables. Such elements can be shown to converge to the formulas for plane triangles in the limit of small size, but can also applied to cover any area smaller than a hemisphere. The difficult volume integrals involved in computing the stiffness of such elements are performed numerically using 7 Gauss integration points on the surface of the sphere, beneath each of which a vertical integral is performed using about 100 points.

Voltage gradient mapping and electrophysiologically guided cryoablation in children with AVNRT.

PubMed

Drago, Fabrizio; Battipaglia, Irma; Russo, Mario Salvatore; Remoli, Romolo; Pazzano, Vincenzo; Grifoni, Gino; Allegretti, Greta; Silvetti, Massimo Stefano

2018-04-01

Recently, voltage gradient mapping of Koch's triangle to find low-voltage connections, or 'voltage bridges', corresponding to the anatomic position of the slow pathway, has been introduced as a method to ablate atrioventricular nodal reentry tachycardia (AVNRT) in children. Thus, we aimed to assess the effectiveness of voltage mapping of Koch's triangle, combined with the search for the slow potential signal in 'low-voltage bridges', to guide cryoablation of AVNRT in children. From June 2015 to May 2016, 35 consecutive paediatric patients (mean age 12.1 ± 4.5 years) underwent 3D-guided cryoablation of AVNRT at our Institution. Fifteen children were enrolled as control group (mean age 14 ± 4 years). A voltage gradient mapping of Koch's triangle was obtained in all patients, showing low-voltage connections in all children with AVNRT but not in controls. Prior to performing cryoablation, we looked for the typical 'hump and spike' electrogram, generally considered to be representative of slow pathway potential within a low-voltage bridge. In all patients the 'hump and spike' electrogram was found inside bridges of low voltage. Focal or high-density linear lesions, extended or not, were delivered guided by low-voltage bridge visualization. Acute success rate was 100%, and no recurrence was reported at a mean follow-up of 8 ± 3 months. Voltage gradient mapping of Koch's triangle, combined with the search for the slow potential signal in low-voltage bridges, is effective in guiding cryoablation of AVNRT in paediatric patients, with a complete acute success rate and no AVNRT recurrences at mid-term follow-up.

The fast and accurate 3D-face scanning technology based on laser triangle sensors

NASA Astrophysics Data System (ADS)

Wang, Jinjiang; Chang, Tianyu; Ge, Baozhen; Tian, Qingguo; Chen, Yang; Kong, Bin

2013-08-01

A laser triangle scanning method and the structure of 3D-face measurement system were introduced. In presented system, a liner laser source was selected as an optical indicated signal in order to scanning a line one times. The CCD image sensor was used to capture image of the laser line modulated by human face. The system parameters were obtained by system calibrated calculated. The lens parameters of image part of were calibrated with machine visual image method and the triangle structure parameters were calibrated with fine wire paralleled arranged. The CCD image part and line laser indicator were set with a linear motor carry which can achieve the line laser scanning form top of the head to neck. For the nose is ledge part and the eyes are sunk part, one CCD image sensor can not obtain the completed image of laser line. In this system, two CCD image sensors were set symmetric at two sides of the laser indicator. In fact, this structure includes two laser triangle measure units. Another novel design is there laser indicators were arranged in order to reduce the scanning time for it is difficult for human to keep static for longer time. The 3D data were calculated after scanning. And further data processing include 3D coordinate refine, mesh calculate and surface show. Experiments show that this system has simply structure, high scanning speed and accurate. The scanning range covers the whole head of adult, the typical resolution is 0.5mm.

Age-related decrements in bone mineral density in women over 65

NASA Technical Reports Server (NTRS)

Steiger, P.; Cummings, S. R.; Black, D. M.; Spencer, N. E.; Genant, H. K.

1992-01-01

Age-related changes in bone density contribute to the risk of fractures. To describe the relationship between age and bone mass in elderly women, we studied a large cohort of women over age 65 years who were recruited from population-based lists in four cities in the United States. Bone density in g/cm2 was measured by single-photon absorptiometry (SPA) and dual x-ray absorptiometry (DXA) at the distal and proximal radius, the calcaneus, the lumbar spine, and the proximal femur. Centralized data collection was used to control data quality and consistency. We found a strong inverse relationship between bone density and age for most sites. Decrements in bone density between women aged 65-69 years and women 85 years and older exceeded 16% in all regions except the spine, where the difference between the two age groups was 6%. Ward's triangle and the calcaneus exhibited the largest decrements, with 26 and 21%, respectively. The estimates of annual changes in bone mineral density by linear regression at sites other than the spine ranged from -0.82% at the femoral neck and trochanter to -1.30% at Ward's triangle. Correlations between the different regions ranged from r = 0.51 between the proximal radius and Ward's triangle to r = 0.66 between the distal radius and calcaneus. We conclude that the inverse relationship between age and bone mass measured by absorptiometry techniques in white women continues into the ninth decade of life. The relationship is strongest for bone density of Ward's triangle and the calcaneus and weakest for the spine.

Reference Models for Multi-Layer Tissue Structures

DTIC Science & Technology

2016-09-01

simulation,  finite   element  analysis 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON USAMRMC...Physiologically realistic, fully specimen-specific, nonlinear reference models. Tasks. Finite element analysis of non-linear mechanics of cadaver...models. Tasks. Finite element analysis of non-linear mechanics of multi-layer tissue regions of human subjects. Deliverables. Partially subject- and

Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

NASA Astrophysics Data System (ADS)

Zhai, Ding; Lu, Anyang; Li, Jinghao; Zhang, Qingling

2016-10-01

This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman-Yakubovic-Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H- and H∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.

Pascal's Triangle: 100% of the Numbers Are Even!

ERIC Educational Resources Information Center

Bhindi, Nayan; McMenamin, Justin

2010-01-01

Pascal's triangle is an arrangement of the binomial coefficients in a triangle. Each number inside Pascal's triangle is calculated by adding the two numbers above it. When all the odd integers in Pascal's triangle are highlighted (black) and the remaining evens are left blank (white), one of many patterns in Pascal's triangle is displayed. By…

Tiling a figure using a height in a tree

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

Remila, E.

1996-12-31

We first give a new presentation of an algorithm from Thurston of tiling with lozenges formed from two cells of the triangular lattice A. Secondly we extend the method to get a linear algorithm of tiling with leaning dominoes (parallelograms formed from four cells of {Lambda}) and triangles (formed from four cells of {Lambda}). Thirdly, we produce a quadratic algorithm of tiling with leaning dominoes.

Final Report: Continuation Study: A Systems Approach to Understanding Post-Traumatic Stress Disorder

DTIC Science & Technology

2017-01-31

Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 Post Traumatic Stress Disorder, HPA-Circadian-metabolic pathway, methylation...17150 remaining probes were located in coding regions. Linear additive models were used to test the interactions among the quantitative loci and...SECURITY CLASSIFICATION OF: Post -Traumatic Stress Disorder (PTSD) is a complex anxiety disorder affecting many combat-exposed soldiers. Current

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

NASA Astrophysics Data System (ADS)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

Combined-probability space and certainty or uncertainty relations for a finite-level quantum system

NASA Astrophysics Data System (ADS)

Sehrawat, Arun

2017-08-01

The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys certain quantum constraints, which are triangle inequalities in our case. Such a restricted set of combined vectors, called the combined-probability space, is presented here for a d -level quantum system (qudit). The combined space is a compact convex subset of a Euclidean space, and all its extreme points come from a family of parametric curves. Considering a suitable concave function on the combined space to estimate the uncertainty, we deliver an uncertainty relation by finding its global minimum on the curves for a qudit. If one chooses an appropriate concave (or convex) function, then there is no need to search for the absolute minimum (maximum) over the whole space; it will be on the parametric curves. So these curves are quite useful for establishing an uncertainty (or a certainty) relation for a general pair of settings. We also demonstrate that many known tight certainty or uncertainty relations for a qubit can be obtained with the triangle inequalities.

Fast algorithms of constrained Delaunay triangulation and skeletonization for band images

NASA Astrophysics Data System (ADS)

Zeng, Wei; Yang, ChengLei; Meng, XiangXu; Yang, YiJun; Yang, XiuKun

2004-09-01

For the boundary polygons of band-images, a fast constrained Delaunay triangulation algorithm is presented and based on it an efficient skeletonization algorithm is designed. In the process of triangulation the characters of uniform grid structure and the band-polygons are utilized to improve the speed of computing the third vertex for one edge within its local ranges when forming a Delaunay triangle. The final skeleton of the band-image is derived after reducing each triangle to local skeleton lines according to its topology. The algorithm with a simple data structure is easy to understand and implement. Moreover, it can deal with multiply connected polygons on the fly. Experiments show that there is a nearly linear dependence between triangulation time and size of band-polygons randomly generated. Correspondingly, the skeletonization algorithm is also an improvement over the previously known results in terms of time. Some practical examples are given in the paper.

Memristors in the electrical network of Aloe vera L.

PubMed Central

Volkov, Alexander G; Reedus, Jada; Mitchell, Colee M; Tucket, Clayton; Forde-Tuckett, Victoria; Volkova, Maya I; Markin, Vladislav S; Chua, Leon

2014-01-01

A memristor is a resistor with memory, which is a non-linear passive two-terminal electrical element relating magnetic flux linkage and electrical charge. Here we found that memristors exist in vivo. The electrostimulation of the Aloe vera by bipolar sinusoidal or triangle periodic waves induce electrical responses with fingerprints of memristors. Uncouplers carbonylcyanide-3-chlorophenylhydrazone and carbonylcyanide-4-trifluoromethoxy-phenyl hydrazone decrease the amplitude of electrical responses at low and high frequencies of bipolar periodic sinusoidal or triangle electrostimulating waves. Memristive behavior of an electrical network in the Aloe vera is linked to the properties of voltage gated ion channels: the K+ channel blocker TEACl reduces the electric response to a conventional resistor. Our results demonstrate that a voltage gated K+ channel in the excitable tissue of plants has properties of a memristor. The discovery of memristors in plants creates a new direction in the modeling and understanding of electrical phenomena in plants. PMID:25763487

Narayanaswamy’s 1971 aging theory and material time

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

Dyre, Jeppe C., E-mail: dyre@ruc.dk

2015-09-21

The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy’s phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely, the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance.more » One of these is the “unique-triangles property” according to which any three points on the system’s path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibrium time-autocorrelation functions, which extends to aging a previously proposed framework for such functions in equilibrium [J. C. Dyre, e-print arXiv:cond-mat/9712222 (1997)].« less

Improved finite element methodology for integrated thermal structural analysis

NASA Technical Reports Server (NTRS)

Dechaumphai, P.; Thornton, E. A.

1982-01-01

An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.

Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

NASA Astrophysics Data System (ADS)

Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.

2012-11-01

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

NASA Technical Reports Server (NTRS)

Bland, S. R.

1982-01-01

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

Theoretical nuclear physics

NASA Astrophysics Data System (ADS)

Rost, E.; Shephard, J. R.

1992-08-01

This report discusses the following topics: Exact 1-loop vacuum polarization effects in 1 + 1 dimensional QHD; exact 1-fermion loop contributions in 1 + 1 dimensional solitons; exact scalar 1-loop contributions in 1 + 3 dimensions; exact vacuum calculations in a hyper-spherical basis; relativistic nuclear matter with self-consistent correlation energy; consistent RHA-RPA for finite nuclei; transverse response functions in the (triangle)-resonance region; hadronic matter in a nontopological soliton model; scalar and vector contributions to (bar p)p yields (bar lambda)lambda reaction; 0+ and 2+ strengths in pion double-charge exchange to double giant-dipole resonances; and nucleons in a hybrid sigma model including a quantized pion field.

Finite element modeling of reinforced concrete structures strengthened with FRP laminates : final report.

DOT National Transportation Integrated Search

2001-05-01

Linear and non-linear finite element method models were developed for a reinforced concrete bridge that had been strengthened with fiber reinforced polymer composites. ANSYS and SAP2000 modeling software were used; however, most of the development ef...

Anatomic Assessment of Variations in Kambin's Triangle: A Surgical and Cadaver Study.

PubMed

Ozer, Ali Fahir; Suzer, Tuncer; Can, Halil; Falsafi, Mani; Aydin, Murat; Sasani, Mehdi; Oktenoglu, Tunc

2017-04-01

The relationship of exiting root and Kambin's triangle is discussed in this article. Transforaminal endoscopic surgery as the gold standard of less invasive lumbar disc surgeries is performed through Kambin's triangle. Existing root damage is one of the most important complication for this type of surgery. Anatomic variations in Kambin's triangle may be the main reason for nerve root damage during endoscopic lumbar disc surgery. Kambin's triangle was investigated with surgical views and cadaver studies. Thirty-four patients with far lateral disc herniation were treated with an extraforaminal approach under the microscope. On the other hand, 48 Kambin's triangles were dissected on 8 cadavers. Three main types of triangle were identified, and patients were grouped according to these 3 types of the triangle. Only 6 of the 34 patients had type 3 triangles, which is the wide classical triangle described by Kambin; however, 17 patients had type 2, with a narrow space in the triangle, and 11 patients had type 1, with no space inside the triangle. Cadaver results were similar; only 10 of the 48 specimens had the type 3 classical triangle, whereas 23 specimens had type 2, and 15 specimens had type 1 triangles. Our results disclosed narrowed or no space in 82.4% of the patients and 79.2% of the cadavers. We observed that a wide and safe room of the triangle may not be exist in some patients. Therefore, more care must be taken during endoscopic lumbar disc surgery to avoid nerve damage. Copyright © 2017 Elsevier Inc. All rights reserved.

Faulhaber's Triangle

ERIC Educational Resources Information Center

Torabi-Dashti, Mohammad

2011-01-01

Like Pascal's triangle, Faulhaber's triangle is easy to draw: all you need is a little recursion. The rows are the coefficients of polynomials representing sums of integer powers. Such polynomials are often called Faulhaber formulae, after Johann Faulhaber (1580-1635); hence we dub the triangle Faulhaber's triangle.

Algebraic signal processing theory: 2-D spatial hexagonal lattice.

PubMed

Pünschel, Markus; Rötteler, Martin

2007-06-01

We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper.

High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1999-01-01

Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

Pb4(OH)4(BrO3)3(NO3): An Example of SHG Crystal in Metal Bromates Containing π-Conjugated Planar Triangle.

PubMed

Kong, Fang; Hu, Chun-Li; Liang, Ming-Li; Mao, Jiang-Gao

2016-01-19

The first example of SHG crystal in the metal bromates containing π-conjugated planar triangle systems, namely, Pb4(OH)4(BrO3)3(NO3), was successfully synthesized via the hydrothermal method. Furthermore, a single crystal of centrosymmetric Pb8O(OH)6(BrO3)6(NO3)2·H2O was also obtained. Both compounds contain similar [Pb4(OH)4] cubane-like tetranuclear clusters, but they display different one-dimensional (1D) chain structures. Pb4(OH)4(BrO3)3(NO3) features a zigzag [Pb4(OH)4(BrO3)3](+) 1D chain, while Pb8O(OH)6(BrO3)6(NO3)2·H2O is composed of two different orthogonal chains: the linear [Pb4(OH)4(BrO3)2](2+) 1D chain along the b-axis and the zigzag [Pb4O2(OH)2(BrO3)4](2-) 1D chain along the a-axis. The NO3 planar triangles of the compounds are all isolated and located in the spaces of the structures. Pb4(OH)4(BrO3)3(NO3) exhibits the first example of SHG crystal in the metal bromates with π-conjugated planar triangle. The second-harmonic generation (SHG) efficiency of Pb4(OH)4(BrO3)3(NO3) is approximately equal to that of KDP and it is phase-matchable. Dipole moment and theory calculations indicate that BrO3, NO3, and PbO4 groups are the origin of its SHG efficiency, although some of the contributions cancel each other out.

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Triangles: Shapes in Math, Science and Nature.

ERIC Educational Resources Information Center

Ross, Catherine Sheldrick

This book examines everything having to do with the triangle. It begins with a basic definition of the triangle and continues with discussions on tetrahedrons, triangular prisms, and pyramid shapes. Some ideas addressed include how triangles are used to measure heights and distances, the importance of triangles to builders, Alexander Graham Bell's…

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Shear-flexible finite-element models of laminated composite plates and shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Mathers, M. D.

1975-01-01

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

Finite-time H∞ control for linear continuous system with norm-bounded disturbance

NASA Astrophysics Data System (ADS)

Meng, Qingyi; Shen, Yanjun

2009-04-01

In this paper, the definition of finite-time H∞ control is presented. The system under consideration is subject to time-varying norm-bounded exogenous disturbance. The main aim of this paper is focused on the design a state feedback controller which ensures that the closed-loop system is finite-time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. A sufficient condition is presented for the solvability of this problem, which can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

A geometric approach to aortic root surgical anatomy.

PubMed

Contino, Monica; Mangini, Andrea; Lemma, Massimo Giovanni; Romagnoni, Claudia; Zerbi, Pietro; Gelpi, Guido; Antona, Carlo

2016-01-01

The aim of this study was the analysis of the geometrical relationships between the different structures constituting the aortic root, with particular attention to interleaflet triangles, haemodynamic ventriculo-arterial junction and functional aortic annulus in normal subjects. Sixteen formol-fixed human hearts with normal aortic roots were studied. The aortic root was isolated, sectioned at the midpoint of the non-coronary sinus, spread apart and photographed by a high-resolution digital camera. After calibration and picture resizing, the software AutoCAD 2004 was used to identify and measure all the elements of the interleaflets triangles and of the aortic root that were objects of our analysis. Multiple comparisons were performed with one-way analysis of variance for continuous data and with Kruskal-Wallis analysis for non-continuous data. Linear regression and Pearson's product correlation were used to correlate root element dimensions when appropriate. Student's t-test was used to compare means for unpaired data. Heron's formula was applied to estimate the functional aortic annular diameters. The non coronary-left coronary interleaflets triangles were larger, followed by inter-coronary and right-non-coronary ones. The apical angle is <60° and its standard deviation can be considered an asymmetry index. The sinu-tubular junction was shown to be 10% larger than the virtual basal ring (VBR). The mathematical relationship between the haemodynamic ventriculo-arterial junction and the VBR calculated by linear regression and expressed in terms of the diameter was: haemodynamic ventriculo-arterial junction = 2.29 VBR (diameter) + 47. Conservative aortic surgery is based on a better understanding of aortic root anatomy and physiology. The relationships among its elements are of paramount importance during aortic valve repair/sparing procedures and they can be useful also in echocardiographic analysis and in computed tomography reconstruction. © The Author 2015. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery. All rights reserved.

The design and implementation of cost-effective algorithms for direct solution of banded linear systems on the vector processor system 32 supercomputer

NASA Technical Reports Server (NTRS)

Samba, A. S.

1985-01-01

The problem of solving banded linear systems by direct (non-iterative) techniques on the Vector Processor System (VPS) 32 supercomputer is considered. Two efficient direct methods for solving banded linear systems on the VPS 32 are described. The vector cyclic reduction (VCR) algorithm is discussed in detail. The performance of the VCR on a three parameter model problem is also illustrated. The VCR is an adaptation of the conventional point cyclic reduction algorithm. The second direct method is the Customized Reduction of Augmented Triangles' (CRAT). CRAT has the dominant characteristics of an efficient VPS 32 algorithm. CRAT is tailored to the pipeline architecture of the VPS 32 and as a consequence the algorithm is implicitly vectorizable.

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

NASA Astrophysics Data System (ADS)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-06-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Electron and donor-impurity-related Raman scattering and Raman gain in triangular quantum dots under an applied electric field

NASA Astrophysics Data System (ADS)

Tiutiunnyk, Anton; Akimov, Volodymyr; Tulupenko, Viktor; Mora-Ramos, Miguel E.; Kasapoglu, Esin; Morales, Alvaro L.; Duque, Carlos Alberto

2016-04-01

The differential cross-section of electron Raman scattering and the Raman gain are calculated and analysed in the case of prismatic quantum dots with equilateral triangle base shape. The study takes into account their dependencies on the size of the triangle, the influence of externally applied electric field as well as the presence of an ionized donor center located at the triangle's orthocenter. The calculations are made within the effective mass and parabolic band approximations, with a diagonalization scheme being applied to obtain the eigenfunctions and eigenvalues of the x- y Hamiltonian. The incident and secondary (scattered) radiation have been considered linearly-polarized along the y-direction, coinciding with the direction of the applied electric field. For the case with an impurity center, Raman scattering with the intermediate state energy below the initial state one has been found to show maximum differential cross-section more than by an order of magnitude bigger than that resulting from the scheme with lower intermediate state energy. The Raman gain has maximum magnitude around 35 nm dot size and electric field of 40 kV/cm for the case without impurity and at maximum considered values of the input parameters for the case with impurity. Values of Raman gain of the order of up to 104cm-1 are predicted in both cases.

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

NASA Astrophysics Data System (ADS)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-04-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Geometric Construction of Pythagorean Triangles

ERIC Educational Resources Information Center

Chandrupatla, Tirupathi R.; Osler, Thomas J.

2004-01-01

A right triangle with legs x and y and hypotenuse z in which x, y and z are all positive integers is called a Pythagorean triangle (PT) and the triple denoted by [x,y,z] is a Pythagorean triple. If x, y and z are all relatively prime (gcd is 1), then the triangle is called a primitive Pythagorean triangle (PPT) and the tripe a primitive…

The Hexaparagon

ERIC Educational Resources Information Center

Hanson, J. R.

2006-01-01

A hexagon with each pair of opposite sides parallel to a side of a triangle will be called a hexaparagon for that triangle. One way to construct a hexaparagon for a given triangle ABC is to use as vertices the centroids P, Q, R, S, T, and U of the six non-overlapping sub-triangles formed by the three medians of triangle ABC. The perimeter of this…

Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems

NASA Astrophysics Data System (ADS)

Arrarás, A.; Portero, L.; Yotov, I.

2014-01-01

We study space and time discretizations for mixed formulations of parabolic problems. The spatial approximation is based on the multipoint flux mixed finite element method, which reduces to an efficient cell-centered pressure system on general grids, including triangles, quadrilaterals, tetrahedra, and hexahedra. The time integration is performed by using a domain decomposition time-splitting technique combined with multiterm fractional step diagonally implicit Runge-Kutta methods. The resulting scheme is unconditionally stable and computationally efficient, as it reduces the global system to a collection of uncoupled subdomain problems that can be solved in parallel without the need for Schwarz-type iteration. Convergence analysis for both the semidiscrete and fully discrete schemes is presented.

MSC products for the simulation of tire behavior

NASA Technical Reports Server (NTRS)

Muskivitch, John C.

1995-01-01

The modeling of tires and the simulation of tire behavior are complex problems. The MacNeal-Schwendler Corporation (MSC) has a number of finite element analysis products that can be used to address the complexities of tire modeling and simulation. While there are many similarities between the products, each product has a number of capabilities that uniquely enable it to be used for a specific aspect of tire behavior. This paper discusses the following programs: (1) MSC/NASTRAN - general purpose finite element program for linear and nonlinear static and dynamic analysis; (2) MSC/ADAQUS - nonlinear statics and dynamics finite element program; (3) MSC/PATRAN AFEA (Advanced Finite Element Analysis) - general purpose finite element program with a subset of linear and nonlinear static and dynamic analysis capabilities with an integrated version of MSC/PATRAN for pre- and post-processing; and (4) MSC/DYTRAN - nonlinear explicit transient dynamics finite element program.

Research on tessellation with triangle strip

NASA Astrophysics Data System (ADS)

Yu, Li; Zhang, Huaisheng

2018-04-01

The tessellation module of graphics pipeline can generate many triangles to specify surface detail characteristics, which are usually organized in triangle lists. However, the number of generated vertices is large and there are many repeated vertices. This paper proposes a new tessellation approach of triangle strips, which makes use of the adjacent relationship among triangles. It decreases the number of generated vertices which will benefits latter computation and storage. Experiments show that the number of generated vertices by the strip approach is about 51% of traditional triangle lists, which can improve the performance of GPU tessellation.

Numerical simulation of weakly ionized hypersonic flow over reentry capsules

NASA Astrophysics Data System (ADS)

Scalabrin, Leonardo C.

The mathematical and numerical formulation employed in the development of a new multi-dimensional Computational Fluid Dynamics (CFD) code for the simulation of weakly ionized hypersonic flows in thermo-chemical non-equilibrium over reentry configurations is presented. The flow is modeled using the Navier-Stokes equations modified to include finite-rate chemistry and relaxation rates to compute the energy transfer between different energy modes. The set of equations is solved numerically by discretizing the flowfield using unstructured grids made of any mixture of quadrilaterals and triangles in two-dimensions or hexahedra, tetrahedra, prisms and pyramids in three-dimensions. The partial differential equations are integrated on such grids using the finite volume approach. The fluxes across grid faces are calculated using a modified form of the Steger-Warming Flux Vector Splitting scheme that has low numerical dissipation inside boundary layers. The higher order extension of inviscid fluxes in structured grids is generalized in this work to be used in unstructured grids. Steady state solutions are obtained by integrating the solution over time implicitly. The resulting sparse linear system is solved by using a point implicit or by a line implicit method in which a tridiagonal matrix is assembled by using lines of cells that are formed starting at the wall. An algorithm that assembles these lines using completely general unstructured grids is developed. The code is parallelized to allow simulation of computationally demanding problems. The numerical code is successfully employed in the simulation of several hypersonic entry flows over space capsules as part of its validation process. Important quantities for the aerothermodynamics design of capsules such as aerodynamic coefficients and heat transfer rates are compared to available experimental and flight test data and other numerical results yielding very good agreement. A sensitivity analysis of predicted radiative heating of a space capsule to several thermo-chemical non-equilibrium models is also performed.

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

NASA Astrophysics Data System (ADS)

Syed Ali, M.; Yogambigai, J.; Kwon, O. M.

2018-03-01

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov-Krasovskii's functional and utilisation of Jensen's inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Galerkin finite difference Laplacian operators on isolated unstructured triangular meshes by linear combinations

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1990-01-01

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formulae in Cartesian coordinates for the Laplacian operator on isolated unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator along with linear combinations of the residual equations are used to develop the algorithm. The algorithm was tested for a wide variety of unstructured meshes and found to give satisfactory results.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model.

PubMed

Gras, Laure-Lise; Mitton, David; Crevier-Denoix, Nathalie; Laporte, Sébastien

2012-01-01

Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

A fast parallel clustering algorithm for molecular simulation trajectories.

PubMed

Zhao, Yutong; Sheong, Fu Kit; Sun, Jian; Sander, Pedro; Huang, Xuhui

2013-01-15

We implemented a GPU-powered parallel k-centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370-residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k-centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc. Copyright © 2012 Wiley Periodicals, Inc.

Frequency analysis via the method of moment functionals

NASA Technical Reports Server (NTRS)

Pearson, A. E.; Pan, J. Q.

1990-01-01

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Comparison of Nonlinear Random Response Using Equivalent Linearization and Numerical Simulation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2000-01-01

A recently developed finite-element-based equivalent linearization approach for the analysis of random vibrations of geometrically nonlinear multiple degree-of-freedom structures is validated. The validation is based on comparisons with results from a finite element based numerical simulation analysis using a numerical integration technique in physical coordinates. In particular, results for the case of a clamped-clamped beam are considered for an extensive load range to establish the limits of validity of the equivalent linearization approach.

On the Stability of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs

NASA Technical Reports Server (NTRS)

Patilkulkarni, Sudarshan; Herencia-Zapana, Heber; Gray, W. Steven; Gonzalez, Oscar R.

2004-01-01

This paper presents two mean-square stability tests for a jump-linear system driven by a finite-state machine with a first-order Markovian input process. The first test is based on conventional Markov jump-linear theory and avoids the use of any higher-order statistics. The second test is developed directly using the higher-order statistics of the machine s output process. The two approaches are illustrated with a simple model for a recoverable computer control system.

Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Oleschko, K.; Khrennikov, A.

2017-10-01

This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.

Validation of drift and diffusion coefficients from experimental data

NASA Astrophysics Data System (ADS)

Riera, R.; Anteneodo, C.

2010-04-01

Many fluctuation phenomena, in physics and other fields, can be modeled by Fokker-Planck or stochastic differential equations whose coefficients, associated with drift and diffusion components, may be estimated directly from the observed time series. Its correct characterization is crucial to determine the system quantifiers. However, due to the finite sampling rates of real data, the empirical estimates may significantly differ from their true functional forms. In the literature, low-order corrections, or even no corrections, have been applied to the finite-time estimates. A frequent outcome consists of linear drift and quadratic diffusion coefficients. For this case, exact corrections have been recently found, from Itô-Taylor expansions. Nevertheless, model validation constitutes a necessary step before determining and applying the appropriate corrections. Here, we exploit the consequences of the exact theoretical results obtained for the linear-quadratic model. In particular, we discuss whether the observed finite-time estimates are actually a manifestation of that model. The relevance of this analysis is put into evidence by its application to two contrasting real data examples in which finite-time linear drift and quadratic diffusion coefficients are observed. In one case the linear-quadratic model is readily rejected while in the other, although the model constitutes a very good approximation, low-order corrections are inappropriate. These examples give warning signs about the proper interpretation of finite-time analysis even in more general diffusion processes.

Perfect commuting-operator strategies for linear system games

NASA Astrophysics Data System (ADS)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

Moisture Transport in Composites during Repair Work,

DTIC Science & Technology

1983-09-01

4 * FINITE DIFFERENCE EQUATIONS. .. . . .. . .. .. .. .. .. 6 INI I A ANBOUNAAYYCONDITIONS................ 7 REASONABLE FIRST...DURING DRYING AND CURING . . . ........ 9 5 CONVERGENCE OF FINITE DIFFERENCE METHOD USING DIFFERENT At . . .. 12 6 CONVERGENCE OF FDA METHOD FOR SAME At...transport we will use a finite difference approach, changing the Fickian equation to a finite number of linear algebraic equations that can be solved by

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

Distributed Leader-Following Finite-Time Consensus Control for Linear Multiagent Systems under Switching Topology

PubMed Central

Xu, Xiaole; Chen, Shengyong

2014-01-01

This paper investigates the finite-time consensus problem of leader-following multiagent systems. The dynamical models for all following agents and the leader are assumed the same general form of linear system, and the interconnection topology among the agents is assumed to be switching and undirected. We mostly consider the continuous-time case. By assuming that the states of neighbouring agents are known to each agent, a sufficient condition is established for finite-time consensus via a neighbor-based state feedback protocol. While the states of neighbouring agents cannot be available and only the outputs of neighbouring agents can be accessed, the distributed observer-based consensus protocol is proposed for each following agent. A sufficient condition is provided in terms of linear matrix inequalities to design the observer-based consensus protocol, which makes the multiagent systems achieve finite-time consensus under switching topologies. Then, we discuss the counterparts for discrete-time case. Finally, we provide an illustrative example to show the effectiveness of the design approach. PMID:24883367

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Non-stationary measurements of Chiral Magnetic Effect

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

Shevchenko, V.I., E-mail: vladimir.i.shevchenko@gmail.com

2013-12-15

We discuss the Chiral Magnetic Effect from the quantum theory of measurements point of view for non-stationary measurements. The effect of anisotropy for fluctuations of electric currents in a magnetic field is addressed. It is shown that anisotropy caused by nonzero axial chemical potential is indistinguishable in this framework from anisotropy caused by finite measurement time or finite lifetime of the magnetic field, and in all cases it is related to abelian triangle anomaly. Possible P-odd effects in central heavy-ion collisions (where the Chiral Magnetic Effect is absent) are discussed in this context. This paper is dedicated to the memorymore » of Professor Mikhail Polikarpov (1952–2013). -- Highlights: •Asymmetry in the response function for vector currents of massless fermions in the magnetic field is computed. •Asymmetry caused by axial chemical potential is practically indistinguishable from the one caused by non-stationarity. •The CME current is non-dissipative in the stationary case and dissipative in the non-stationary case. •Importance of studies of P-odd signatures in central collisions is emphasized.« less

76 FR 52649 - Golden Triangle Storage, Inc.; Notice of Application

Federal Register 2010, 2011, 2012, 2013, 2014

2011-08-23

... Triangle Storage, Inc.; Notice of Application On August 5, 2011, Golden Triangle Storage, Inc. (Golden... construct and operate two new salt dome storage caverns at its existing storage site located in Jefferson... Triangle Storage, Inc., 1200 Smith Street, Suite 900, Houston, TX 77002, (832) 397-8642 or John F...

TerraFERMA: The Transparent Finite Element Rapid Model Assembler for multi-physics problems in the solid Earth sciences

NASA Astrophysics Data System (ADS)

Spiegelman, M. W.; Wilson, C. R.; Van Keken, P. E.

2013-12-01

We announce the release of a new software infrastructure, TerraFERMA, the Transparent Finite Element Rapid Model Assembler for the exploration and solution of coupled multi-physics problems. The design of TerraFERMA is driven by two overarching computational needs in Earth sciences. The first is the need for increased flexibility in both problem description and solution strategies for coupled problems where small changes in model assumptions can often lead to dramatic changes in physical behavior. The second is the need for software and models that are more transparent so that results can be verified, reproduced and modified in a manner such that the best ideas in computation and earth science can be more easily shared and reused. TerraFERMA leverages three advanced open-source libraries for scientific computation that provide high level problem description (FEniCS), composable solvers for coupled multi-physics problems (PETSc) and a science neutral options handling system (SPuD) that allows the hierarchical management of all model options. TerraFERMA integrates these libraries into an easier to use interface that organizes the scientific and computational choices required in a model into a single options file, from which a custom compiled application is generated and run. Because all models share the same infrastructure, models become more reusable and reproducible. TerraFERMA inherits much of its functionality from the underlying libraries. It currently solves partial differential equations (PDE) using finite element methods on simplicial meshes of triangles (2D) and tetrahedra (3D). The software is particularly well suited for non-linear problems with complex coupling between components. We demonstrate the design and utility of TerraFERMA through examples of thermal convection and magma dynamics. TerraFERMA has been tested successfully against over 45 benchmark problems from 7 publications in incompressible and compressible convection, magmatic solitary waves and Stokes flow with free surfaces. We have been using it extensively for research in basic magma dynamics, fluid flow in subduction zones and reactive cracking in poro-elastic materials. TerraFERMA is open-source and available as a git repository at bitbucket.org/tferma/tferma and through CIG. Instability of a 1-D magmatic solitary wave to spherical 3D waves calculated using TerraFERMA

Competitions between Rayleigh-Taylor instability and Kelvin-Helmholtz instability with continuous density and velocity profiles

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

Ye, W. H.; He, X. T.; CAPT, Peking University, Beijing 100871

2011-02-15

In this research, competitions between Rayleigh-Taylor instability (RTI) and Kelvin-Helmholtz instability (KHI) in two-dimensional incompressible fluids within a linear growth regime are investigated analytically. Normalized linear growth rate formulas for both the RTI, suitable for arbitrary density ratio with continuous density profile, and the KHI, suitable for arbitrary density ratio with continuous density and velocity profiles, are obtained. The linear growth rates of pure RTI ({gamma}{sub RT}), pure KHI ({gamma}{sub KH}), and combined RTI and KHI ({gamma}{sub total}) are investigated, respectively. In the pure RTI, it is found that the effect of the finite thickness of the density transition layermore » (L{sub {rho}}) reduces the linear growth of the RTI (stabilizes the RTI). In the pure KHI, it is found that conversely, the effect of the finite thickness of the density transition layer increases the linear growth of the KHI (destabilizes the KHI). It is found that the effect of the finite thickness of the density transition layer decreases the ''effective'' or ''local'' Atwood number (A) for both the RTI and the KHI. However, based on the properties of {gamma}{sub RT}{proportional_to}{radical}(A) and {gamma}{sub KH}{proportional_to}{radical}(1-A{sup 2}), the effect of the finite thickness of the density transition layer therefore has a completely opposite role on the RTI and the KHI noted above. In addition, it is found that the effect of the finite thickness of the velocity shear layer (L{sub u}) stabilizes the KHI, and for the most cases, the combined effects of the finite thickness of the density transition layer and the velocity shear layer (L{sub {rho}=}L{sub u}) also stabilize the KHI. Regarding the combined RTI and KHI, it is found that there is a competition between the RTI and the KHI because of the completely opposite effect of the finite thickness of the density transition layer on these two kinds of instability. It is found that the competitions between the RTI and the KHI depend, respectively, on the Froude number, the density ratio of the light fluid to the heavy one, and the finite thicknesses of the density transition layer and the velocity shear layer. Furthermore, for the fixed Froude number, the linear growth rate ratio of the RTI to the KHI decreases with both the density ratio and the finite thickness of the density transition layer, but increases with the finite thickness of the velocity shear layer and the combined finite thicknesses of the density transition layer and the velocity shear layer (L{sub {rho}=}L{sub u}). In summary, our analytical results show that the effect of the finite thickness of the density transition layer stabilizes the RTI and the overall combined effects of the finite thickness of the density transition layer and the velocity shear layer (L{sub {rho}=}L{sub u}) also stabilize the KHI. Thus, it should be included in applications where the transition layer effect plays an important role, such as the formation of large-scale structures (jets) in high energy density physics and astrophysics and turbulent mixing.« less

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Finite Element Analysis and Optimization of Flexure Bearing for Linear Motor Compressor

NASA Astrophysics Data System (ADS)

Khot, Maruti; Gawali, Bajirao

Nowadays linear motor compressors are commonly used in miniature cryocoolers instead of rotary compressors because rotary compressors apply large radial forces to the piston, which provide no useful work, cause large amount of wear and usually require lubrication. Recent trends favour flexure supported configurations for long life. The present work aims at designing and geometrical optimization of flexure bearings using finite element analysis and the development of design charts for selection purposes. The work also covers the manufacturing of flexures using different materials and the validation of the experimental finite element analysis results.

A triangle voting algorithm based on double feature constraints for star sensors

NASA Astrophysics Data System (ADS)

Fan, Qiaoyun; Zhong, Xuyang

2018-02-01

A novel autonomous star identification algorithm is presented in this study. In the proposed algorithm, each sensor star constructs multi-triangle with its bright neighbor stars and obtains its candidates by triangle voting process, in which the triangle is considered as the basic voting element. In order to accelerate the speed of this algorithm and reduce the required memory for star database, feature extraction is carried out to reduce the dimension of triangles and each triangle is described by its base and height. During the identification period, the voting scheme based on double feature constraints is proposed to implement triangle voting. This scheme guarantees that only the catalog star satisfying two features can vote for the sensor star, which improves the robustness towards false stars. The simulation and real star image test demonstrate that compared with the other two algorithms, the proposed algorithm is more robust towards position noise, magnitude noise and false stars.

Calot's triangle.

PubMed

Abdalla, Sala; Pierre, Sacha; Ellis, Harold

2013-05-01

Calot's triangle is an anatomical landmark of special value in cholecystectomy. First described by Jean-François Calot as an "isosceles" triangle in his doctoral thesis in 1891, this anatomical space requires careful dissection before the ligation and division of the cystic artery and cystic duct during cholecystectomy. The modern definition of the boundaries of Calot's triangle varies from Calot's original description, although the exact timing of this change is not entirely clear. The structures within Calot's triangle and their anatomical relationships can present the surgeon with difficulties, particularly when anatomical variations are encountered. Sound knowledge of the normal anatomy of the extrahepatic biliary tract and vasculature, as well as understanding of congenital variation, is thus essential in the prevention of iatrogenic injury. The authors describe the normal anatomy of Calot's triangle and common anatomical anomalies. The incidence of structural injury is discussed, and new techniques in surgery for enhancing the visualisation of Calot's triangle are reviewed. © . Copyright © 2012 Wiley Periodicals, Inc.

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1981-09-01

This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

Finite-time mixed outer synchronization of complex networks with coupling time-varying delay.

PubMed

He, Ping; Ma, Shu-Hua; Fan, Tao

2012-12-01

This article is concerned with the problem of finite-time mixed outer synchronization (FMOS) of complex networks with coupling time-varying delay. FMOS is a recently developed generalized synchronization concept, i.e., in which different state variables of the corresponding nodes can evolve into finite-time complete synchronization, finite-time anti-synchronization, and even amplitude finite-time death simultaneously for an appropriate choice of the controller gain matrix. Some novel stability criteria for the synchronization between drive and response complex networks with coupling time-varying delay are derived using the Lyapunov stability theory and linear matrix inequalities. And a simple linear state feedback synchronization controller is designed as a result. Numerical simulations for two coupled networks of modified Chua's circuits are then provided to demonstrate the effectiveness and feasibility of the proposed complex networks control and synchronization schemes and then compared with the proposed results and the previous schemes for accuracy.

Periodic trim solutions with hp-version finite elements in time

NASA Technical Reports Server (NTRS)

Peters, David A.; Hou, Lin-Jun

1990-01-01

Finite elements in time as an alternative strategy for rotorcraft trim problems are studied. The research treats linear flap and linearized flap-lag response both for quasi-trim and trim cases. The connection between Fourier series analysis and hp-finite elements for periodic a problem is also examined. It is proved that Fourier series is a special case of space-time finite elements in which one element is used with a strong displacement formulation. Comparisons are made with respect to accuracy among Fourier analysis, displacement methods, and mixed methods over a variety parameters. The hp trade-off is studied for the periodic trim problem to provide an optimum step size and order of polynomial for a given error criteria. It is found that finite elements in time can outperform Fourier analysis for periodic problems, and for some given error criteria. The mixed method provides better results than does the displacement method.

A Description of a Family of Heron Quadrilaterals

ERIC Educational Resources Information Center

Sastry, K. R. S.

2005-01-01

Mathematical historians place Heron in the first century. Right-angled triangles with integer sides and area had been determined before Heron, but he discovered such a "non" right-angled triangle, viz 13, 14, 15; 84. In view of this, triangles with integer sides and area are named "Heron triangles." The Indian mathematician Brahmagupta, born in…

Alternative Fuels Data Center: Triangle Clean Cities Resource Gives CNG

Science.gov Websites

, 2015 Triangle Clean Cities Resource Gives CNG Installation a Boost " Although North Carolina has ; Lacey Jane Wolfe, Triangle Clean Cities Coalition, Coordinator, Durham, North Carolina When the Triangle Clean Cities Coalition (TCCC) set out to promote compressed natural gas (CNG) fueling stations in North

Young Children's Conceptual Understanding of Triangle

ERIC Educational Resources Information Center

Dagli, Ümmühan Yesil; Halat, Erdogan

2016-01-01

This study explored 5-6 year-old children's conceptual understanding of one geometric shape, the triangle. It focused on whether children could draw a triangle from memory, and identify triangles of different types, sizes, and orientations. The data were collected from 82 children attending state preschool programs through a one-on-one interview,…

The Characterizations of Triangles Using the Nine-Point Circles

ERIC Educational Resources Information Center

Srinivasan, V. K.

2012-01-01

In this note, primarily intended for high school students and high school teachers, characterizations of a right triangle and an equilateral triangle in the Euclidean plane are presented using the nine-point circle of a given triangle. Geometrical applications are explored along with their possible uses in the teaching environment. (Contains 4…

Surface plasmon resonance and polarization change properties in centrosymmetric nanoright-triangle dimer arrays

NASA Astrophysics Data System (ADS)

Ma, Qilin; Liu, Guangqiang; Chen, Yiqing; Zhao, Qian; Guo, Jing; Yang, Shaosong; Cai, Weiping

2018-03-01

Dimer nanoparticles in a sandwich structure exhibit a large electric-field intensity enhancement. The dispersion relation between the surface plasmon resonance (SPR) and particle size has not been reported yet, owing to the effects of the particle size, shape, materials, etc. A sandwich structure, which contains a nano-right-triangle dimer array, SiO2 spacer, and Au film, is proposed, with a significant electric-field intensity enhancement and polarization-changing properties. The dependence of the peak positions of the two localized surface plasmon resonance (LSPR) modes as a function of the triangle thicknesses is discussed; different trends are observed for the different LSPR modes. We introduce a concept on the rule for LSPR peak position change, which can contribute to a better understanding of the LSPR modes. In addition, centrosymmetric but not axisymmetric structures, which like in our study exhibit surface plasmon polaritons typically show different responses to a different polarization of the incident light. Here, we showed that our centrosymmetric but not axisymmetric structure can change the linearly polarized light into a circularly or elliptically polarized wave, by surface plasmon-induced polarization properties. Far-field distribution maps are used to study the properties of the surface plasmons-induced circular or elliptic polarization wave. These findings could be employed to better understand the surface plasmon-induced polarization properties showed in previous reports and near-field of surface plasmons. These findings could be employed to better understand the near-field of surface plasmons and polarization properties.

Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae

NASA Technical Reports Server (NTRS)

Rosu, Grigore; Havelund, Klaus

2001-01-01

The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.

Realization of non-linear coherent states by photonic lattices

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

Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn

2015-06-15

In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.

An anatomical study of the transversus abdominis plane block: location of the lumbar triangle of Petit and adjacent nerves.

PubMed

Jankovic, Zorica B; du Feu, Frances M; McConnell, Patricia

2009-09-01

The transversus abdominis plane (TAP) block is a new technique for providing analgesia to the anterior abdominal wall. Most previous studies have used the lumbar triangle of Petit as a landmark for the block. In this cadaveric study, we determined the exact position and size of the lumbar triangle of Petit and identified the nerves affected by the TAP block. The position of the lumbar triangle of Petit was assessed unilaterally in 26 cadaveric specimens relative to reliably palpable surface landmarks. In addition, a series of dissections were performed to explore the course of the nerves blocked by the TAP. The mean distance from the midaxillary line along the iliac crest to the center of the base of the lumbar triangle of Petit at the level of the subcutaneous tissue and over the skin surface was 6.9 cm (range, 4.5-9.2 cm) and 9.3 cm (range, 4-15.1 cm), respectively. The center of the lumbar triangle of Petit was 1.4 cm above the iliac crest. The depth of the TAP at the lumbar triangle of Petit position was 0.5-4 cm and at the midaxillary line it was 0.5-2 cm. The average size of the lumbar triangle of Petit was 2.3 cm x 3.3 cm x 2.2 cm, with an average area of 3.63 +/- 1.93 cm2. The three cadaveric specimens we explored showed the nerves blocked by TAP passed lateral to the triangle. An incidental finding was that in 66% of specimens the lumbar triangle of Petit contained small branches of the subcostal artery. The lumbar triangles of Petit found in the specimens in this study were more posterior than the literature suggests. The position of the lumbar triangle of Petit varies largely and the size is relatively small. The relevant nerves to be blocked had not entered the TAP in the specimens in this study at the point of the lumbar triangle of Petit. At the midaxillary line, however, all the nerves were in the TAP.

Synthetic Aperture Acoustic Imaging of Canonical Targets with a 2-15 kHz Linear FM Chirp

DTIC Science & Technology

2011-04-25

PERFORMING ORGANIZATION NAMES AND ADDRESSES U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS...55997-CS.1 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR/MONITOR’S ACRONYM(S) ARO 8. PERFORMING ORGANIZATION REPORT NUMBER 19a. NAME OF...targets (bowling ball and softball ) • on dirt and grass • behind a metallic chain link fence d. Material study • open and closed cell foam • ceiling

Self-Avoiding Walks Over Adaptive Triangular Grids

NASA Technical Reports Server (NTRS)

Heber, Gerd; Biswas, Rupak; Gao, Guang R.; Saini, Subhash (Technical Monitor)

1999-01-01

Space-filling curves is a popular approach based on a geometric embedding for linearizing computational meshes. We present a new O(n log n) combinatorial algorithm for constructing a self avoiding walk through a two dimensional mesh containing n triangles. We show that for hierarchical adaptive meshes, the algorithm can be locally adapted and easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the runtime partitioning and load balancing of adaptive unstructured grids.

[Research on the photoelectric conversion efficiency of grating antireflective layer solar cells].

PubMed

Zhong, Hui; Gao, Yong-Yi; Zhou, Ren-Long; Zhou, Bing-ju; Tang, Li-qiang; Wu, Ling-xi; Li, Hong-jian

2011-07-01

A numerical investigation of the effect of grating antireflective layer structure on the photoelectric conversion efficiency of solar cells was carried out by the finite-difference time-domain method. The influence of grating shape, height and the metal film thickness coated on grating surface on energy storage was analyzed in detail. It was found that the comparison between unoptimized and optimized surface grating structure on solar cells shows that the optimization of surface by grating significantly increases the energy storage capability and greatly improves the efficiency, especially of the photoelectric conversion efficiency and energy storage of the triangle grating. As the film thickness increases, energy storage effect increases, while as the film thickness is too thick, energy storage effect becomes lower and lower.

Pascal's Infinite Set of Triangles

ERIC Educational Resources Information Center

Skurnick, Ronald

2005-01-01

Pascal's Triangle is, without question, the most well-known triangular array of numbers in all of mathematics. A well-known algorithm for constructing Pascal's Triangle is based on the following two observations. The outer edges of the triangle consist of all 1's. Each number not lying on the outer edges is the sum of the two numbers above it in…

Enjoyment of Euclidean Planar Triangles

ERIC Educational Resources Information Center

Srinivasan, V. K.

2013-01-01

This article adopts the following classification for a Euclidean planar [triangle]ABC, purely based on angles alone. A Euclidean planar triangle is said to be acute angled if all the three angles of the Euclidean planar [triangle]ABC are acute angles. It is said to be right angled at a specific vertex, say B, if the angle ?ABC is a right angle…

A high-accuracy optical linear algebra processor for finite element applications

NASA Technical Reports Server (NTRS)

Casasent, D.; Taylor, B. K.

1984-01-01

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

Issues in the digital implementation of control compensators. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Moroney, P.

1979-01-01

Techniques developed for the finite-precision implementation of digital filters were used, adapted, and extended for digital feedback compensators, with particular emphasis on steady state, linear-quadratic-Gaussian compensators. Topics covered include: (1) the linear-quadratic-Gaussian problem; (2) compensator structures; (3) architectural issues: serialism, parallelism, and pipelining; (4) finite wordlength effects: quantization noise, quantizing the coefficients, and limit cycles; and (5) the optimization of structures.

Leptonic Unitarity Triangle and CP-Violation

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

Farzan, Yasaman

2002-02-01

The area of the unitarity triangle is a measure of CP-violation. We introduce the leptonic unitarity triangles and study their properties. We consider the possibility of reconstructing the unitarity triangle in future oscillation and non-oscillation experiments. A set of measurements is suggested which will, in principle, allow us to measure all sides of the triangle, and consequently to establish CP-violation. For different values of the CP-violating phase, {delta}{sub D}, the required accuracy of measurements is estimated. The key elements of the method include determination of |U{sub e3}| and studies of the {nu}{sub {mu}} - {nu}{sub {mu}} survival probability in oscillationsmore » driven by the solar mass splitting {Delta}m{sub sun}{sup 2}. We suggest additional astrophysical measurements which may help to reconstruct the triangle. The method of the unitarity triangle is complementary to the direct measurements of CP-asymmetry. It requires mainly studies of the survival probabilities and processes where oscillations are averaged or the coherence of the state is lost.« less

P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems

NASA Technical Reports Server (NTRS)

Kang, Kab S.

2002-01-01

The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning

A Classroom Note on Generating Examples for the Laws of Sines and Cosines from Pythagorean Triangles

ERIC Educational Resources Information Center

Sher, Lawrence; Sher, David

2007-01-01

By selecting certain special triangles, students can learn about the laws of sines and cosines without wrestling with long decimal representations or irrational numbers. Since the law of cosines requires only one of the three angles of a triangle, there are many examples of triangles with integral sides and a cosine that can be represented exactly…

Piecewise linear approximation for hereditary control problems

NASA Technical Reports Server (NTRS)

Propst, Georg

1987-01-01

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Adaptive finite element methods for two-dimensional problems in computational fracture mechanics

NASA Technical Reports Server (NTRS)

Min, J. B.; Bass, J. M.; Spradley, L. W.

1994-01-01

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Model checking for linear temporal logic: An efficient implementation

NASA Technical Reports Server (NTRS)

Sherman, Rivi; Pnueli, Amir

1990-01-01

This report provides evidence to support the claim that model checking for linear temporal logic (LTL) is practically efficient. Two implementations of a linear temporal logic model checker is described. One is based on transforming the model checking problem into a satisfiability problem; the other checks an LTL formula for a finite model by computing the cross-product of the finite state transition graph of the program with a structure containing all possible models for the property. An experiment was done with a set of mutual exclusion algorithms and tested safety and liveness under fairness for these algorithms.

Bayesian inversion of refraction seismic traveltime data

NASA Astrophysics Data System (ADS)

Ryberg, T.; Haberland, Ch

2018-03-01

We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test for a synthetic data set from a known model is also presented.

Chiral Redox-Active Isosceles Triangles

DOE PAGES

Nalluri, Siva Krishna Mohan; Liu, Zhichang; Wu, Yilei; ...

2016-04-12

Designing small-molecule organic redox-active materials, with potential applications in energy storage, has received considerable interest of late. Herein, we report on the synthesis, characterization, and application of two rigid chiral triangles, each of which consist of non-identical pyromellitic diimide (PMDI) and naphthalene diimide (NDI)-based redox-active units. 1H and 13C NMR spectroscopic investigations in solution confirm the lower symmetry (C2 point group) associated with these two isosceles triangles. Single-crystal X-ray diffraction analyses reveal their rigid triangular prism-like geometries. Unlike previously investigated equilateral triangle containing three identical NDI subunits, both isosceles triangles do not choose to form one-dimensional supramolecular nanotubes by dintmore » of [C–H···O] interaction-driven columnar stacking. The rigid isosceles triangle, composed of one NDI and two PMDI subunits, forms—in the presence of N,N-dimethylformamide—two different types of intermolecular NDI–NDI and NDI–PMDI π–π stacked dimers with opposite helicities in the solid state. Cyclic voltammetry reveals that both isosceles triangles can accept reversibly up to six electrons. Continuous-wave electron paramagnetic resonance and electron–nuclear double-resonance spectroscopic investigations, supported by density functional theory calculations, on the single-electron reduced radical anions of the isosceles triangles confirm the selective sharing of unpaired electrons among adjacent redox-active NDI subunit(s) within both molecules. The isosceles triangles have been employed as electrode-active materials in organic rechargeable lithium-ion batteries. The evaluation of the structure–performance relationships of this series of diimide-based triangles reveals that the increase in the number of NDI subunits, replacing PMDI ones, within the molecules improves the electrochemical cell performance of the batteries.« less

Air Vehicles Division Computational Structural Analysis Facilities Policy and Guidelines for Users

DTIC Science & Technology

2005-05-01

34 Thermal " as appropriate and the tolerance set to "default". b) Create the model geometry. c) Create the finite elements. d) Create the...linear, non-linear, dynamic, thermal , acoustic analysis. The modelling of composite materials, creep, fatigue and plasticity are also covered...perform professional, high quality finite element analysis (FEA). FE analysts from many tasks within AVD are using the facilities to conduct FEA with

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

NASA Technical Reports Server (NTRS)

Nett, C. N.; Jacobson, C. A.; Balas, M. J.

1983-01-01

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

NASA Astrophysics Data System (ADS)

Makino, Hiroki; Suzuki, Hiroshi

2015-03-01

It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) non-linear sigma model possesses a similar property: The flowed N-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a (2+1)-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the O(N) non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, Gerald W.; Mahadevan, L.

1987-01-01

A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.

An accurate nonlinear finite element analysis and test correlation of a stiffened composite wing panel

NASA Astrophysics Data System (ADS)

Davis, D. D., Jr.; Krishnamurthy, T.; Stroud, W. J.; McCleary, S. L.

1991-05-01

State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.

An accurate nonlinear finite element analysis and test correlation of a stiffened composite wing panel

NASA Technical Reports Server (NTRS)

Davis, D. D., Jr.; Krishnamurthy, T.; Stroud, W. J.; Mccleary, S. L.

1991-01-01

State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.

[Analysis of stress in periodontal ligament of the maxillary first molar on distal movement by nonlinear finite element method].

PubMed

Dong, Jing; Zhang, Zhe-chen; Zhou, Guo-liang

2015-06-01

To analyze the stress distribution in periodontal ligament of maxillary first molar during distal movement with nonlinear finite element analysis, and to compare it with the result of linear finite element analysis, consequently to provide biomechanical evidence for clinical application. The 3-D finite element model including a maxillary first molar, periodontal ligament, alveolar bone, cancellous bone, cortical bone and a buccal tube was built up by using Mimics, Geomagic, ProE and Ansys Workbench. The material of periodontal ligament was set as nonlinear material and linear elastic material, respectively. Loads of different combinations were applied to simulate the clinical situation of distalizing the maxillary first molar. There were channels of low stress in peak distribution of Von Mises equivalent stress and compressive stress of periodontal ligament in nonlinear finite element model. The peak of Von Mises equivalent stress was lower when it was satisfied that Mt/F minus Mr/F approximately equals 2. The peak of compressive stress was lower when it was satisfied that Mt/F was approximately equal to Mr/F. The relative stress of periodontal ligament was higher and violent in linear finite element model and there were no channels of low stress in peak distribution. There are channels in which stress of periodontal ligament is lower. The condition of low stress should be satisfied by applied M/F during the course of distalizing the maxillary first molar.

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Greene, William H.

1989-01-01

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

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

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

Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and ground-based aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, view-dependent triangle meshes and texture maps that produce good images at the required frame rate. We present an algorithm for constructing triangle meshes that optimizes flexible view-dependent error metrics, produces guaranteed error bounds, achieves specified triangle counts directly, and uses frame-to-frame coherence to operate at high frame rates for thousands of triangles per frame. Our method, dubbed Real-time Optimally Adaptingmore » Meshes (ROAM), uses two priority queues to drive split and merge operations that maintain continuous triangulations built from pre-processed bintree triangles. We introduce two additional performance optimizations: incremental triangle stripping and priority-computation deferral lists. ROAM execution time is proportionate to the number of triangle changes per frame, which is typically a few percent of the output mesh size, hence ROAM performance is insensitive to the resolution and extent of the input terrain. Dynamic terrain and simple vertex morphing are supported.« less

Detecting Statistically Significant Communities of Triangle Motifs in Undirected Networks

DTIC Science & Technology

2016-04-26

REPORT TYPE Final 3. DATES COVERED (From - To) 15 Oct 2014 to 14 Jan 2015 4. TITLE AND SUBTITLE Detecting statistically significant clusters of...extend the work of Perry et al. [6] by developing a statistical framework that supports the detection of triangle motif-based clusters in complex...priori, the need for triangle motif-based clustering . 2. Developed an algorithm for clustering undirected networks, where the triangle con guration was

Solution-adaptive finite element method in computational fracture mechanics

NASA Technical Reports Server (NTRS)

Min, J. B.; Bass, J. M.; Spradley, L. W.

1993-01-01

Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.

Self Diagnostic Adhesive for Bonded Joints in Aircraft Structures

DTIC Science & Technology

2016-10-04

validated under the fatigue/dynamic loading condition. 3) Both SEM (Spectral Element Modeling) and FEM ( Finite Element Modeling) simulation of the...Sensors ..................................................................... 22 Parametric Study of Sensor Performance via Finite Element Simulation...The frequency range that we are interested is around 800 kHz. Conventional linear finite element method (FEM) requires a very fine spatial

A compact finite element method for elastic bodies

NASA Technical Reports Server (NTRS)

Rose, M. E.

1984-01-01

A nonconforming finite method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.

On the two-loop virtual QCD corrections to Higgs boson pair production in the standard model

DOE PAGES

Degrassi, Giuseppe; Giardino, Pier Paolo; Gröber, Ramona

2016-07-21

Here, we compute the next-to-leading order virtual QCD corrections to Higgs-pair production via gluon fusion. We also present analytic results for the two-loop contributions to the spin-0 and spin-2 form factors in the amplitude. The reducible contributions, given by the double-triangle diagrams, are evaluated exactly while the two-loop irreducible diagrams are evaluated by an asymptotic expansion in heavy top-quark mass up to and including terms of O(1/mmore » $$8\\atop{t}$$). We estimate that mass effects can reduce the hadronic cross section by at most 10 %, assuming that the finite top-quark mass effects are of similar size in the entire range of partonic energies.« less

Potential energy surface and vibrational band origins of the triatomic lithium cation

NASA Astrophysics Data System (ADS)

Searles, Debra J.; Dunne, Simon J.; von Nagy-Felsobuki, Ellak I.

The 104 point CISD Li +3 potential energy surface and its analytical representation is reported. The calculations predict the minimum energy geometry to be an equilateral triangle of side RLiLi = 3.0 Å and of energy - 22.20506 E h. A fifth-order Morse—Dunham type analytical force field is used in the Carney—Porter normal co-ordinate vibrational Hamiltonian, the corresponding eigenvalue problem being solved variationally using a 560 configurational finite-element basis set. The predicted assignment of the vibrational band origins is in accord with that reported for H +3. Moreover, for 6Li +3 and 7Li +3 the lowest i.r. accessible band origin is the overlineν0,1,±1 predicted to be at 243.6 and 226.0 cm -1 respectively.

Comment on "Hearing the signal of dark sectors with gravitational wave detectors"

NASA Astrophysics Data System (ADS)

Huang, Da; Lu, Bo-Qiang

2018-03-01

We revisit the calculation of the gravitational wave spectra generated in a classically scale-invariant S U (2 ) gauge sector with a scalar field in the adjoint representation, as discussed by J. Jaeckel, et al. The finite-temperature potential at 1-loop level can induce a strong first-order phase transition, during which gravitational waves can be generated. With the accurate numerical computation of the on-shell Euclidean actions of the nucleation bubbles, we find that the triangle approximation employed by J. Jaeckel et al. strongly distorts the actual potential near its maximum and thus greatly underestimates the action values. As a result, the gravitational wave spectra predicted by J. Jaeckel et al. deviate significantly from the exact ones in peak frequencies and shapes.

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

1992-01-01

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology.

Gravity flow of powder in a lunar environment. Part 2: Analysis of flow initiation

NASA Technical Reports Server (NTRS)

Pariseau, W. G.

1971-01-01

A small displacement-small strain finite element technique utilizing the constant strain triangle and incremental constitutive equations for elasticplastic (media nonhardening and obeying a Coulomb yield condition) was applied to the analysis of gravity flow initiation. This was done in a V-shaped hopper containing a powder under lunar environmental conditions. Three methods of loading were examined. Of the three, the method of computing the initial state of stress in a filled hopper prior to drawdown, by adding material to the hopper layer by layer, was the best. Results of the analysis of a typical hopper problem show that the initial state of stress, the elastic moduli, and the strength parameters have an important influence on material response subsequent to the opening of the hopper outlet.

Modelling Viscoelastic Behaviour of Polymer by A Mixed Velocity, Displacement Formulation - Numerical and Experimental Results

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

Pham, VT.; Silva, L.; Digonnet, H.

2011-05-04

The objective of this work is to model the viscoelastic behaviour of polymer from the solid state to the liquid state. With this objective, we perform experimental tensile tests and compare with simulation results. The chosen polymer is a PMMA whose behaviour depends on its temperature. The computation simulation is based on Navier-Stokes equations where we propose a mixed finite element method with an interpolation P1+/P1 using displacement (or velocity) and pressure as principal variables. The implemented technique uses a mesh composed of triangles (2D) or tetrahedra (3D). The goal of this approach is to model the viscoelastic behaviour ofmore » polymers through a fluid-structure coupling technique with a multiphase approach.« less

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

NASA Technical Reports Server (NTRS)

Butler, T. D.; Weatherill, W. H.; Sebastian, J. D.; Ehlers, F. E.

1977-01-01

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method.

Equivalent Linearization Analysis of Geometrically Nonlinear Random Vibrations Using Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2002-01-01

Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

Development and validation of a subject-specific finite element model of the functional spinal unit to predict vertebral strength.

PubMed

Lee, Chu-Hee; Landham, Priyan R; Eastell, Richard; Adams, Michael A; Dolan, Patricia; Yang, Lang

2017-09-01

Finite element models of an isolated vertebral body cannot accurately predict compressive strength of the spinal column because, in life, compressive load is variably distributed across the vertebral body and neural arch. The purpose of this study was to develop and validate a patient-specific finite element model of a functional spinal unit, and then use the model to predict vertebral strength from medical images. A total of 16 cadaveric functional spinal units were scanned and then tested mechanically in bending and compression to generate a vertebral wedge fracture. Before testing, an image processing and finite element analysis framework (SpineVox-Pro), developed previously in MATLAB using ANSYS APDL, was used to generate a subject-specific finite element model with eight-node hexahedral elements. Transversely isotropic linear-elastic material properties were assigned to vertebrae, and simple homogeneous linear-elastic properties were assigned to the intervertebral disc. Forward bending loading conditions were applied to simulate manual handling. Results showed that vertebral strengths measured by experiment were positively correlated with strengths predicted by the functional spinal unit finite element model with von Mises or Drucker-Prager failure criteria ( R 2  = 0.80-0.87), with areal bone mineral density measured by dual-energy X-ray absorptiometry ( R 2  = 0.54) and with volumetric bone mineral density from quantitative computed tomography ( R 2  = 0.79). Large-displacement non-linear analyses on all specimens did not improve predictions. We conclude that subject-specific finite element models of a functional spinal unit have potential to estimate the vertebral strength better than bone mineral density alone.

A Technique of Treating Negative Weights in WENO Schemes

NASA Technical Reports Server (NTRS)

Shi, Jing; Hu, Changqing; Shu, Chi-Wang

2000-01-01

High order accurate weighted essentially non-oscillatory (WENO) schemes have recently been developed for finite difference and finite volume methods both in structural and in unstructured meshes. A key idea in WENO scheme is a linear combination of lower order fluxes or reconstructions to obtain a high order approximation. The combination coefficients, also called linear weights, are determined by local geometry of the mesh and order of accuracy and may become negative. WENO procedures cannot be applied directly to obtain a stable scheme if negative linear weights are present. Previous strategy for handling this difficulty is by either regrouping of stencils or reducing the order of accuracy to get rid of the negative linear weights. In this paper we present a simple and effective technique for handling negative linear weights without a need to get rid of them.

Annual Review of Research Under the Joint Services Electronics Program.

DTIC Science & Technology

1983-12-01

Total Number of Professionals: PI 2 RA 2 (1/2 time ) 6. Sunmmary: Our research into the theory of nonlinear control systems and appli- * cations to...known that all linear time -invariant controllable systems can be transformed to Brunovsky canonical form by a transformation consist- ing only of...estimating the impulse response ( = transfer matrix) of a discrete- time linear system x(t+l) = Fx(t) + Gu(t) y(t) = Hx(t) from a finite set of finite

Evaluation of the Historic Triangle Wayfinding Sign System.

DOT National Transportation Integrated Search

2009-01-01

The "Historic Triangle" in Virginia is named for the historic areas comprising and surrounding Williamsburg, Jamestown, and Yorktown, Virginia. A Historic Triangle Wayfinding Sign System was designed to lead travelers from I-64 to historic sites in W...

Building Intuitive Arguments for the Triangle Congruence Conditions

ERIC Educational Resources Information Center

Piatek-Jimenez, Katrina

2008-01-01

The triangle congruence conditions are a central focus to nearly any course in Euclidean geometry. The author presents a hands-on activity that uses straws and pipe cleaners to explore and justify the triangle congruence conditions. (Contains 4 figures.)

Proceedings of the IDA Workshop on Formal Specification and Verification of Ada (Trade Name) (3rd) Held in Research Triangle Park, North Carolina on 14-16 May 1986

DTIC Science & Technology

1986-08-01

sensitivity to software or hardware failures (bit transformation, register perversion, interface failures, etc .) which could cause the system to operate in a...of systems . She pointed to the need for 40 safety concerns in a continually growing number of computer applications (e.g., monitor and/or control of...informal, definition. Finally, the definition is based on the SMoLCS (Structured Monitored Linear Concurrent Systems ) methodology, an approach to the

Influence of Metal Ion and Polymer Core on the Melt Rheology of Metallosupramolecular Films

DTIC Science & Technology

2012-01-01

60:40, ( F ) 50:50. Storage modulus (triangles), loss modulus (circles), and complex viscosity (squares) vs oscillatory angular frequency. Tref = 30 C...λω), where n is the number of cross-links per unit volume, kB is Boltzmann’s constant, T is temperature, and f (λω) is a function describing the...system at hand. For linear polymer melts n can be written as FNA/M where F is the mass density, NA is Avogadro’s number, andM is molecular weight

Fractional finite Fourier transform.

PubMed

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Design and performance testing of an ultrasonic linear motor with dual piezoelectric actuators.

PubMed

Smithmaitrie, Pruittikorn; Suybangdum, Panumas; Laoratanakul, Pitak; Muensit, Nantakan

2012-05-01

In this work, design and performance testing of an ultrasonic linear motor with dual piezoelectric actuator patches are studied. The motor system consists of a linear stator, a pre-load weight, and two piezoelectric actuator patches. The piezoelectric actuators are bonded with the linear elastic stator at specific locations. The stator generates propagating waves when the piezoelectric actuators are subjected to harmonic excitations. Vibration characteristics of the linear stator are analyzed and compared with finite element and experimental results. The analytical, finite element, and experimental results show agreement. In the experiments, performance of the ultrasonic linear motor is tested. Relationships between velocity and pre-load weight, velocity and applied voltage, driving force and applied voltage, and velocity and driving force are reported. The design of the dual piezoelectric actuators yields a simpler structure with a smaller number of actuators and lower stator stiffness compared with a conventional design of an ultrasonic linear motor with fully laminated piezoelectric actuators.

A decentralized process for finding equilibria given by linear equations.

PubMed Central

Reiter, S

1994-01-01

I present a decentralized process for finding the equilibria of an economy characterized by a finite number of linear equilibrium conditions. The process finds all equilibria or, if there are none, reports that, in a finite number of steps at most equal to the number of equations. The communication and computational complexity compare favorably with other decentralized processes. The process may also be interpreted as an algorithm for solving a distributed system of linear equations. Comparisons with the Linpack program for LU (lower and upper triangular decomposition of the matrix of the equation system, a version of Gaussian elimination) are presented. PMID:11607486

Optical laboratory solution and error model simulation of a linear time-varying finite element equation

NASA Technical Reports Server (NTRS)

Taylor, B. K.; Casasent, D. P.

1989-01-01

The use of simplified error models to accurately simulate and evaluate the performance of an optical linear-algebra processor is described. The optical architecture used to perform banded matrix-vector products is reviewed, along with a linear dynamic finite-element case study. The laboratory hardware and ac-modulation technique used are presented. The individual processor error-source models and their simulator implementation are detailed. Several significant simplifications are introduced to ease the computational requirements and complexity of the simulations. The error models are verified with a laboratory implementation of the processor, and are used to evaluate its potential performance.

Probabilistic finite elements for transient analysis in nonlinear continua

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Exponential convergence through linear finite element discretization of stratified subdomains

NASA Astrophysics Data System (ADS)

Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali

2016-10-01

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.

Testing Linear Temporal Logic Formulae on Finite Execution Traces

NASA Technical Reports Server (NTRS)

Havelund, Klaus; Rosu, Grigore; Norvig, Peter (Technical Monitor)

2001-01-01

We present an algorithm for efficiently testing Linear Temporal Logic (LTL) formulae on finite execution traces. The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive. In most past applications of LTL. theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications. Such tests correspond to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property. We then suggest an optimized algorithm based on transforming LTL formulae. The work is done using the Maude rewriting system. which turns out to provide a perfect notation and an efficient rewriting engine for performing these experiments.

Dynamic Right Triangles

ERIC Educational Resources Information Center

Koyunkaya, Melike Yigit; Kastberg, Signe; Quinlan, James; Edwards, Michael Todd; Keiser, Jane

2015-01-01

Right triangles play a significant role in mathematics. In this favorite lesson, the authors help students understand variant and invariant properties by considering relationships among angle measures and side lengths in right triangles. Students explore these relationships using interactive mathematics software, changing one angle and observing…

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.

PubMed

An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan

2017-01-01

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.

Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation

NASA Astrophysics Data System (ADS)

Popescu, Mihaela; Shyy, Wei; Garbey, Marc

2005-12-01

In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.

Comparison of Linear Induction Motor Theories for the LIMRV and TLRV Motors

DOT National Transportation Integrated Search

1978-01-01

The Oberretl, Yamamura, and Mosebach theories of the linear induction motor are described and also applied to predict performance characteristics of the TLRV & LIMRV linear induction motors. The effect of finite motor width and length on performance ...

Ten Triangles around Cavernous Sinus for Surgical Approach, Described by Schematic Diagram and Three Dimensional Models with the Sectioned Images.

PubMed

Chung, Beom Sun; Ahn, Young Hwan; Park, Jin Seo

2016-09-01

For the surgical approach to lesions around the cavernous sinus (CS), triangular spaces around CS have been devised. However, educational materials for learning the triangles were insufficient. The purpose of this study is to present educational materials about the triangles, consisting of a schematic diagram and 3-dimensional (3D) models with sectioned images. To achieve the purposes, other studies were analyzed to establish new definitions and names of the triangular spaces. Learning materials including schematic diagrams and 3D models with cadaver's sectioned images were manufactured. Our new definition was attested by observing the sectioned images and 3D models. The triangles and the four representative surgical approaches were stereoscopically indicated on the 3D models. All materials of this study were put into Portable Document Format file and were distributed freely at our homepage (anatomy.dongguk.ac.kr/triangles). By using our schematic diagram and the 3D models with sectioned images, ten triangles and the related structures could be understood and observed accurately. We expect that our data will contribute to anatomy education, surgery training, and radiologic understanding of the triangles and related structures.

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

Ergodicity of two hard balls in integrable polygons

NASA Astrophysics Data System (ADS)

Bálint, Péter; Troubetzkoy, Serge

2004-11-01

We prove the hyperbolicity, ergodicity and thus the Bernoulli property of two hard balls in one of the following four polygons: the square, the equilateral triangle, the 45°-45°-90° triangle or the 30°-60°-90° triangle.

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time: application to non-rigid neuroimage registration.

PubMed

Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol

2010-12-01

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.

Development of Meteorological Towers Using Advanced Composite Materials

NASA Astrophysics Data System (ADS)

Alshurafa, Sami A.

The research program involved both numerical and experimental work. The numerical analysis was conducted to simulate the static and dynamic behaviour of the 81 m meteorological FRP guyed tower under wind and ice loading. The FRP tower consisted of 16 segments each made of 3 cells connected together to form an equilateral triangle having equal sides of 450 mm. The segments were interconnected using internal sleeves. Various non-linear finite element models were developed to study a number of design parameters for the 81 m FRP tower such as, different laminates containing a variety of stacking sequences of laminate orientations with various thicknesses, different cable diameters, and appropriate guy cable spacing levels. The effect of pre-stressing the guy cables up to 10 % of their breaking strength was investigated. The effect of fibre volume fraction on the design of the FRP tower was also examined. Furthermore, an 8.6 m FRP tower segment was designed using the finite element analysis and subject to the same loading conditions experienced by the bottom section of the 81 m FRP tower. A modal analysis was carried out for both the 8.6 m FRP tower segment with and without a mass on the top as well as for the 81 m FRP guyed tower to evaluate the vibration performance of these towers. The experimental work involved extensive material testing to define the material properties for use in the analysis of the 81 m FRP tower. It also involved the design and fabrication of a special collapsible mandrel for fabricating the FRP cells for the 8.6 m tower segment. The 8.6 m tower was tested horizontally under static lateral loading to 80 % of its estimated failure load using a "whiffle tree" arrangement, in order to simulate a uniformly distributed wind loading. Later, the same FRP tower was erected in a vertical position and was tested with and without a mass on top under dynamic loading to obtain the natural frequencies. Lastly, a comparative study was conducted between two 81 m FRP towers having different fibre volume fractions and a steel tower having a circular cross section.

Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

NASA Astrophysics Data System (ADS)

Saakian, David B.

2017-08-01

We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

Discrete-time Markovian-jump linear quadratic optimal control

NASA Technical Reports Server (NTRS)

Chizeck, H. J.; Willsky, A. S.; Castanon, D.

1986-01-01

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

Reduced modeling of flexible structures for decentralized control

NASA Technical Reports Server (NTRS)

Yousuff, A.; Tan, T. M.; Bahar, L. Y.; Konstantinidis, M. F.

1986-01-01

Based upon the modified finite element-transfer matrix method, this paper presents a technique for reduced modeling of flexible structures for decentralized control. The modeling decisions are carried out at (finite-) element level, and are dictated by control objectives. A simply supported beam with two sets of actuators and sensors (linear force actuator and linear position and velocity sensors) is considered for illustration. In this case, it is conjectured that the decentrally controlled closed loop system is guaranteed to be at least marginally stable.

Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN

NASA Technical Reports Server (NTRS)

Sheerer, T. J.

1986-01-01

The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.

Indexed triangle strips optimization for real-time visualization using genetic algorithm: preliminary study

NASA Astrophysics Data System (ADS)

Tanaka, Kiyoshi; Takano, Shuichi; Sugimura, Tatsuo

2000-10-01

In this work we focus on the indexed triangle strips that is an extended representation of triangle strips to improve the efficiency for geometrical transformation of vertices, and present a method to construct optimum indexed triangle strips using Genetic Algorithm (GA) for real-time visualization. The main objective of this work is how to optimally construct indexed triangle strips by improving the ratio that reuses the data stored in the cash memory and simultaneously reducing the total index numbers with GA. Simulation results verify that the average index numbers and cache miss ratio per polygon cold be small, and consequently the total visualization time required for the optimum solution obtained by this scheme could be remarkably reduced.

DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems

NASA Astrophysics Data System (ADS)

Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske

2008-12-01

We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q1- p0) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results from the finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized. We present example results including the onset of a Rayleigh-Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.

Partitioning Pythagorean Triangles Using Pythagorean Angles

ERIC Educational Resources Information Center

Swenson, Carl E.; Yandl, Andre L.

2012-01-01

Inside any Pythagorean right triangle, it is possible to find a point M so that drawing segments from M to each vertex of the triangle yields angles whose sines and cosines are all rational. This article describes an algorithm that generates an infinite number of such points.

Relations between Some Characteristic Lengths in a Triangle

ERIC Educational Resources Information Center

Koepf, Wolfram; Brede, Markus

2005-01-01

The paper's aim is to note a remarkable (and apparently unknown) relation for right triangles, its generalisation to arbitrary triangles and the possibility to derive these and some related relations by elimination using Groebner basis computations with a modern computer algebra system. (Contains 9 figures.)

Graphing trillions of triangles.

PubMed

Burkhardt, Paul

2017-07-01

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.

Rapid deposition of triangular silver nanoplates on planar surfaces: application to metal-enhanced fluorescence.

PubMed

Aslan, Kadir; Lakowicz, Joseph R; Geddes, Chris D

2005-04-07

A simple and rapid wet-chemical technique for the deposition of silver triangles on conventional glass substrates, which alleviates the need for lithography, has been developed. The technique is based on the seed-mediated cetyltrimethylammonium-bromide-directed growth of silver triangles on glass surfaces, where smaller spherical silver seeds that were attached to the surface were subsequently converted and grown into silver triangles in the presence of a cationic surfactant and silver ions. The size of the silver triangles was controlled by sequential immersion of silver seed-coated glass substrates into a growth solution and by the duration time of immersion. Atomic force microscopy studies revealed that the size of the silver triangles ranged between 100 and 500 nm. Interestingly, these new surfaces are a significant improvement over traditional silver island films for applications in metal-enhanced fluorescence. A routine 16-fold enhancement in emission intensity was typically observed, for protein-immobilized indocyanine green, with a relatively very low loading density of silver triangles on the glass surface.

Coulomb excitations for a short linear chain of metallic shells

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

Zhemchuzhna, Liubov, E-mail: lzhemchuzhna@unm.edu; Center for High Technology Materials, University of New Mexico, Albuquerque, New Mexico 87106; Gumbs, Godfrey

2015-03-15

A self-consistent-field theory is given for the electronic collective modes of a chain containing a finite number, N, of Coulomb-coupled spherical two-dimensional electron gases arranged with their centers along a straight line, for simulating electromagnetic response of a narrow-ribbon of metallic shells. The separation between nearest-neighbor shells is arbitrary and because of the quantization of the electron energy levels due to their confinement to the spherical surface, all angular momenta L of the Coulomb excitations, as well as their projections M on the quantization axis, are coupled. However, for incoming light with a given polarization, only one angular momentum quantummore » number is usually required. Therefore, the electromagnetic response of the narrow-ribbon of metallic shells is expected to be controlled externally by selecting different polarizations for incident light. We show that, when N = 3, the next-nearest-neighbor Coulomb coupling is larger than its value if they are located at opposite ends of a right-angle triangle forming the triad. Additionally, the frequencies of the plasma excitations are found to depend on the orientation of the line joining them with respect to the axis of quantization since the magnetic field generated from the induced oscillating electric dipole moment on one sphere can couple to the induced magnetic dipole moment on another. Although the transverse inter-shell electromagnetic coupling can be modeled by an effective dynamic medium, the longitudinal inter-shell Coulomb coupling, on the other hand, can still significantly modify the electromagnetic property of this effective medium between shells.« less

Numerical and Experimental Dynamic Characteristics of Thin-Film Membranes

NASA Technical Reports Server (NTRS)

Young, Leyland G.; Ramanathan, Suresh; Hu, Jia-Zhu; Pai, P. Frank

2004-01-01

Presented is a total-Lagrangian displacement-based non-linear finite-element model of thin-film membranes for static and dynamic large-displacement analyses. The membrane theory fully accounts for geometric non-linearities. Fully non-linear static analysis followed by linear modal analysis is performed for an inflated circular cylindrical Kapton membrane tube under different pressures, and for a rectangular membrane under different tension loads at four comers. Finite element results show that shell modes dominate the dynamics of the inflated tube when the inflation pressure is low, and that vibration modes localized along four edges dominate the dynamics of the rectangular membrane. Numerical dynamic characteristics of the two membrane structures were experimentally verified using a Polytec PI PSV-200 scanning laser vibrometer and an EAGLE-500 8-camera motion analysis system.

Calculation of cogging force in a novel slotted linear tubular brushless permanent magnet motor

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

Zhu, Z.Q.; Hor, P.J.; Howe, D.

1997-09-01

There is an increasing requirement for controlled linear motion over short and long strokes, in the factory automation and packaging industries, for example. Linear brushless PM motors could offer significant advantages over conventional actuation technologies, such as motor driven cams and linkages and pneumatic rams--in terms of efficiency, operating bandwidth, speed and thrust control, stroke and positional accuracy, and indeed over other linear motor technologies, such as induction motors. Here, a finite element/analytical based technique for the prediction of cogging force in a novel topology of slotted linear brushless permanent magnet motor has been developed and validated. The various forcemore » components, which influence cogging are pre-calculated by the finite element analysis of some basic magnetic structures, facilitate the analytical synthesis of the resultant cogging force. The technique can be used to aid design for the minimization of cogging.« less

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Improved Equivalent Linearization Implementations Using Nonlinear Stiffness Evaluation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2001-01-01

This report documents two new implementations of equivalent linearization for solving geometrically nonlinear random vibration problems of complicated structures. The implementations are given the acronym ELSTEP, for "Equivalent Linearization using a STiffness Evaluation Procedure." Both implementations of ELSTEP are fundamentally the same in that they use a novel nonlinear stiffness evaluation procedure to numerically compute otherwise inaccessible nonlinear stiffness terms from commercial finite element programs. The commercial finite element program MSC/NASTRAN (NASTRAN) was chosen as the core of ELSTEP. The FORTRAN implementation calculates the nonlinear stiffness terms and performs the equivalent linearization analysis outside of NASTRAN. The Direct Matrix Abstraction Program (DMAP) implementation performs these operations within NASTRAN. Both provide nearly identical results. Within each implementation, two error minimization approaches for the equivalent linearization procedure are available - force and strain energy error minimization. Sample results for a simply supported rectangular plate are included to illustrate the analysis procedure.

A diffuse-interface method for two-phase flows with soluble surfactants

PubMed Central

Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

2010-01-01

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

Benchmark solution of the dynamic response of a spherical shell at finite strain

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

Versino, Daniele; Brock, Jerry S.

2016-09-28

Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method bymore » means of numerical examples with finite deformations and material non-linearities and inelasticity.« less

A Bermuda Triangle of Science

ERIC Educational Resources Information Center

Winkelsas, John

2006-01-01

The Bermuda Triangle is famous for the unexplained disappearances of ships and aircraft, and for strange meteorological phenomena that allegedly have occurred within its boundaries. This article presents an activity wherein students are asked to create their own geographical triangles to research, but instead of focusing on the unexplainable,…

Some Unusual Expressions for the Inradius of a Triangle

ERIC Educational Resources Information Center

Osler, Thomas J.; Chandrupatla, Tirupathi R.

2005-01-01

Several formulae for the inradius of various types of triangles are derived. Properties of the inradius and trigonometric functions of the angles of Pythagorean and Heronian triangles are also presented. The entire presentation is elementary and suitable for classes in geometry, precalculus mathematics and number theory.

Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes

NASA Astrophysics Data System (ADS)

Pasquetti, Richard; Rapetti, Francesca

2017-10-01

In a recent JCP paper [9], a higher order triangular spectral element method (TSEM) is proposed to address seismic wave field modeling. The main interest of this TSEM is that the mass matrix is diagonal, so that an explicit time marching becomes very cheap. This property results from the fact that, similarly to the usual SEM (say QSEM), the basis functions are Lagrange polynomials based on a set of points that shows both nice interpolation and quadrature properties. In the quadrangle, i.e. for the QSEM, the set of points is simply obtained by tensorial product of Gauss-Lobatto-Legendre (GLL) points. In the triangle, finding such an appropriate set of points is however not trivial. Thus, the work of [9] follows anterior works that started in 2000's [2,6,11] and now provides cubature nodes and weights up to N = 9, where N is the total degree of the polynomial approximation. Here we wish to evaluate the accuracy of this cubature nodes TSEM with respect to the Fekete-Gauss one, see e.g.[12], that makes use of two sets of points, namely the Fekete points and the Gauss points of the triangle for interpolation and quadrature, respectively. Because the Fekete-Gauss TSEM is in the spirit of any nodal hp-finite element methods, one may expect that the conclusions of this Note will remain relevant if using other sets of carefully defined interpolation points.

Design, Optimization and Evaluation of Integrally Stiffened Al 7050 Panel with Curved Stiffeners

NASA Technical Reports Server (NTRS)

Slemp, Wesley C. H.; Bird, R. Keith; Kapania, Rakesh K.; Havens, David; Norris, Ashley; Olliffe, Robert

2011-01-01

A curvilinear stiffened panel was designed, manufactured, and tested in the Combined Load Test Fixture at NASA Langley Research Center. The panel was optimized for minimum mass subjected to constraints on buckling load, yielding, and crippling or local stiffener failure using a new analysis tool named EBF3PanelOpt. The panel was designed for a combined compression-shear loading configuration that is a realistic load case for a typical aircraft wing panel. The panel was loaded beyond buckling and strains and out-of-plane displacements were measured. The experimental data were compared with the strains and out-of-plane deflections from a high fidelity nonlinear finite element analysis and linear elastic finite element analysis of the panel/test-fixture assembly. The numerical results indicated that the panel buckled at the linearly elastic buckling eigenvalue predicted for the panel/test-fixture assembly. The experimental strains prior to buckling compared well with both the linear and nonlinear finite element model.

Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Liu, Di

2015-01-01

In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions.

PubMed

Liu, Qingshan; Wang, Jun

2011-04-01

This paper presents a one-layer recurrent neural network for solving a class of constrained nonsmooth optimization problems with piecewise-linear objective functions. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter in the model. The number of neurons in the neural network is the same as the number of decision variables of the optimization problem. Compared with existing neural networks for optimization, the proposed neural network has a couple of salient features such as finite-time convergence and a low model complexity. Specific models for two important special cases, namely, linear programming and nonsmooth optimization, are also presented. In addition, applications to the shortest path problem and constrained least absolute deviation problem are discussed with simulation results to demonstrate the effectiveness and characteristics of the proposed neural network.

The Finite Lamplighter Groups: A Guided Tour

ERIC Educational Resources Information Center

Siehler, Jacob A.

2012-01-01

In this article, we present a family of finite groups, which provide excellent examples of the basic concepts of group theory. To work out the center, conjuagacy classes, and commutators of these groups, all that's required is a bit of linear algebra.

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.

Environmental stress and whole-tree physiology

Treesearch

Peter L. Jr. Lorio

1993-01-01

Interactions among bark beetles, pathogens, and conifers constitute a triangle. Another triangle of interactions exist among the invading organism (bark beetles and pathogens), the trees, and the environment. How important, variable or constant, simple or complex, is the role of trees in these triangles? Understanding the wide range of interactions that take place...

From Concept to Reality in Implementing the Knowledge Triangle

ERIC Educational Resources Information Center

Sjoer, Ellen; Nørgaard, Bente; Goossens, Marc

2016-01-01

The concept of Knowledge Triangle (KT) links together research, education and innovation and replaces the traditional "one way" flow of knowledge, essentially from research to education, by a "both ways" circular motion between all the corners of a triangle that, besides research and education, also includes innovation, the…

77 FR 60448 - National Institute of Environmental Health Sciences Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-03

... Health Sciences, Building 101, Rodbell Auditorium, 111 T. W. Alexander Drive, Research Triangle Park, NC..., Rodbell Auditorium, 111 T. W. Alexander Drive, Research Triangle Park, NC 27709. Closed: November 5, 2012... Sciences, Building 101, Rodbell Auditorium, 111 T. W. Alexander Drive, Research Triangle Park, NC 27709...

The DNA Triangle and Its Application to Learning Meiosis

ERIC Educational Resources Information Center

Wright, L. Kate; Catavero, Christina M.; Newman, Dina L.

2017-01-01

Although instruction on meiosis is repeated many times during the undergraduate curriculum, many students show poor comprehension even as upper-level biology majors. We propose that the difficulty lies in the complexity of understanding DNA, which we explain through a new model, the DNA triangle. The "DNA triangle" integrates three…

75 FR 61788 - Triangle Capital Corporation, et al.; Notice of Application

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-06

... to the issuers of such securities. 2. TMF, a North Carolina limited liability limited partnership, is... same investment objectives and strategies as Triangle. Triangle owns a 99.9% limited partnership... persons who are interested persons of TMF. 3. SBIC II, a Delaware limited partnership, is an SBIC licensed...

Teaching Pascal's Triangle from a Computer Science Perspective

ERIC Educational Resources Information Center

Skurnick, Ronald

2004-01-01

Pascal's Triangle is named for the seventeenth-century French philosopher and mathematician Blaise Pascal (the same person for whom the computer programming language is named). Students are generally introduced to Pascal's Triangle in an algebra or precalculus class in which the Binomial Theorem is presented. This article, presents a new method…

Beyond Pascal's Triangle

ERIC Educational Resources Information Center

Minor, Darrell P.

2005-01-01

In "Beyond Pascals Triangle" the author demonstrates ways of using "Pascallike" triangles to expand polynomials raised to powers in a fairly quick and easy fashion. The recursive method could easily be implemented within a spreadsheet, or simply by using paper and pencil. An explanation of why the method works follows the several examples that are…

The Bermuda Triangle of Education.

ERIC Educational Resources Information Center

Bertrand, Yves

The pedagogical triangle of teacher, learner, and subject matter has in its center a fourth element: the communication system. Each feature of the pedagogical triangle, and the communication system as well, relies on a very important cultural component. Problems occur when communication processes in a classroom are fragmented and related to…

Using a Simple Optical Rangefinder To Teach Similar Triangles.

ERIC Educational Resources Information Center

Cuicchi, Paul M.; Hutchison, Paul S.

2003-01-01

Describes how the concept of similar triangles was taught using an optical method of estimating large distances as a corresponding activity. Includes the derivation of a formula to calculate one source of measurement error and is a nice exercise in the use of the properties of similar triangles. (Author/NB)

Dalitz plot distributions in presence of triangle singularities

DOE PAGES

Szczepaniak, Adam P.

2016-03-25

We discuss properties of three-particle Dalitz distributions in coupled channel systems in presence of triangle singularities. The single channel case was discussed long ago where it was found that as a consequence of unitarity, effects of a triangle singularity seen in the Dalitz plot are not seen in Dalitz plot projections. In the coupled channel case we find the same is true for the sum of intensities of all interacting channels. As a result, unlike the single channel case, however, triangle singularities do remain visible in Dalitz plot projections of individual channels.

Dalitz plot distributions in presence of triangle singularities

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

Szczepaniak, Adam P.

We discuss properties of three-particle Dalitz distributions in coupled channel systems in presence of triangle singularities. The single channel case was discussed long ago where it was found that as a consequence of unitarity, effects of a triangle singularity seen in the Dalitz plot are not seen in Dalitz plot projections. In the coupled channel case we find the same is true for the sum of intensities of all interacting channels. As a result, unlike the single channel case, however, triangle singularities do remain visible in Dalitz plot projections of individual channels.

An efficient finite element technique for sound propagation in axisymmetric hard wall ducts carrying high subsonic Mach number flows

NASA Technical Reports Server (NTRS)

Tag, I. A.; Lumsdaine, E.

1978-01-01

The general non-linear three-dimensional equation for acoustic potential is derived by using a perturbation technique. The linearized axisymmetric equation is then solved by using a finite element algorithm based on the Galerkin formulation for a harmonic time dependence. The solution is carried out in complex number notation for the acoustic velocity potential. Linear, isoparametric, quadrilateral elements with non-uniform distribution across the duct section are implemented. The resultant global matrix is stored in banded form and solved by using a modified Gauss elimination technique. Sound pressure levels and acoustic velocities are calculated from post element solutions. Different duct geometries are analyzed and compared with experimental results.

Lie algebras and linear differential equations.

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Rahimi, A.

1972-01-01

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

The subatlantic triangle: gateway to early localization of the atlantoaxial vertebral artery.

PubMed

Tayebi Meybodi, Ali; Gandhi, Sirin; Preul, Mark C; Lawton, Michael T

2018-04-27

OBJECTIVE Exposure of the vertebral artery (VA) between C-1 and C-2 vertebrae (atlantoaxial VA) may be necessary in a variety of pathologies of the craniovertebral junction. Current methods to expose this segment of the VA entail sharp dissection of muscles close to the internal jugular vein and the spinal accessory nerve. The present study assesses the technique of exposing the atlantoaxial VA through a newly defined muscular triangle at the craniovertebral junction. METHODS Five cadaveric heads were prepared for surgical simulation in prone position, turned 30°-45° toward the side of exposure. The atlantoaxial VA was exposed through the subatlantic triangle after reflecting the sternocleidomastoid and splenius capitis muscles inferiorly. The subatlantic triangle was formed by 3 groups of muscles: 1) the levator scapulae and splenius cervicis muscles inferiorly and laterally, 2) the longissimus capitis muscle inferiorly and medially, and 3) the inferior oblique capitis superiorly. The lengths of the VA exposed through the triangle before and after unroofing the C-2 transverse foramen were measured. RESULTS The subatlantic triangle consistently provided access to the whole length of atlantoaxial VA. The average length of the VA exposed via the subatlantic triangle was 19.5 mm. This average increased to 31.5 mm after the VA was released at the C-2 transverse foramen. CONCLUSIONS The subatlantic triangle provides a simple and straightforward pathway to expose the atlantoaxial VA. The proposed method may be useful during posterior approaches to the craniovertebral junction should early exposure and control of the atlantoaxial VA become necessary.

"Triangle of safety": anatomic considerations in transvaginal natural orifice surgery.

PubMed

Roberts, Kurt; Solomon, Daniel; Bell, Robert; Duffy, Andrew

2013-08-01

The introduction of transvaginal (TV) natural orifice transluminal endoscopic surgery (NOTES) brings the loss of traditionally used cutaneous landmarks for safe peritoneal access. This video describes the use of landmarks within the posterior vaginal fornix to define a "triangle of safety" wherein the peritoneal cavity can be accessed while minimizing the risk of injury to surrounding structures. The triangle of safety is best identified in the following way. The cervix and posterior fornix are visualized. Then an imaginary clock located at the base of the cervix is envisioned. The superior two corners of the triangle are represented by the 4 and 8 o'clock positions on this imaginary clock. Sometimes the cervix needs to be grasped and elevated anteriorly so that the inferior apex of the triangle delineated by the center of the rectovaginal fold is better visualized. During hybrid TV NOTES, the rectovaginal pouch of Douglas is visualized from the umbilicus, and the vaginal port can then be safely passed through the center of the triangle. It is important that the vaginal port should be angled upward, aiming toward the umbilicus to avoid injury to the rectum. During pure TV NOTES, the incision is made with electrocautery from the 5 o'clock position to the 7 o'clock position within the triangle. The peritoneum is sharply entered, and the colpotomy is dilated with the surgeons' fingers. The triangle of safety defines a set of landmarks between the base of the cervix and the rectovaginal fold. It allows for a safe TV access for hybrid and pure TV NOTES while minimizing the risk of injury to surrounding structures.

A Universal Ts-VI Triangle Method for the Continuous Retrieval of Evaporative Fraction From MODIS Products

NASA Astrophysics Data System (ADS)

Zhu, Wenbin; Jia, Shaofeng; Lv, Aifeng

2017-10-01

The triangle method based on the spatial relationship between remotely sensed land surface temperature (Ts) and vegetation index (VI) has been widely used for the estimates of evaporative fraction (EF). In the present study, a universal triangle method was proposed by transforming the Ts-VI feature space from a regional scale to a pixel scale. The retrieval of EF is only related to the boundary conditions at pixel scale, regardless of the Ts-VI configuration over the spatial domain. The boundary conditions of each pixel are composed of the theoretical dry edge determined by the surface energy balance principle and the wet edge determined by the average air temperature of open water. The universal triangle method was validated using the EF observations collected by the Energy Balance Bowen Ratio systems in the Southern Great Plains of the United States of America (USA). Two parameterization schemes of EF were used to demonstrate their applicability with Terra Moderate Resolution Imaging Spectroradiometer (MODIS) products over the whole year 2004. The results of this study show that the accuracy produced by both of these two parameterization schemes is comparable to that produced by the traditional triangle method, although the universal triangle method seems specifically suited to the parameterization scheme proposed in our previous research. The independence of the universal triangle method from the Ts-VI feature space makes it possible to conduct a continuous monitoring of evapotranspiration and soil moisture. That is just the ability the traditional triangle method does not possess.

Multipoint propagators in cosmological gravitational instability

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

Bernardeau, Francis; Crocce, Martin; Scoccimarro, Roman

2008-11-15

We introduce the concept of multipoint propagators between linear cosmic fields and their nonlinear counterparts in the context of cosmological perturbation theory. Such functions express how a nonlinearly evolved Fourier mode depends on the full ensemble of modes in the initial density field. We identify and resum the dominant diagrams in the large-k limit, showing explicitly that multipoint propagators decay into the nonlinear regime at the same rate as the two-point propagator. These analytic results generalize the large-k limit behavior of the two-point propagator to arbitrary order. We measure the three-point propagator as a function of triangle shape in numericalmore » simulations and confirm the results of our high-k resummation. We show that any n-point spectrum can be reconstructed from multipoint propagators, which leads to a physical connection between nonlinear corrections to the power spectrum at small scales and higher-order correlations at large scales. As a first application of these results, we calculate the reduced bispectrum at one loop in renormalized perturbation theory and show that we can predict the decrease in its dependence on triangle shape at redshift zero, when standard perturbation theory is least successful.« less

Three-Dimensional Hierarchical Plasmonic Nano-Architecture Enhanced Surface-Enhanced Raman Scattering Immuno-Sensor for Cancer Biomarker Detection in Blood Plasma

PubMed Central

Li, Ming; Cushing, Scott K.; Zhang, Jianming; Suri, Savan; Evans, Rebecca; Petros, William P.; Gibson, Laura F.; Ma, Dongling; Liu, Yuxin; Wu, Nianqiang

2013-01-01

A three-dimensional (3D) hierarchical plasmonic nano-architecture has been designed for a sensitive surface-enhanced Raman scattering (SERS) immuno-sensor for protein biomarker detection. The capture antibody molecules are immobilized on a plasmonic gold triangle nano-array pattern. On the other hand, the detection antibody molecules are linked to the gold nano-star@Raman-reporter@silica sandwich nanoparticles. When protein biomarkers are present, the sandwich nanoparticles are captured over the gold triangle nano-array, forming a confined 3D plasmonic field, leading to the enhanced electromagnetic field in intensity and in 3D space. As a result, the Raman reporter molecules are exposed to a high density of “hot spots”, which amplifies the Raman signal remarkably, improving the sensitivity of the SERS immuno-sensor. This SERS immuno-sensor exhibits a wide linear range (0.1 pg/mL to 10 ng/mL), and a low limit of detection (7 fg/mL) toward human immunoglobulin G (IgG) protein in the buffer solution. This biosensor has been successfully used for detection of the vascular endothelial growth factor (VEGF) in the human blood plasma from clinical breast cancer patient samples. PMID:23659430

What's Your Answer? Searching for Triangles

ERIC Educational Resources Information Center

Meagher, Michael S.; Edwards, Michael Todd; Özgün-Koca, S. Asli

2016-01-01

The article opens with a Geoboard Triangle Quest in this form: "How many noncongruent triangles can be constructed on a 4 × 4 geoboard? How do you know? Justify your answer with significant supporting work." The use of advanced digital technologies as tools for problem solving receives much attention in the methods classes if the…

Homothetic Transformations and Geometric Loci: Properties of Triangles and Quadrilaterals

ERIC Educational Resources Information Center

Mammana, Maria Flavia

2016-01-01

In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the…

76 FR 46823 - National Institute of Environmental Health Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2011-08-03

..., Rodbell Auditorium, 111 T. W. Alexander Drive, Research Triangle Park, NC 27709. Closed: September 1, 2011... Environmental Health Sciences, Building 101, Rodbell Auditorium, 111 T. W. Alexander Drive, Research Triangle... Auditorium, 111 T. W. Alexander Drive, Research Triangle Park, NC 27709. Contact Person: Gwen W Collman, PhD...

Triangles with Given Distances from a Centre

ERIC Educational Resources Information Center

Maloo, Alok K.; Lal, Arbind K.; Singh, Arindama

2002-01-01

There are four Euclidean centres of a triangle--the circumcentre, the centroid, the incentre and the orthocentre. In this article, the authors prove the following: if the centre is the incentre (resp. orthocentre) then there exists a triangle with given distances of its vertices from its incentre (resp. orthocentre). They also consider uniqueness…

What Do You Find? Students Investigating Patterns in Pascal's Triangle

ERIC Educational Resources Information Center

Obara, Samuel

2012-01-01

In this paper, students used problem-solving skills to investigate what patterns exist in the Pascal triangle and incorporated technology using Geometer's Sketchpad (GSP) in the process. Students came up with patterns such as natural numbers, triangular numbers, and Fibonacci numbers. Although the patterns inherent in Pascal's triangle may seem…

78 FR 66107 - National Emissions Standards for Hazardous Air Pollutants Residual Risk and Technology Review for...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-11-04

.... Alexander Drive in Research Triangle Park, North Carolina. If EPA holds a public hearing, the EPA will keep... Drive in Research Triangle Park, North Carolina. Persons interested in presenting oral testimony or... Agency, Research Triangle Park, North Carolina 27711; telephone number: (919) 541-7966; fax number: (919...

Relations among Five Radii of Circles in a Triangle, Its Sides and Other Segments

ERIC Educational Resources Information Center

Sigler, Avi; Stupel, Moshe; Flores, Alfinio

2017-01-01

Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas…

A characterization of positive linear maps and criteria of entanglement for quantum states

NASA Astrophysics Data System (ADS)

Hou, Jinchuan

2010-09-01

Let H and K be (finite- or infinite-dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from {\\mathcal B}(H) into {\\mathcal B}(K) is given, which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras. This characterization is then applied to give a representation of quantum channels (operations) between infinite-dimensional systems. A necessary and sufficient criterion of separability is given which shows that a state ρ on HotimesK is separable if and only if (ΦotimesI)ρ >= 0 for all positive finite-rank elementary operators Φ. Examples of NCP and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the PPT criterion and the realignment criterion.

Graphing trillions of triangles

PubMed Central

Burkhardt, Paul

2016-01-01

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed. PMID:28690426

Anatomical study of phrenic nerve course in relation to neck dissection.

PubMed

Hamada, Tomohiro; Usami, Akinobu; Kishi, Asuka; Kon, Hideki; Takada, Satoshi

2015-04-01

The present study sought to clarify the course of the phrenic nerve and its correlation with anatomical landmarks in the neck region. We examined 17 cadavers (30 sides). In each, the phrenic nerves was dissected from the lateral side of the neck, and its position within the triangle formed by the mastoid process and sternal and acromial ends of the clavicle was determined. The point where the phrenic nerve arises in the posterior triangle was found to be similar to the point where the cutaneous blanches of the cervical plexus emerge at the middle of the posterior border of the sternocleidomastoid muscle. In the supraclavian triangle, the phrenic nerve crosses the anterior border of the anterior scalene muscle near Erb's point where the superficial point is 2-3 cm superior from the clavicle and posterior border of the sternocleidomastoid muscle. The phrenic nerve arises in the posterior triangle near the nerve point, then descends to the anterior surface of the anterior scalene muscle in the supraclavian triangle. It is necessary to be aware of the supraclavian triangle below Erb's point during neck dissection procedures.

3D Gaussian Beam Modeling

DTIC Science & Technology

2011-09-01

optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators

NASA Astrophysics Data System (ADS)

Siudzińska, Katarzyna; Chruściński, Dariusz

2018-03-01

In matrix algebras, we introduce a class of linear maps that are irreducibly covariant with respect to the finite group generated by the Weyl operators. In particular, we analyze the irreducibly covariant quantum channels, that is, the completely positive and trace-preserving linear maps. Interestingly, imposing additional symmetries leads to the so-called generalized Pauli channels, which were recently considered in the context of the non-Markovian quantum evolution. Finally, we provide examples of irreducibly covariant positive but not necessarily completely positive maps.

Linear and Nonlinear Finite Elements.

DTIC Science & Technology

1983-12-01

Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y𔃾 , (1-y𔃼)’ 1-y’ 2 - y" (6) that change eq. (5) to V𔃺) = , [yŖ(1 + y") - Qy𔃼

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

A proof of the Woodward-Lawson sampling method for a finite linear array

NASA Technical Reports Server (NTRS)

Somers, Gary A.

1993-01-01

An extension of the continuous aperture Woodward-Lawson sampling theorem has been developed for a finite linear array of equidistant identical elements with arbitrary excitations. It is shown that by sampling the array factor at a finite number of specified points in the far field, the exact array factor over all space can be efficiently reconstructed in closed form. The specified sample points lie in real space and hence are measurable provided that the interelement spacing is greater than approximately one half of a wavelength. This paper provides insight as to why the length parameter used in the sampling formulas for discrete arrays is larger than the physical span of the lattice points in contrast with the continuous aperture case where the length parameter is precisely the physical aperture length.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

ISPAN (Interactive Stiffened Panel Analysis): A tool for quick concept evaluation and design trade studies

NASA Technical Reports Server (NTRS)

Hairr, John W.; Dorris, William J.; Ingram, J. Edward; Shah, Bharat M.

1993-01-01

Interactive Stiffened Panel Analysis (ISPAN) modules, written in FORTRAN, were developed to provide an easy to use tool for creating finite element models of composite material stiffened panels. The modules allow the user to interactively construct, solve and post-process finite element models of four general types of structural panel configurations using only the panel dimensions and properties as input data. Linear, buckling and post-buckling solution capability is provided. This interactive input allows rapid model generation and solution by non finite element users. The results of a parametric study of a blade stiffened panel are presented to demonstrate the usefulness of the ISPAN modules. Also, a non-linear analysis of a test panel was conducted and the results compared to measured data and previous correlation analysis.

Weak Galerkin method for the Biot’s consolidation model

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

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

CT artifact recognition for the nuclear technologist.

PubMed

Popilock, Robert; Sandrasagaren, Kumar; Harris, Lowell; Kaser, Keith A

2008-06-01

The goal of this article is to make the PET/CT and SPECT/CT operator aware of common artifacts found in CT. In diagnostic imaging, the ability to render an accurate diagnosis requires the technologist to take steps to optimize image quality and recognize when image quality has been compromised-that is, when there is an image artifact. One way these artifacts occur is through the inability of the CT linear attenuation image to precisely represent the linear attenuation map of a 2-dimensional section through the body. The reasons for this inability are multifold. First, CT is subject to the laws of x-ray quantum physics resulting in noise in all CT images. Moreover, all current CT x-ray systems generate a spectrum of energies. Also, CT scanners use detectors of finite dimension, as are the x-ray focal spots; reconstruct images from a finite number of samples distributed over a finite number of views; and acquire the data for each reconstruction over a finite period.

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

PubMed

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Integration of system identification and finite element modelling of nonlinear vibrating structures

NASA Astrophysics Data System (ADS)

Cooper, Samson B.; DiMaio, Dario; Ewins, David J.

2018-03-01

The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

The Gasket of Circles: A Fractal of Circular Nature

ERIC Educational Resources Information Center

Haggar, Fred; Kricic, Senida

2017-01-01

Subdividing an equilateral triangle into four congruent triangles, then doing likewise to each of the three non-central triangles, and then again and again, leads to the Sierpinski gasket, from which the chaos game originated. An analogous procedure is hereforth applied to a circle, where a subdivision consists of two pairs of inscribed circles,…

Dynamic Investigation of Triangles Inscribed in a Circle, Which Tend to an Equilateral Triangle

ERIC Educational Resources Information Center

Stupel, Moshe; Oxman, Victor; Sigler, Avi

2017-01-01

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

Parent-Child-Caregiver: The Attachment Triangle

ERIC Educational Resources Information Center

Caldwell, Bettye

2005-01-01

One of the most consistently recurring themes in great literature is the love triangle--Arthur and Guinevere and Lancelot, Tristan and Isolde and King Mark, and countless others. No one has produced an immortal story about it; but a love triangle plays itself out day after day in the lives of parents, young children, and caregivers. In this…

High-resolution mapping of the triangle of Koch: Spatial heterogeneity of fast pathway atrionodal connections.

PubMed

Chua, Kelvin; Upadhyay, Gaurav A; Lee, Elliot; Aziz, Zaid; Beaser, Andrew D; Ozcan, Cevher; Broman, Michael; Nayak, Hemal M; Tung, Roderick

2018-03-01

Dedicated mapping studies of the triangle of Koch to characterize retrograde fast pathway activation have not been previously performed using high-resolution, 3-dimensional, multielectrode mapping technology. To delineate the activation pattern and spatial distribution of the retrograde fast pathway within the triangle of Koch during typical atrioventricular nodal reentrant tachycardia (AVNRT) and right ventricular pacing in a consecutive series of patients using the Rhythmia mapping system (Boston Scientific, Natick, MA). A total of 18 patients with symptomatic typical AVNRT referred for ablation underwent ultra high-density mapping of atrial activation with minielectrode basket configuration during tachycardia. The earliest atrial activation was mapped using automated annotation, with manual overreading by 2 independent observers. The triangle of Koch was classified into 3 anatomic regions: anteroseptal (His), midseptal, and posteroseptal (coronary sinus roof). Thirteen patients underwent mapping of atrial activation during ventricular pacing. A median of 422 mapping points (interquartile range 258-896 points) was acquired within the triangle of Koch during tachycardia. The most common site of earliest atrial activation within the triangle of Koch was anterior in 67% of patients (n = 12). Midseptal early atrial activation was seen in 17% (n = 3), and posteroseptal activation was observed in 11% (n = 2). One patient exhibited broad simultaneous activation of the entire triangle of Koch. Slow pathway potentials were not identified. With high-resolution multielectrode mapping, atrial activation during typical AVNRT exhibited anatomic variability and spatially heterogeneous activation within the triangle of Koch. These findings highlight the limitations of an anatomically based classification of atrioventricular nodal retrograde pathways. Copyright © 2017 Heart Rhythm Society. Published by Elsevier Inc. All rights reserved.

Finite element analyses of a linear-accelerator electron gun

NASA Astrophysics Data System (ADS)

Iqbal, M.; Wasy, A.; Islam, G. U.; Zhou, Z.

2014-02-01

Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.

Finite element analyses of a linear-accelerator electron gun.

PubMed

Iqbal, M; Wasy, A; Islam, G U; Zhou, Z

2014-02-01

Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.

Elastic collisions of classical point particles on a finite frictionless linear track with perfectly reflecting endpoints

NASA Astrophysics Data System (ADS)

DeLuca, R.

2006-03-01

Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected.

Vectorized image segmentation via trixel agglomeration

DOEpatents

Prasad, Lakshman [Los Alamos, NM; Skourikhine, Alexei N [Los Alamos, NM

2006-10-24

A computer implemented method transforms an image comprised of pixels into a vectorized image specified by a plurality of polygons that can be subsequently used to aid in image processing and understanding. The pixelated image is processed to extract edge pixels that separate different colors and a constrained Delaunay triangulation of the edge pixels forms a plurality of triangles having edges that cover the pixelated image. A color for each one of the plurality of triangles is determined from the color pixels within each triangle. A filter is formed with a set of grouping rules related to features of the pixelated image and applied to the plurality of triangle edges to merge adjacent triangles consistent with the filter into polygons having a plurality of vertices. The pixelated image may be then reformed into an array of the polygons, that can be represented collectively and efficiently by standard vector image.

Investigation of pitch and angle in the gradual-triangle lenticular lens for point-blank LED fog lamp.

PubMed

Chen, Hsi-Chao; Yang, Chi-Hao

2014-05-10

The effects of different pitch and angle of gradual-triangle lenticular lens for the point-blank LED fog lamp were investigated under the standard of ECE R19. The novel LED fog lamp was assembled from a point-blank LED light source, a parabolic reflector, and a gradual-triangle lenticular lens. Light tracing analysis was used for the design of the gradual-triangle lenticular lens. The pitch, which varied from 1 to 6 mm, and the apex angle, which changed from 5 to 32 deg, were both investigated in regard to the gradual-triangle lenticular lens. The optimum pitch was 5 mm, and the efficiency of the lamp system and lenticular lens could reach 93% and 98.1% by simulation, respectively. The results of experiment had over 94%, which is similar to that of simulation by normalized cross correlation (NCC) for the light intensity.

A Locally Modal B-Spline Based Full-Vector Finite-Element Method with PML for Nonlinear and Lossy Plasmonic Waveguide

NASA Astrophysics Data System (ADS)

Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan

2016-09-01

In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

Application of finite element approach to transonic flow problems

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C., Jr.

1976-01-01

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed.

Recent Progress in the p and h-p Version of the Finite Element Method.

DTIC Science & Technology

1987-07-01

code PROBE which was developed recently by NOETIC Technologies, St. Louis £54]. PROBE solves two dimensional problems of linear elasticity, stationary...of the finite element method was studied in detail from various point of view. We will mention here some essential illustrative results. In one...28) Bathe, K. J., Brezzi, F., Studies of finite element procedures - the INF-SUP condition, equivalent forms and applications in Reliability of

Cooperative Solutions in Multi-Person Quadratic Decision Problems: Finite-Horizon and State-Feedback Cost-Cumulant Control Paradigm

DTIC Science & Technology

2007-01-01

CONTRACT NUMBER Problems: Finite -Horizon and State-Feedback Cost-Cumulant Control Paradigm (PREPRINT) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...cooperative cost-cumulant control regime for the class of multi-person single-objective decision problems characterized by quadratic random costs and... finite -horizon integral quadratic cost associated with a linear stochastic system . Since this problem formation is parameterized by the number of cost

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

DTIC Science & Technology

2006-01-01

i.e., data flows of finite size arrive at the system randomly. For such a system , we propose a modified dual scheduling algorithm that stabilizes ...demon. We compute the efficiency of the controller over finite and infinite time intervals, and since the controller is optimal, this yields hard limits...and highly optimized tolerance. PNAS, 102, 2005. 51. G. N. Nair and R. J. Evans. Stabilizability of stochastic linear systems with finite feedback

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of finite-element equations and comparisons with analytical solutions

USGS Publications Warehouse

Cooley, Richard L.

1992-01-01

MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.

Three-dimensional modeling of flexible pavements : executive summary, August 2001.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Three dimensional modeling of flexible pavements : final report, March 2002.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Modeling the interactions between a prosthetic socket, polyurethane liners and the residual limb in transtibial amputees using non-linear finite element analysis.

PubMed

Simpson, G; Fisher, C; Wright, D K

2001-01-01

Continuing earlier studies into the relationship between the residual limb, liner and socket in transtibial amputees, we describe a geometrically accurate non-linear model simulating the donning of a liner and then a socket. The socket is rigid and rectified and the liner is a polyurethane geltype which is accurately described using non-linear (Mooney-Rivlin) material properties. The soft tissue of the residual limb is modelled as homogeneous, non-linear and hyperelastic and the bone structure within the residual limb is taken as rigid. The work gives an indication of how the stress induced by the process of donning the rigid socket is redistributed by the liner. Ultimately we hope to understand how the liner design might be modified to reduce discomfort. The ANSYS finite element code, version 5.6 is used.

Non-linear effects in finite amplitude wave propagation through ducts and nozzles

NASA Technical Reports Server (NTRS)

Salikuddin, M.; Brown, W. H.

1986-01-01

In this paper an extensive study of non-linear effects in finite amplitude wave propagation through ducts and nozzles is summarized. Some results from earlier studies are included to illustrate the non-linear effects on the transmission characteristics of duct and nozzle terminations. Investigaiations, both experimental and analytical, were carried out to determine the magnitudes of the effects for high intensity pulse propagation. The results derived from these investigations are presented in this paper. They include the effect of the sound intensity on the acoustic characteristics of duct and nozzle terminations, the extent of the non-linearities in the propagation of high intensity impulsive sound inside the duct and out into free field, the acoustic energy dissipation mechanism at a termination as shown by flow visualizations, and quantitative evaluations by experimental and analytical means of the influence of the intensity of a sound pulse on the dissipation of its acoustic power.

Variation of linear and circular polarization persistence for changing field of view and collection area in a forward scattering environment

NASA Astrophysics Data System (ADS)

van der Laan, John D.; Wright, Jeremy B.; Scrymgeour, David A.; Kemme, Shanalyn A.; Dereniak, Eustace L.

2016-05-01

We present experimental and simulation results for a laboratory-based forward-scattering environment, where 1 μm diameter polystyrene spheres are suspended in water to model the optical scattering properties of fog. Circular polarization maintains its degree of polarization better than linear polarization as the optical thickness of the scattering environment increases. Both simulation and experiment quantify circular polarization's superior persistence, compared to that of linear polarization, and show that it is much less affected by variations in the field of view and collection area of the optical system. Our experimental environment's lateral extent was physically finite, causing a significant difference between measured and simulated degree of polarization values for incident linearly polarized light, but not for circularly polarized light. Through simulation we demonstrate that circular polarization is less susceptible to the finite environmental extent as well as the collection optic's limiting configuration.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Revisiting the Pink Triangle Exercise: An Exploration of Experiential Learning in Graduate Social Work Education

ERIC Educational Resources Information Center

Pugh, Greg L.

2014-01-01

The pink triangle exercise is an example of an experiential learning exercise that creates cognitive dissonance and deep learning of unrealized internalized biases among social work students. Students wear a button with a pink triangle on it for 1 day and write a reflection paper. The exercise increases self-awareness, cultural competence, and the…

Developing Formulas by Skipping Rows in Pascal's Triangle

ERIC Educational Resources Information Center

Buonpastore, Robert J.; Osler, Thomas J.

2007-01-01

A table showing the first thirteen rows of Pascal's triangle, where the rows are, as usual numbered from 0 to 12 is presented. The entries in the table are called binomial coefficients. In this note, the authors systematically delete rows from Pascal's triangle and, by trial and error, try to find a formula that allows them to add new rows to the…

The DNA Triangle and Its Application to Learning Meiosis

PubMed Central

Wright, L. Kate; Catavero, Christina M.; Newman, Dina L.

2017-01-01

Although instruction on meiosis is repeated many times during the undergraduate curriculum, many students show poor comprehension even as upper-level biology majors. We propose that the difficulty lies in the complexity of understanding DNA, which we explain through a new model, the DNA triangle. The DNA triangle integrates three distinct scales at which one can think about DNA: chromosomal, molecular, and informational. Through analysis of interview and survey data from biology faculty and students through the lens of the DNA triangle, we illustrate important differences in how novices and experts are able to explain the concepts of ploidy, homology, and mechanism of homologous pairing. Similarly, analysis of passages from 16 different biology textbooks shows a large divide between introductory and advanced material, with introductory books omitting explanations of meiosis-linked concepts at the molecular level of DNA. Finally, backed by textbook findings and feedback from biology experts, we show that the DNA triangle can be applied to teaching and learning meiosis. By applying the DNA triangle to topics on meiosis we present a new framework for educators and researchers that ties concepts of ploidy, homology, and mechanism of homologous pairing to knowledge about DNA on the chromosomal, molecular, and informational levels. PMID:28798212

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Design of Beneficial Wave Dynamics for Engine Life and Operability Enhancement

DTIC Science & Technology

2010-07-30

ST^(A), where S is the Dirac delta measure. Stochastic transition 9 function can be used to define two linear transfer operators called as Perron ... Frobenius and Koopman operators. Here we consider the finite dimensional approximation of the P-F operator. To do this we consider the finite

Beta Regression Finite Mixture Models of Polarization and Priming

ERIC Educational Resources Information Center

Smithson, Michael; Merkle, Edgar C.; Verkuilen, Jay

2011-01-01

This paper describes the application of finite-mixture general linear models based on the beta distribution to modeling response styles, polarization, anchoring, and priming effects in probability judgments. These models, in turn, enhance our capacity for explicitly testing models and theories regarding the aforementioned phenomena. The mixture…

Two Propositions on the Application of Point Elasticities to Finite Price Changes.

ERIC Educational Resources Information Center

Daskin, Alan J.

1992-01-01

Considers counterintuitive propositions about using point elasticities to estimate quantity changes in response to price changes. Suggests that elasticity increases with price along a linear demand curve, but falling quantity demand offsets it. Argues that point elasticity with finite percentage change in price only approximates percentage change…

High-Order Thermal Radiative Transfer

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

Woods, Douglas Nelson; Cleveland, Mathew Allen; Wollaeger, Ryan Thomas

2017-09-18

The objective of this research is to asses the sensitivity of the linearized thermal radiation transport equations to finite element order on unstructured meshes and to investigate the sensitivity of the nonlinear TRT equations due to evaluating the opacities and heat capacity at nodal temperatures in 2-D using high-order finite elements.

Phase-space finite elements in a least-squares solution of the transport equation

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

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

From Finite Time to Finite Physical Dimensions Thermodynamics: The Carnot Engine and Onsager's Relations Revisited

NASA Astrophysics Data System (ADS)

Feidt, Michel; Costea, Monica

2018-04-01

Many works have been devoted to finite time thermodynamics since the Curzon and Ahlborn [1] contribution, which is generally considered as its origin. Nevertheless, previous works in this domain have been revealed [2], [3], and recently, results of the attempt to correlate Finite Time Thermodynamics with Linear Irreversible Thermodynamics according to Onsager's theory were reported [4]. The aim of the present paper is to extend and improve the approach relative to thermodynamic optimization of generic objective functions of a Carnot engine with linear response regime presented in [4]. The case study of the Carnot engine is revisited within the steady state hypothesis, when non-adiabaticity of the system is considered, and heat loss is accounted for by an overall heat leak between the engine heat reservoirs. The optimization is focused on the main objective functions connected to engineering conditions, namely maximum efficiency or power output, except the one relative to entropy that is more fundamental. Results given in reference [4] relative to the maximum power output and minimum entropy production as objective function are reconsidered and clarified, and the change from finite time to finite physical dimension was shown to be done by the heat flow rate at the source. Our modeling has led to new results of the Carnot engine optimization and proved that the primary interest for an engineer is mainly connected to what we called Finite Physical Dimensions Optimal Thermodynamics.

Stabilized Finite Elements in FUN3D

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Newman, James C.; Karman, Steve L.

2017-01-01

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Variations in the surface anatomy of the spinal accessory nerve in the posterior triangle.

PubMed

Symes, A; Ellis, H

2005-12-01

Iatrogenic injury to the spinal accessory nerve has been widely documented and can have medico-legal implications. The resulting syndrome of pain, paralysis and winging of the scapula are often the source of considerable morbidity. This paper researches the degree of accuracy achievable in mapping the surface anatomy of the spinal accessory nerve in the region of the posterior triangle with a view to creating a cartographical aid to surgical procedures. The necks of 25 adult cadavers were dissected bilaterally to expose the spinal accessory nerve. Variations in the course and distribution of the spinal accessory nerve in the posterior triangle were recorded along with its relationship to the borders of sternocleidomastoid and trapezius. Considerable variation was seen in the surface and regional anatomy of the nerve and in the contribution of the cervical plexus to the spinal accessory nerve in the posterior triangle. Measurements of the running course and exit point of the nerve into and from the posterior triangle differed significantly from those previously recorded. Delineation of an accurate surface anatomy was not possible. Creating a map to define the surface anatomy of the spinal accessory nerve in the posterior triangle is an unrealistic goal given its wide variations in man. Avoidance of damage to the spinal accessory nerve cannot be achieved by slavishly adhering to surface markings given in textbooks, but only by cautious dissection during operations on the posterior triangle.

Accuracy of methods for calculating volumetric wear from coordinate measuring machine data of retrieved metal-on-metal hip joint implants.

PubMed

Lu, Zhen; McKellop, Harry A

2014-03-01

This study compared the accuracy and sensitivity of several numerical methods employing spherical or plane triangles for calculating the volumetric wear of retrieved metal-on-metal hip joint implants from coordinate measuring machine measurements. Five methods, one using spherical triangles and four using plane triangles to represent the bearing and the best-fit surfaces, were assessed and compared on a perfect hemisphere model and a hemi-ellipsoid model (i.e. unworn models), computer-generated wear models and wear-tested femoral balls, with point spacings of 0.5, 1, 2 and 3 mm. The results showed that the algorithm (Method 1) employing spherical triangles to represent the bearing surface and to scale the mesh to the best-fit surfaces produced adequate accuracy for the wear volume with point spacings of 0.5, 1, 2 and 3 mm. The algorithms (Methods 2-4) using plane triangles to represent the bearing surface and to scale the mesh to the best-fit surface also produced accuracies that were comparable to that with spherical triangles. In contrast, if the bearing surface was represented with a mesh of plane triangles and the best-fit surface was taken as a smooth surface without discretization (Method 5), the algorithm produced much lower accuracy with a point spacing of 0.5 mm than Methods 1-4 with a point spacing of 3 mm.

Elasto-Plastic Analysis of Tee Joints Using HOT-SMAC

NASA Technical Reports Server (NTRS)

Arnold, Steve M. (Technical Monitor); Bednarcyk, Brett A.; Yarrington, Phillip W.

2004-01-01

The Higher Order Theory - Structural/Micro Analysis Code (HOT-SMAC) software package is applied to analyze the linearly elastic and elasto-plastic response of adhesively bonded tee joints. Joints of this type are finding an increasing number of applications with the increased use of composite materials within advanced aerospace vehicles, and improved tools for the design and analysis of these joints are needed. The linearly elastic results of the code are validated vs. finite element analysis results from the literature under different loading and boundary conditions, and new results are generated to investigate the inelastic behavior of the tee joint. The comparison with the finite element results indicates that HOT-SMAC is an efficient and accurate alternative to the finite element method and has a great deal of potential as an analysis tool for a wide range of bonded joints.

Calculation of skin-stiffener interface stresses in stiffened composite panels

NASA Technical Reports Server (NTRS)

Cohen, David; Hyer, Michael W.

1987-01-01

A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.

The weight hierarchies and chain condition of a class of codes from varieties over finite fields

NASA Technical Reports Server (NTRS)

Wu, Xinen; Feng, Gui-Liang; Rao, T. R. N.

1996-01-01

The generalized Hamming weights of linear codes were first introduced by Wei. These are fundamental parameters related to the minimal overlap structures of the subcodes and very useful in several fields. It was found that the chain condition of a linear code is convenient in studying the generalized Hamming weights of the product codes. In this paper we consider a class of codes defined over some varieties in projective spaces over finite fields, whose generalized Hamming weights can be determined by studying the orbits of subspaces of the projective spaces under the actions of classical groups over finite fields, i.e., the symplectic groups, the unitary groups and orthogonal groups. We give the weight hierarchies and generalized weight spectra of the codes from Hermitian varieties and prove that the codes satisfy the chain condition.

Multiresolution and Explicit Methods for Vector Field Analysis and Visualization

NASA Technical Reports Server (NTRS)

1996-01-01

We first report on our current progress in the area of explicit methods for tangent curve computation. The basic idea of this method is to decompose the domain into a collection of triangles (or tetrahedra) and assume linear variation of the vector field over each cell. With this assumption, the equations which define a tangent curve become a system of linear, constant coefficient ODE's which can be solved explicitly. There are five different representation of the solution depending on the eigenvalues of the Jacobian. The analysis of these five cases is somewhat similar to the phase plane analysis often associate with critical point classification within the context of topological methods, but it is not exactly the same. There are some critical differences. Moving from one cell to the next as a tangent curve is tracked, requires the computation of the exit point which is an intersection of the solution of the constant coefficient ODE and the edge of a triangle. There are two possible approaches to this root computation problem. We can express the tangent curve into parametric form and substitute into an implicit form for the edge or we can express the edge in parametric form and substitute in an implicit form of the tangent curve. Normally the solution of a system of ODE's is given in parametric form and so the first approach is the most accessible and straightforward. The second approach requires the 'implicitization' of these parametric curves. The implicitization of parametric curves can often be rather difficult, but in this case we have been successful and have been able to develop algorithms and subsequent computer programs for both approaches. We will give these details along with some comparisons in a forthcoming research paper on this topic.

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

The triangle of the urinary bladder in American mink (Mustela vision (Brisson, 1756)).

PubMed

Gościcka, D; Krakowiak, E; Kepczyńska, M

1994-01-01

60 bladders of American minks were dissected according to conventional method. Biometrical analysis with the use of digital image analysis system was applied to the triangles of the bladders. It was found that these triangles differ both in shape (narrow, broad) and symmetry (considerable asymmetry). The ureteral orifices also showed a variety in shape (five types) and number (double orifices).

The Effect of Internet-Based Education on Student Success in Teaching of 8th Grade Triangles Subject

ERIC Educational Resources Information Center

Kaya, Deniz; Kesan, Cenk; Izgiol, Dilek

2013-01-01

In the study, it was researched the effect of internet-based application on student success. Internet-based application was used at the teaching of triangles subject which is included in 8th grade units of triangles and algebra. The study was carried out over the internet with a computer software program: Vitamin Program. The study was carried out…

In Search of More Triangle Centres. a Source of Classroom Projects in Euclidean Geometry

ERIC Educational Resources Information Center

Abu-Saymeh, S.; Hajja, M.

2005-01-01

A point "E" inside a triangle "ABC" can be coordinatized by the areas of the triangles "EBC," "ECA," and "EAB." These are called the barycentric coordinates of "E." It can also be coordinatized using the six segments into which the cevians through "E" divide the sides of "ABC," or the six angles into which the cevians through "E" divide the angles…

Linear and nonlinear pattern selection in Rayleigh-Benard stability problems

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1993-01-01

A new algorithm is introduced to compute finite-amplitude states using primitive variables for Rayleigh-Benard convection on relatively coarse meshes. The algorithm is based on a finite-difference matrix-splitting approach that separates all physical and dimensional effects into one-dimensional subsets. The nonlinear pattern selection process for steady convection in an air-filled square cavity with insulated side walls is investigated for Rayleigh numbers up to 20,000. The internalization of disturbances that evolve into coherent patterns is investigated and transient solutions from linear perturbation theory are compared with and contrasted to the full numerical simulations.

Runtime Analysis of Linear Temporal Logic Specifications

NASA Technical Reports Server (NTRS)

Giannakopoulou, Dimitra; Havelund, Klaus

2001-01-01

This report presents an approach to checking a running program against its Linear Temporal Logic (LTL) specifications. LTL is a widely used logic for expressing properties of programs viewed as sets of executions. Our approach consists of translating LTL formulae to finite-state automata, which are used as observers of the program behavior. The translation algorithm we propose modifies standard LTL to B chi automata conversion techniques to generate automata that check finite program traces. The algorithm has been implemented in a tool, which has been integrated with the generic JPaX framework for runtime analysis of Java programs.

Accurate evaluation of exchange fields in finite element micromagnetic solvers

NASA Astrophysics Data System (ADS)

Chang, R.; Escobar, M. A.; Li, S.; Lubarda, M. V.; Lomakin, V.

2012-04-01

Quadratic basis functions (QBFs) are implemented for solving the Landau-Lifshitz-Gilbert equation via the finite element method. This involves the introduction of a set of special testing functions compatible with the QBFs for evaluating the Laplacian operator. The results by using QBFs are significantly more accurate than those via linear basis functions. QBF approach leads to significantly more accurate results than conventionally used approaches based on linear basis functions. Importantly QBFs allow reducing the error of computing the exchange field by increasing the mesh density for structured and unstructured meshes. Numerical examples demonstrate the feasibility of the method.

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

Electromagnetic density of modes for a finite-size three-dimensional structure.

PubMed

D'Aguanno, Giuseppe; Mattiucci, Nadia; Centini, Marco; Scalora, Michael; Bloemer, Mark J

2004-05-01

The concept of the density of modes has been lacking a precise mathematical definition for a finite-size structure. With the explosive growth in the fabrication of photonic crystals and nanostructures, which are inherently finite in size, a workable definition is imperative. We give a simple and physically intuitive definition of the electromagnetic density of modes based on the Green's function for a generic three-dimensional open cavity filled with a linear, isotropic, dielectric material.

Scaling in the vicinity of the four-state Potts fixed point

NASA Astrophysics Data System (ADS)

Blöte, H. W. J.; Guo, Wenan; Nightingale, M. P.

2017-08-01

We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.

Revisiting the factors which control the angle of shear bands in geodynamic numerical models of brittle deformation

NASA Astrophysics Data System (ADS)

Thieulot, Cedric

2017-04-01

In this work I present Finite Element numerical simulations of brittle deformation in two-dimensional Cartesian systems subjected to compressional or extensional kinematical boundary conditions with a basal velocity discontinuity. The rheology is visco-plastic and is characterised by a cohesion and an angle of internal friction (Drucker-Prager type). I will explore the influence of the following factors on the recovered shear band angles when the angle of internal friction is varied: a) element type (quadrilateral vs triangle), b) element order, c) continuous vs discontinous pressure, d) visco-plasticity model implementation, e) the nonlinear tolerance value, f) the use of markers, g) Picard vs Newton-Raphson, h) velocity discontinuity nature. I will present these results in the light of already published literature (e.g. Lemiale et al, PEPI 171, 2008; Kaus, Tectonophysics 484, 2010).

Conical Euler solution for a highly-swept delta wing undergoing wing-rock motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

Modifications to an unsteady conical Euler code for the free-to-roll analysis of highly-swept delta wings are described. The modifications involve the addition of the rolling rigid-body equation of motion for its simultaneous time-integration with the governing flow equations. The flow solver utilized in the Euler code includes a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization on an unstructured mesh made up of triangles. Steady and unsteady results are presented for a 75 deg swept delta wing at a freestream Mach number of 1.2 and an angle of attack of 30 deg. The unsteady results consist of forced harmonic and free-to-roll calculations. The free-to-roll case exhibits a wing rock response produced by unsteady aerodynamics consistent with the aerodynamics of the forced harmonic results. Similarities are shown with a wing-rock time history from a low-speed wind tunnel test.

An equilibrium method for prediction of transverse shear stresses in a thick laminated plate

NASA Technical Reports Server (NTRS)

Chaudhuri, R. Z.

1986-01-01

First two equations of equilibrium are utilized to compute the transverse shear stress variation through thickness of a thick laminated plate after in-plane stresses have been computed using an assumed quadratic displacement triangular element based on transverse inextensibility and layerwise constant shear angle theory (LCST). Centroid of the triangle is the point of exceptional accuracy for transverse shear stresses. Numerical results indicate close agreement with elasticity theory. An interesting comparison between the present theory and that based on assumed stress hybrid finite element approach suggests that the latter does not satisfy the condition of free normal traction at the edge. Comparison with numerical results obtained by using constant shear angle theory suggests that LCST is close to the elasticity solution while the CST is closer to classical (CLT) solution. It is also demonstrated that the reduced integration gives faster convergence when the present theory is applied to a thin plate.

Finite element analyses of a linear-accelerator electron gun

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

Iqbal, M., E-mail: muniqbal.chep@pu.edu.pk, E-mail: muniqbal@ihep.ac.cn; Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049; Wasy, A.

Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gunmore » is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.« less

The assessment of nanofluid in a Von Karman flow with temperature relied viscosity

NASA Astrophysics Data System (ADS)

Tanveer, Anum; Salahuddin, T.; Khan, Mumtaz; Alshomrani, Ali Saleh; Malik, M. Y.

2018-06-01

This work endeavor to study the heat and mass transfer viscous nanofluid features in a Von Karman flow invoking the variable viscosity mechanism. Moreover, we have extended our study in view of heat generation and uniform suction effects. The flow triggering non-linear partial differential equations are inscribed in the non-dimensional form by manipulating suitable transformations. The resulting non-linear ordinary differential equations are solved numerically via implicit finite difference scheme in conjecture with the Newton's linearization scheme afterwards. The sought solutions are plotted graphically to present comparison between MATLAB routine bvp4c and implicit finite difference schemes. Impact of different parameters on the concentration/temperature/velocity profiles are highlighted. Further Nusselt number, skin friction and Sherwood number characteristics are discussed for better exposition.

Models for short-wave instability in inviscid shear flows

NASA Astrophysics Data System (ADS)

Grimshaw, Roger

1999-11-01

The generation of instability in an invsicid fluid occurs by a resonance between two wave modes, where here the resonance occurs by a coincidence of phase speeds for a finite, non-zero wavenumber. We show that in the weakly nonlinear limit, the appropriate model consists of two coupled equations for the envelopes of the wave modes, in which the nonlinear terms are balanced with low-order cross-coupling linear dispersive terms rather than the more familiar high-order terms which arise in the nonlinear Schrodinger equation, for instance. We will show that this system may either contain gap solitons as solutions in the linearly stable case, or wave breakdown in the linearly unstable case. In this latter circumstance, the system either exhibits wave collapse in finite time, or disintegration into fine-scale structures.

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Finite-time resilient decentralized control for interconnected impulsive switched systems with neutral delay.

PubMed

Ren, Hangli; Zong, Guangdeng; Hou, Linlin; Yang, Yi

2017-03-01

This paper is concerned with the problem of finite-time control for a class of interconnected impulsive switched systems with neutral delay in which the time-varying delay appears in both the state and the state derivative. The concepts of finite-time boundedness and finite-time stability are respectively extended to interconnected impulsive switched systems with neutral delay for the first time. By applying the average dwell time method, sufficient conditions are first derived to cope with the problem of finite-time boundedness and finite-time stability for interconnected impulsive switched systems with neutral delay. In addition, the purpose of finite-time resilient decentralized control is to construct a resilient decentralized state-feedback controller such that the closed-loop system is finite-time bounded and finite-time stable. All the conditions are formulated in terms of linear matrix inequalities to ensure finite-time boundedness and finite-time stability of the given system. Finally, an example is presented to illustrate the effectiveness of the proposed approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Membrane triangles with corner drilling freedoms. III - Implementation and performance evaluation

NASA Technical Reports Server (NTRS)

Felippa, Carlos A.; Alexander, Scott

1992-01-01

This paper completes a three-part series on the formulation of 3-node, 9-dof membrane triangles with corner drilling freedoms based on parametrized variational principles. The first four sections cover element implementation details including determination of optimal parameters and treatment of distributed loads. Then three elements of this type, labeled ALL, FF and EFF-ANDES, are tested on standard plane stress problems. ALL represents numerically integrated versions of Allman's 1988 triangle; FF is based on the free formulation triangle presented by Bergan and Felippa in 1985; and EFF-ANDES represent two different formulations of the optimal triangle derived in Parts I and II. The numerical studies indicate that the ALL, FF and EFF-ANDES elements are comparable in accuracy for elements of unitary aspect ratios. The ALL elements are found to stiffen rapidly in inplane bending for high aspect ratios, whereas the FF and EFF elements maintain accuracy. The EFF and ANDES implementations have a moderate edge in formation speed over the FF.

Low frequency ac waveform generator

DOEpatents

Bilharz, O.W.

1983-11-22

Low frequency sine, cosine, triangle and square waves are synthesized in circuitry which allows variation in the waveform amplitude and frequency while exhibiting good stability and without requiring significant stablization time. A triangle waveform is formed by a ramped integration process controlled by a saturation amplifier circuit which produces the necessary hysteresis for the triangle waveform. The output of the saturation circuit is tapped to produce the square waveform. The sine waveform is synthesized by taking the absolute value of the triangular waveform, raising this absolute value to a predetermined power, multiplying the raised absolute value of the triangle wave with the triangle wave itself and properly scaling the resultant waveform and subtracting it from the triangular waveform to a predetermined power and adding the squared waveform raised to the predetermined power with a DC reference and subtracting the squared waveform therefrom, with all waveforms properly scaled. The resultant waveform is then multiplied with a square wave in order to correct the polarity and produce the resultant cosine waveform.

Evaluation of a Nonlinear Finite Element Program - ABAQUS.

DTIC Science & Technology

1983-03-15

anisotropic properties. * MATEXP - Linearly elastic thermal expansions with isotropic, orthotropic and anisotropic properties. * MATELG - Linearly...elastic materials for general sections (options available for beam and shell elements). • MATEXG - Linearly elastic thermal expansions for general...decomposition of a matrix. * Q-R algorithm • Vector normalization, etc. Obviously, by consolidating all the utility subroutines in a library, ABAQUS has

Finite element modeling of concrete structures strengthened with FRP laminates

DOT National Transportation Integrated Search

2001-05-01

Linear and non-linear method models were developed for a reinforced concrete bridge that had been strengthened with fiber reinforced polymer (FRP) composites. ANSYS and SAP2000 modeling software were used; however, most of the development effort used...

The PBS Triangle: Does It Fit as a Heuristic? A Reflection on the First International Conference on Positive Behavior Support

ERIC Educational Resources Information Center

Baker, Candace Kay

2005-01-01

In this article, the author explores the evolution of the use of the triangle as a communication tool for describing positive behavior support (PBS) systems. The conceptual framework for the triangle used for PBS is credited to Walker et al. In that seminal work, the a model of school-based prevention strategies for children displaying antisocial…

Improved Modeling of Three-Point Estimates for Decision Making: Going Beyond the Triangle

DTIC Science & Technology

2016-03-01

OF THREE-POINT ESTIMATES FOR DECISION MAKING: GOING BEYOND THE TRIANGLE by Daniel W. Mulligan March 2016 Thesis Advisor: Mark Rhoades...REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE IMPROVED MODELING OF THREE-POINT ESTIMATES FOR DECISION MAKING: GOING BEYOND...unlimited IMPROVED MODELING OF THREE-POINT ESTIMATES FOR DECISION MAKING: GOING BEYOND THE TRIANGLE Daniel W. Mulligan Civilian, National

When Can One Expect a Stronger Triangle Inequality?

ERIC Educational Resources Information Center

Faiziev, Valerii; Powers, Robert; Sahoo, Prasanna

2013-01-01

In 1997, Bailey and Bannister showed that a + b greater than c + h holds for all triangles with [gamma] less than arctan (22/7)where a, b, and c are the sides of the triangle, "h" is the altitude to side "c", and [gamma] is the angle opposite c. In this paper, we show that a + b greater than c + h holds approximately 92% of the time for all…

SUPG Finite Element Simulations of Compressible Flows for Aerothermodynamic Applications

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.

2007-01-01

This viewgraph presentation reviews the Streamline-Upwind Petrov-Galerkin (SUPG) Finite Element Simulation. It covers the background, governing equations, weak formulation, shock capturing, inviscid flux discretization, time discretization, linearization, and implicit solution strategies. It also reviews some applications such as Type IV Shock Interaction, Forward-Facing Cavity and AEDC Sharp Double Cone.

SIMULATIONS OF 2D AND 3D THERMOCAPILLARY FLOWS BY A LEAST-SQUARES FINITE ELEMENT METHOD. (R825200)

EPA Science Inventory

Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matri...

Recursive Inversion By Finite-Impulse-Response Filters

NASA Technical Reports Server (NTRS)

Bach, Ralph E., Jr.; Baram, Yoram

1991-01-01

Recursive approximation gives least-squares best fit to exact response. Algorithm yields finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Applicable to such system-inversion problems as suppression of echoes and identification of target from its scatter response to incident impulse.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

Valuation of financial models with non-linear state spaces

NASA Astrophysics Data System (ADS)

Webber, Nick

2001-02-01

A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.

Non-linear dual-phase-lag model for analyzing heat transfer phenomena in living tissues during thermal ablation.

PubMed

Kumar, P; Kumar, Dinesh; Rai, K N

2016-08-01

In this article, a non-linear dual-phase-lag (DPL) bio-heat transfer model based on temperature dependent metabolic heat generation rate is derived to analyze the heat transfer phenomena in living tissues during thermal ablation treatment. The numerical solution of the present non-linear problem has been done by finite element Runge-Kutta (4,5) method which combines the essence of Runge-Kutta (4,5) method together with finite difference scheme. Our study demonstrates that at the thermal ablation position temperature predicted by non-linear and linear DPL models show significant differences. A comparison has been made among non-linear DPL, thermal wave and Pennes model and it has been found that non-linear DPL and thermal wave bio-heat model show almost same nature whereas non-linear Pennes model shows significantly different temperature profile at the initial stage of thermal ablation treatment. The effect of Fourier number and Vernotte number (relaxation Fourier number) on temperature profile in presence and absence of externally applied heat source has been studied in detail and it has been observed that the presence of externally applied heat source term highly affects the efficiency of thermal treatment method. Copyright © 2016 Elsevier Ltd. All rights reserved.

Triangle network motifs predict complexes by complementing high-error interactomes with structural information.

PubMed

Andreopoulos, Bill; Winter, Christof; Labudde, Dirk; Schroeder, Michael

2009-06-27

A lot of high-throughput studies produce protein-protein interaction networks (PPINs) with many errors and missing information. Even for genome-wide approaches, there is often a low overlap between PPINs produced by different studies. Second-level neighbors separated by two protein-protein interactions (PPIs) were previously used for predicting protein function and finding complexes in high-error PPINs. We retrieve second level neighbors in PPINs, and complement these with structural domain-domain interactions (SDDIs) representing binding evidence on proteins, forming PPI-SDDI-PPI triangles. We find low overlap between PPINs, SDDIs and known complexes, all well below 10%. We evaluate the overlap of PPI-SDDI-PPI triangles with known complexes from Munich Information center for Protein Sequences (MIPS). PPI-SDDI-PPI triangles have ~20 times higher overlap with MIPS complexes than using second-level neighbors in PPINs without SDDIs. The biological interpretation for triangles is that a SDDI causes two proteins to be observed with common interaction partners in high-throughput experiments. The relatively few SDDIs overlapping with PPINs are part of highly connected SDDI components, and are more likely to be detected in experimental studies. We demonstrate the utility of PPI-SDDI-PPI triangles by reconstructing myosin-actin processes in the nucleus, cytoplasm, and cytoskeleton, which were not obvious in the original PPIN. Using other complementary datatypes in place of SDDIs to form triangles, such as PubMed co-occurrences or threading information, results in a similar ability to find protein complexes. Given high-error PPINs with missing information, triangles of mixed datatypes are a promising direction for finding protein complexes. Integrating PPINs with SDDIs improves finding complexes. Structural SDDIs partially explain the high functional similarity of second-level neighbors in PPINs. We estimate that relatively little structural information would be sufficient for finding complexes involving most of the proteins and interactions in a typical PPIN.

Triangle network motifs predict complexes by complementing high-error interactomes with structural information

PubMed Central

Andreopoulos, Bill; Winter, Christof; Labudde, Dirk; Schroeder, Michael

2009-01-01

Background A lot of high-throughput studies produce protein-protein interaction networks (PPINs) with many errors and missing information. Even for genome-wide approaches, there is often a low overlap between PPINs produced by different studies. Second-level neighbors separated by two protein-protein interactions (PPIs) were previously used for predicting protein function and finding complexes in high-error PPINs. We retrieve second level neighbors in PPINs, and complement these with structural domain-domain interactions (SDDIs) representing binding evidence on proteins, forming PPI-SDDI-PPI triangles. Results We find low overlap between PPINs, SDDIs and known complexes, all well below 10%. We evaluate the overlap of PPI-SDDI-PPI triangles with known complexes from Munich Information center for Protein Sequences (MIPS). PPI-SDDI-PPI triangles have ~20 times higher overlap with MIPS complexes than using second-level neighbors in PPINs without SDDIs. The biological interpretation for triangles is that a SDDI causes two proteins to be observed with common interaction partners in high-throughput experiments. The relatively few SDDIs overlapping with PPINs are part of highly connected SDDI components, and are more likely to be detected in experimental studies. We demonstrate the utility of PPI-SDDI-PPI triangles by reconstructing myosin-actin processes in the nucleus, cytoplasm, and cytoskeleton, which were not obvious in the original PPIN. Using other complementary datatypes in place of SDDIs to form triangles, such as PubMed co-occurrences or threading information, results in a similar ability to find protein complexes. Conclusion Given high-error PPINs with missing information, triangles of mixed datatypes are a promising direction for finding protein complexes. Integrating PPINs with SDDIs improves finding complexes. Structural SDDIs partially explain the high functional similarity of second-level neighbors in PPINs. We estimate that relatively little structural information would be sufficient for finding complexes involving most of the proteins and interactions in a typical PPIN. PMID:19558694

Analysis of the transient behavior of rubbing components

NASA Technical Reports Server (NTRS)

Quezdou, M. B.; Mullen, R. L.

1986-01-01

Finite element equations are developed for studying deformations and temperatures resulting from frictional heating in sliding system. The formulation is done for linear steady state motion in two dimensions. The equations include the effect of the velocity on the moving components. This gives spurious oscillations in their solutions by Galerkin finite element methods. A method called streamline upwind scheme is used to try to deal with this deficiency. The finite element program is then used to investigate the friction of heating in gas path seal.

The growth rate of vertex-transitive planar graphs

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

Babai, L.

1997-06-01

A graph is vertex-transitive if all of its vertices axe equivalent under automorphisms. Confirming a conjecture of Jon Kleinberg and Eva Tardos, we prove the following trichotomy theorem concerning locally finite vertex-transitive planar graphs: the rate of growth of a graph with these properties is either linear or quadratic or exponential. The same result holds more generally for locally finite, almost vertex-transitive planar graphs (the automorphism group has a finite number of orbits). The proof uses the elements of hyperbolic plane geometry.

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

NASA Astrophysics Data System (ADS)

Lonsdale, R. D.; Webster, R.

This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

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

Mohanty, Subhasish; Majumdar, Saurindranath

Irradiation creep plays a major role in the structural integrity of the graphite components in high temperature gas cooled reactors. Finite element procedures combined with a suitable irradiation creep model can be used to simulate the time-integrated structural integrity of complex shapes, such as the reactor core graphite reflector and fuel bricks. In the present work a comparative study was undertaken to understand the effect of linear and nonlinear irradiation creep on results of finite element based stress analysis. Numerical results were generated through finite element simulations of a typical graphite reflector.

Error analysis of finite element method for Poisson–Nernst–Planck equations

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

Sun, Yuzhou; Sun, Pengtao; Zheng, Bin

A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.

Wakefield Simulation of CLIC PETS Structure Using Parallel 3D Finite Element Time-Domain Solver T3P

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

Candel, A.; Kabel, A.; Lee, L.

In recent years, SLAC's Advanced Computations Department (ACD) has developed the parallel 3D Finite Element electromagnetic time-domain code T3P. Higher-order Finite Element methods on conformal unstructured meshes and massively parallel processing allow unprecedented simulation accuracy for wakefield computations and simulations of transient effects in realistic accelerator structures. Applications include simulation of wakefield damping in the Compact Linear Collider (CLIC) power extraction and transfer structure (PETS).

Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2014-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

A Novel Arterial Constitutive Model in a Commercial Finite Element Package: Application to Balloon Angioplasty

PubMed Central

Zhao, Xuefeng; Liu, Yi; Zhang, Wei; Wang, Cong; Kassab, Ghassan S.

2011-01-01

Recently, a novel linearized constitutive model with a new strain measure that absorbs the material nonlinearity was validated for arteries. In this study, the linearized arterial stress-strain relationship is implemented into a finite element method package ANSYS, via the user subroutine USERMAT. The reference configuration is chosen to be the closed cylindrical tube (no-load state) rather than the open sector (zero-stress state). The residual strain is taken into account by analytic calculation and the incompressibility condition is enforced with Lagrange penalty method. Axisymmetric finite element analyses are conducted to demonstrate potential applications of this approach in a complex boundary value problem where angioplasty balloon interacts with the vessel wall. The model predictions of transmural circumferential and compressive radial stress distributions were also validated against an exponential-type Fung model, and the mean error was found to be within 6%. PMID:21689665

Linear finite-difference bond graph model of an ionic polymer actuator

NASA Astrophysics Data System (ADS)

Bentefrit, M.; Grondel, S.; Soyer, C.; Fannir, A.; Cattan, E.; Madden, J. D.; Nguyen, T. M. G.; Plesse, C.; Vidal, F.

2017-09-01

With the recent growing interest for soft actuation, many new types of ionic polymers working in air have been developed. Due to the interrelated mechanical, electrical, and chemical properties which greatly influence the characteristics of such actuators, their behavior is complex and difficult to understand, predict and optimize. In light of this challenge, an original linear multiphysics finite difference bond graph model was derived to characterize this ionic actuation. This finite difference scheme was divided into two coupled subparts, each related to a specific physical, electrochemical or mechanical domain, and then converted into a bond graph model as this language is particularly suited for systems from multiple energy domains. Simulations were then conducted and a good agreement with the experimental results was obtained. Furthermore, an analysis of the power efficiency of such actuators as a function of space and time was proposed and allowed to evaluate their performance.

Actively Learning Specific Function Properties with Applications to Statistical Inference

DTIC Science & Technology

2007-12-01

the columns correspond to K different simulations of the sub-matrix sample j. ( b ) Pictorial strategies sets (Y and Z) for players y (light triangle...and Z are shown in Figure 3.4( b ), where, for simplicity of illustration, we let I = K = 3 and α = 0.33. While y is free to choose any point from the...running of spectral index 0.0 α = dns/d ln( k ) b galaxy bias 0.0 – 3.0 Qnl non-linear correction 30.81 Ωk spatial curvature -1.0 – 0.9 Ωk = 1− ΩΛ − ΩM ΩT

STRUCTURAL DIVERSITY IN SOLID STATE CHEMISTRY:A Story of Squares and Triangles

NASA Astrophysics Data System (ADS)

Lee, Stephen

1996-10-01

A simple method for calculating the electronic energy of extended solids is discussed in this review. This method is based on the Huckel or tight-binding theory in which an explicit pairwise repulsion is added to the generally attractive forces of the partially filled valence electron bands. An expansion based on the power moments of the electronic density of states is discussed, and the structural energy difference theorem is reviewed. The repulsive energy is found to vary linearly with the second power moment of the electronic density of states. These results are then used to show why there is such a diversity of structure in the solid state. The elemental structures of the main group are rationalized by the above methods. It is the third and fourth power moments (which correspond in part to triangles and squares of bonded atoms) that account for much of the elemental structures of the main group elements of the periodic table. This serves as an introduction to further rationalizations of transition for noble metal alloy, binary and ternary telluride and selenide, and other intermetallic structures.Thus a cohesive picture of both covalent and metallic bonding is presented in this review, illustrating the importance of atomic orbitals and their overlap integrals.

Factors associated with quality of life among the elderly in the community of the southern triangle macro-region, Minas Gerais, Brazil.

PubMed

Paiva, Michelle Helena Pereira de; Pegorari, Maycon Sousa; Nascimento, Janaína Santos; Santos, Álvaro da Silva

2016-11-01

This study sought to establish the socioeconomic and health factors associated with quality of life among the elderly in the community. An analytical study with a cross-sectional and quantitative approach was conducted in 2012 and 2013 with 3430 senior citizens in 24 municipalities in the Southern Triangle Macro-region of the State of Minas Gerais in Brazil. A structured questionnaire was used for socioeconomic and health variables, as well as the Katz scale, the World Health Organization Quality of Life-Bref (WHOQOL-BREF) and the World Health Organization Quality of Life Assessment for Older Adults (WHOQOL-OLD). Descriptive, bivariate statistical analysis was performed and a multiple linear regression model (p < 0.05) was created. Lower quality of life (QoL) scores were found in the environment and autonomy domains associated with advanced age, lack of schooling and income, a negative perception of health and functional disability. The salient key factor was negative health perception. The conclusion drawn was that socioeconomic and health factors were associated with the quality of life of the elderly, highlighting the lowest scores in the environmental domain and from the aspect of autonomy, a key influencing factor being negative health perception.

miniTri Mantevo miniapp v. 1.0

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

Berry, Johathan; Stark, Dylan; Wolf, Michael

2016-02-02

miniTri is a miniapplication developed as part of the Mantevo project. Given a graph, miniTri enumerates all triangles in this graph and computes a metric for each triangle based on the triangle edge and vertex degree. The output of miniTri is a summary of this metric. miniTri mimics the computational requirements of an important set of data science applications. Several approaches to this problem are included in the miniTri software.

Seismicity map of the state of Indiana

USGS Publications Warehouse

Stover, C.W.; Reagor, B.G.; Algermissen, S.T.

1987-01-01

The latitude and longitude coordinates of each epicenter were rounded to the nearest tenth of a degree and sorted so that all identical locations were grouped and counted. These locations are represented on the map by a triangle. The number of earthquakes at each location is shown on the map by the arabic number to the right of the triangle. A Roman numeral to the left of a triangle is the maximum Modified Mercalli intensity (Wood and Neumann, 1931) of all earthquakes at that geographic location. The absence of an intensity value indicates that no intensities have been assigned to earthquakes at that location. The year shown below each triangle is the latest year for which the maximum intensity was recorded.

Seismicity map of the state of Idaho

USGS Publications Warehouse

Stover, Carl W.; Reagor, B.G.; Algermissen, S.T.

1991-01-01

The latitude and longitude coordinates of each epicenter were rounded to the nearest tenth of a degree and sorted so that all identical locations were grouped and counted. These locations are represented on the map by a triangle. The number of earthquakes at each location is shown on the map by the Arabic number to the right of the triangle. A Roman numeral to the left of a triangle is the maximum Modified Mercalli intensity (Wood and Neumann, 1931) of all earthquakes at that geographic location. The absence of an intensity value indicates that no intensities have been assigned to earthquakes at that location. The year shown below each triangle is the latest year for which the maximum intensity was recorded.

Seismicity map of the state of North Carolina

USGS Publications Warehouse

Reagor, B.G.; Stover, C.W.; Algermissen, S.T.

1987-01-01

The latitude and longitude coordinates of each epicenter were rounded to the nearest tenth of a degree and sorted so that all identical locations were grouped and counted. These locations are represented on the map by a triangle. The number of earthquakes at each location is shown on the map by the arabic number to the right of the triangle. A Roman numeral to the left of a triangle is the maximum Modified Mercalli intensity (Wood and Neumann, 1931) of a11 earthquakes at that geographic location. The absence of an intensity value indicates that no intensities have been assigned to earthquakes at that location. The year shown below each triangle is the latest year for which the maximum intensity was recorded.

Seismicity map of the state of Vermont

USGS Publications Warehouse

Stover, C.W.; Reagor, B.G.; Highland, L.M.; Algermissen, S.T.

1987-01-01

The latitude and longitude coordinates of each epicenter were rounded to the nearest tenth of a degree and sorted so that all identical locations were grouped and counted. These locations are represented on the map by a triangle. The number of earthquakes at each location is shown on the map by the arabic number to the right of the triangle. A Roman numeral to the 1eft of a triangle is the maximum Modified Mercalli intensity (Wood and Neumann, 1931) of all earthquakes at that geographic location. The absence of an intensity value indicates that no intensities have been assigned to earthquakes at that location. The year shown below each triangle is the latest year for which the maximum intensity was recorded.

Seismicity map of the state of Ohio

USGS Publications Warehouse

Stover, C.W.; Reagor, B.G.; Algermissen, S.T.

1987-01-01

The latitude and longitude coordinates of each epicenter were rounded to the nearest tenth of a degree and sorted so that all identical locations were grouped and counted . These locations are represented on the map by a triangle. The number of earthquakes at each location is shown on the map by the arabic number to the right of the triangle. A Roman numeral to the left of a triangle is the maximum Modified Mercalli intensity (Wood and Neumann, 1931) of all earthquakes at that geographic location. The absence of an intensity value indicates that no intensities have been assigned to earthquakes at that location. The year shown below each triangle is the latest year for which the maximum intensity was recorded.

Analysis of Surface Roughness at Overlapping Laser Shock Peening

NASA Astrophysics Data System (ADS)

Dai, F. Z.; Zhang, Z. D.; Zhou, J. Z.; Lu, J. Z.; Zhang, Y. K.

2016-02-01

The overlapping effects on surface roughness are studied when samples are treated by laser shock peening (LSP). Surface roughness of overlapped circular laser spot is calculated by ISO 25178 height parameters. The usually used overlapping styles namely isosceles-right-triangle-style (AAP) and equilateral-triangle-style (AAA) are carefully investigated when the overlapping degree in x-axis (ηx) is below 50%. Surface roughness of isosceles-right-triangle-style attains its minimum value at ηx of 29.3%, and attains its maximum value at ηx of 43.6%. Surface roughness of equilateral-triangle-style attains its minimum value at ηx of 42.3%, and attains its maximum value at ηx of 32%. Experimental results are well consistent with theoretical analysis.

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

2018-04-01

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

Programming Pascal's Triangle

ERIC Educational Resources Information Center

Curley, Walter

1974-01-01

After a brief discussion of Pascal's triangle and description of four methods of hand construction, the author provides FORTRAN and BASIC programs for computer construction based on recursive definition. (SD)

New results on finite-time parameter identification and synchronization of uncertain complex dynamical networks with perturbation

NASA Astrophysics Data System (ADS)

Zhao, Hui; Zheng, Mingwen; Li, Shudong; Wang, Weiping

2018-03-01

Some existing papers focused on finite-time parameter identification and synchronization, but provided incomplete theoretical analyses. Such works incorporated conflicting constraints for parameter identification, therefore, the practical significance could not be fully demonstrated. To overcome such limitations, the underlying paper presents new results of parameter identification and synchronization for uncertain complex dynamical networks with impulsive effect and stochastic perturbation based on finite-time stability theory. Novel results of parameter identification and synchronization control criteria are obtained in a finite time by utilizing Lyapunov function and linear matrix inequality respectively. Finally, numerical examples are presented to illustrate the effectiveness of our theoretical results.

Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks

NASA Astrophysics Data System (ADS)

Zheng, Mingwen; Li, Lixiang; Peng, Haipeng; Xiao, Jinghua; Yang, Yixian; Zhang, Yanping; Zhao, Hui

2018-06-01

This paper mainly studies the finite-time stability and synchronization problems of memristor-based fractional-order fuzzy cellular neural network (MFFCNN). Firstly, we discuss the existence and uniqueness of the Filippov solution of the MFFCNN according to the Banach fixed point theorem and give a sufficient condition for the existence and uniqueness of the solution. Secondly, a sufficient condition to ensure the finite-time stability of the MFFCNN is obtained based on the definition of finite-time stability of the MFFCNN and Gronwall-Bellman inequality. Thirdly, by designing a simple linear feedback controller, the finite-time synchronization criterion for drive-response MFFCNN systems is derived according to the definition of finite-time synchronization. These sufficient conditions are easy to verify. Finally, two examples are given to show the effectiveness of the proposed results.

Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

NASA Technical Reports Server (NTRS)

Wu, R. W.; Witmer, E. A.

1972-01-01

Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

NASA Astrophysics Data System (ADS)

Virella, Juan C.; Prato, Carlos A.; Godoy, Luis A.

2008-05-01

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.

Iterative methods for mixed finite element equations

NASA Technical Reports Server (NTRS)

Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.

1985-01-01

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

A finite-element method for large-amplitude, two-dimensional panel flutter at hypersonic speeds

NASA Technical Reports Server (NTRS)

Mei, Chuh; Gray, Carl E.

1989-01-01

The nonlinear flutter behavior of a two-dimensional panel in hypersonic flow is investigated analytically. An FEM formulation based unsteady third-order piston theory (Ashley and Zartarian, 1956; McIntosh, 1970) and taking nonlinear structural and aerodynamic phenomena into account is derived; the solution procedure is outlined; and typical results are presented in extensive tables and graphs. A 12-element finite-element solution obtained using an alternative method for linearizing the assumed limit-cycle time function is shown to give predictions in good agreement with classical analytical results for large-amplitude vibration in a vacuum and large-amplitude panel flutter, using linear aerodynamics.

Equilibrium finite-frequency noise of an interacting mesoscopic capacitor studied in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-03-01

We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time perturbation theory and find excellent agreement for noise frequencies below the reservoir temperature.

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

NASA Technical Reports Server (NTRS)

Hsu, Su-Yuen; Chang, Chau-Lyan

2007-01-01

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

Formation of an active thrust triangle zone associated with structural inversion in a subduction setting, eastern New Zealand

NASA Astrophysics Data System (ADS)

Barnes, Philip M.; Nicol, Andrew

2004-02-01

We analyze a thrust triangle zone, which underlies the continental shelf of Hawke Bay, eastern New Zealand, within the Hikurangi subduction margin. This triangle zone differs from many other examples in that it is active, 90 km from the leading edge of the overriding plate, and formed due to polyphase deformation involving opposed dipping thrust duplex and backthrust, with the later structure forming in response to inversion of an extensional graben. The component structures of the zone mainly developed sequentially rather than synchronously. High-quality marine seismic reflection lines, tied to well and seabed samples, reveal the three-dimensional structure of the zone, together with its 25 Myr evolution and late Quaternary activity. The triangle zone occurs in the lateral overlap between a stack of NW dipping blind thrusts, and a principal backthrust, the Kidnappers fault. The NW dipping thrusts initiated in the early-middle Miocene during the early stages of subduction, with subsequent thrust duplex formation producing major uplift and erosion in the late Miocene-early Pliocene. The active backthrust formed during the late Miocene to early Pliocene as a thin-skinned listric extensional fault confined to the cover sequence. Structural inversion of the extensional fault commenced in the early-middle Pliocene, produced the backthrust and marks the formation of the thrust triangle zone. The thrust duplex and backthrust accrued strain following inversion; however, the later structure accommodated most of the surface deformation in the Quaternary. Section balancing of the triangle zone together with a detailed analysis of reverse displacements along the backthrust reveal spatial and temporal variations of strain accumulation on the two principal components of the zone. Although the formation of the triangle zone is strongly influenced by regional tectonics of the subduction system, these variations may also, in part, reflect local fault interaction. For example, high Quaternary displacement rates on the backthrust accounts for ˜70% of the displacement loss that occurs on the southern segments of the overlapping, Lachlan fault. Understanding the tectonic evolution of such complex, polyphase thrust triangle zones requires the preservation of growth strata that record sequential deformation history. In the absence of such data, synchroneity of opposed dipping thrusts in triangle zones cannot be assumed.

Study of non-linear deformation of vocal folds in simulations of human phonation

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Bodony, Daniel

2014-11-01

Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).

A Linear Programming Approach to Routing Control in Networks of Constrained Nonlinear Positive Systems with Concave Flow Rates

NASA Technical Reports Server (NTRS)

Arneson, Heather M.; Dousse, Nicholas; Langbort, Cedric

2014-01-01

We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.

The Abstraction Ability in Constructing Relation Within Triangles by The Seventh Grade Students of Junior High School

NASA Astrophysics Data System (ADS)

Annas, Suwardi; Djadir; Mutmainna Hasma, Sitti

2018-01-01

on is an activity to organize a mathematical concept that has been previously owned into a new mathematical structure. Activites in abstraction are recognizing, organizing and constructing. Recognizing is a process of identifying a mathematical structure that had existed before. Organizing is a process of using structural knowledge to be assembled into a solution of a problem and constructing is a process of organizing the characteristics of the object into a new structure that does not exist. In abstraction process, the students use attributes to address the object, including routine attribute, nonroutine attributes, and meaningless attributes. This research applied descriptive qualitative research which aimed to describe the abstraction ability of students from high, moderate, and low groups to construct a relation within triangle. In collecting the data, this research used students’ pre-ability math test, abstraction test, and guided interview. The sampling technique in this research was based on the students’ scores in pre-ability math test, which were divided into three groups. Two students from each group were opted as the subjects of this research. Questions of the test are based on the indicators of steps in abstraction activity. Thus, based on the data gained in this research, researcher determined the tendency of attributes used in each abstraction activity. The result of this research revealed that students from high, moderate and low groups were prone to use routine attributes in recognizing triangles. In organizing the characteristics within triangles, high group tended to organize the triangle correctly, while the moderate and low groups tended to organize the triangle incorrectly. In constructing relation within triangles, students in high, moderate and low groups construct it incompletely.

The oncogenic triangle of HMGA2, LIN28B and IGF2BP1 antagonizes tumor-suppressive actions of the let-7 family.

PubMed

Busch, Bianca; Bley, Nadine; Müller, Simon; Glaß, Markus; Misiak, Danny; Lederer, Marcell; Vetter, Martina; Strauß, Hans-Georg; Thomssen, Christoph; Hüttelmaier, Stefan

2016-05-05

The tumor-suppressive let-7 microRNA family targets various oncogene-encoding mRNAs. We identify the let-7 targets HMGA2, LIN28B and IGF2BP1 to form a let-7 antagonizing self-promoting oncogenic triangle. Surprisingly, 3'-end processing of IGF2BP1 mRNAs is unaltered in aggressive cancers and tumor-derived cells although IGF2BP1 synthesis was proposed to escape let-7 attack by APA-dependent (alternative polyadenylation) 3' UTR shortening. However, the expression of the triangle factors is inversely correlated with let-7 levels and promoted by LIN28B impairing let-7 biogenesis. Moreover, IGF2BP1 enhances the expression of all triangle factors by recruiting the respective mRNAs in mRNPs lacking AGO proteins and let-7 miRNAs. This indicates that the downregulation of let-7, largely facilitated by LIN28B upregulation, and the protection of let-7 target mRNAs by IGF2BP1-directed shielding in mRNPs synergize in enhancing the expression of triangle factors. The oncogenic potential of this triangle was confirmed in ovarian cancer (OC)-derived ES-2 cells transduced with let-7 targeting decoys. In these, the depletion of HMGA2 only diminishes tumor cell growth under permissive conditions. The depletion of LIN28B and more prominently IGF2BP1 severely impairs tumor cell viability, self-renewal and 2D as well as 3D migration. In conclusion, this suggests the targeting of the HMGA2-LIN28B-IGF2BP1 triangle as a promising strategy in cancer treatment. © The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.

The oncogenic triangle of HMGA2, LIN28B and IGF2BP1 antagonizes tumor-suppressive actions of the let-7 family

PubMed Central

Busch, Bianca; Bley, Nadine; Müller, Simon; Glaß, Markus; Misiak, Danny; Lederer, Marcell; Vetter, Martina; Strauß, Hans-Georg; Thomssen, Christoph; Hüttelmaier, Stefan

2016-01-01

The tumor-suppressive let-7 microRNA family targets various oncogene-encoding mRNAs. We identify the let-7 targets HMGA2, LIN28B and IGF2BP1 to form a let-7 antagonizing self-promoting oncogenic triangle. Surprisingly, 3′-end processing of IGF2BP1 mRNAs is unaltered in aggressive cancers and tumor-derived cells although IGF2BP1 synthesis was proposed to escape let-7 attack by APA-dependent (alternative polyadenylation) 3′ UTR shortening. However, the expression of the triangle factors is inversely correlated with let-7 levels and promoted by LIN28B impairing let-7 biogenesis. Moreover, IGF2BP1 enhances the expression of all triangle factors by recruiting the respective mRNAs in mRNPs lacking AGO proteins and let-7 miRNAs. This indicates that the downregulation of let-7, largely facilitated by LIN28B upregulation, and the protection of let-7 target mRNAs by IGF2BP1-directed shielding in mRNPs synergize in enhancing the expression of triangle factors. The oncogenic potential of this triangle was confirmed in ovarian cancer (OC)-derived ES-2 cells transduced with let-7 targeting decoys. In these, the depletion of HMGA2 only diminishes tumor cell growth under permissive conditions. The depletion of LIN28B and more prominently IGF2BP1 severely impairs tumor cell viability, self-renewal and 2D as well as 3D migration. In conclusion, this suggests the targeting of the HMGA2-LIN28B-IGF2BP1 triangle as a promising strategy in cancer treatment. PMID:26917013

A clear map of the lower cranial nerves at the superior carotid triangle.

PubMed

Cavalcanti, Daniel D; Garcia-Gonzalez, Ulises; Agrawal, Abhishek; Tavares, Paulo L M S; Spetzler, Robert F; Preul, Mark C

2010-07-01

The lower cranial nerves must be identified to avoid iatrogenic injury during skull base and high cervical approaches. Prompt recognition of these structures using basic landmarks could reduce surgical time and morbidity. The anterior triangle of the neck was dissected in 30 cadaveric head sides. The most superficial segments of the glossopharyngeal, vagus and its superior laryngeal nerves, accessory, and hypoglossal nerves were exposed and designated into smaller anatomic triangles. The midpoint of each nerve segment inside the triangles was correlated to the angle of the mandible (AM), mastoid tip (MT), and bifurcation of the common carotid artery. A triangle bounded by the styloglossus muscle, external carotid artery, and facial artery housed the glossopharyngeal nerve. This nerve segment was 0.06 ± 0.71 cm posterior to the AM and 2.50 ± 0.59 cm inferior to the MT. The vagus nerve ran inside the carotid sheath posterior to internal carotid artery and common carotid artery bifurcation in 48.3% of specimens. A triangle formed by the posterior belly of digastric muscle, sternocleidomastoid muscle, and internal jugular vein housed the accessory nerve, 1.90 ± 0.60 cm posterior to the AM and 2.30 ± 0.57 cm inferior to the MT. A triangle outlined by the posterior belly of digastric muscle, internal jugular vein, and common facial vein housed the hypoglossal nerve, which was 0.82 ± 0.84 cm posterior to the AM and 3.64 ± 0.70 cm inferior to the MT. Comprehensible landmarks can be defined to help expose the lower cranial nerves to avoid injury to this complex region. Copyright © 2010 Elsevier Inc. All rights reserved.

Crystal structure of a new polar borate Na{sub 2}Ce{sub 2}[BO{sub 2}(OH)][BO{sub 3}]{sub 2} · H{sub 2}O with isolated boron triangles

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

Topnikova, A. P.; Belokoneva, E. L., E-mail: elbel@geol.msu.ru; Dimitrova, O. V.

2016-11-15

Crystals of a new polar borate Na{sub 2}Ce{sub 2}[BO{sub 2}(OH)][BO{sub 3}]{sub 2} · H{sub 2}O were prepared by hydrothermal synthesis. The crystals are orthorhombic, a = 7.2295(7) Å, b = 11.2523(8) Å, c = 5.1285(6) Å, Z = 2, sp. gr. C2mm (Amm2), R = 0.0253. The formula of the compound was derived from the structure determination. The Ce and Na atoms are coordinated by nine and six O atoms, respectively. The Ce position is split, and a small amount of Ce is incorporated into the Na1 site with the isomorphous substitution for Na. The anionic moieties exist as isolatedmore » BO{sub 3} and BO{sub 2}(OH) triangles. The planes of the BO{sub 2}(OH) triangles with mm2 symmetry are parallel to the ab plane. The planes of the BO{sub 3} triangles with m symmetry are perpendicular to the ab plane and are rotated in a diagonal way. The splitting of the Ce positions and the polar arrangement of the BO{sub 2}(OH) triangles, water molecules, and Na atoms are observed along the polar a axis. The new structure is most similar to the new borate NaCa{sub 4}[BO{sub 3}]{sub 3} (sp. gr. Ama2), in which triangles of one type are arranged in a polar fashion along the c axis. Weak nonlinear-optical properties of both polar borates are attributed to the quenching of the second-harmonic generation due to the mutually opposite orientation of two-thirds of B triangles in the unit cell.« less

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model Description and User's Manual

USGS Publications Warehouse

Torak, L.J.

1993-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or bead-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration. The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems; Part 1, Model description and user's manual

USGS Publications Warehouse

Torak, Lynn J.

1992-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration.The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

Bootstrapping quarks and gluons

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

Chew, G.F.

1979-04-01

Dual topological unitarization (DTU) - the approach to S-matrix causality and unitarity through combinatorial topology - is reviewed. Amplitudes associated with triangulated spheres are shown to constitute the core of particle physics. Each sphere is covered by triangulated disc faces corresponding to hadrons. The leading current candidate for the hadron-face triangulation pattern employs 3-triangle basic subdiscs whose orientations correspond to baryon number and topological color. Additional peripheral triangles lie along the hadron-face perimeter. Certain combinations of peripheral triangles with a basic-disc triangle can be identified as quarks, the flavor of a quark corresponding to the orientation of its edges thatmore » lie on the hadron-face perimeter. Both baryon number and flavor are additively conserved. Quark helicity, which can be associated with triangle-interior orientation, is not uniformly conserved and interacts with particle momentum, whereas flavor does not. Three different colors attach to the 3 quarks associated with a single basic subdisc, but there is no additive physical conservation law associated with color. There is interplay between color and quark helicity. In hadron faces with more than one basic subdisc, there may occur pairs of adjacent flavorless but colored triangles with net helicity +-1 that are identifiable as gluons. Broken symmetry is an automatic feature of the bootstrap. T, C and P symmetries, as well as up-down flavor symmetry, persist on all orientable surfaces.« less

Holliday Triangle Hunter (HolT Hunter): Efficient Software for Identifying Low Strain DNA Triangular Configurations

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

Sherman, W.B.

2012-04-16

Synthetic DNA nanostructures are typically held together primarily by Holliday junctions. One of the most basic types of structures possible to assemble with only DNA and Holliday junctions is the triangle. To date, however, only equilateral triangles have been assembled in this manner - primarily because it is difficult to figure out what configurations of Holliday triangles have low strain. Early attempts at identifying such configurations relied upon calculations that followed the strained helical paths of DNA. Those methods, however, were computationally expensive, and failed to find many of the possible solutions. I have developed a new approach to identifyingmore » Holliday triangles that is computationally faster, and finds well over 95% of the possible solutions. The new approach is based on splitting the problem into two parts. The first part involves figuring out all the different ways that three featureless rods of the appropriate length and diameter can weave over and under one another to form a triangle. The second part of the computation entails seeing whether double helical DNA backbones can fit into the shape dictated by the rods in such a manner that the strands can cross over from one domain to the other at the appropriate spots. Structures with low strain (that is, good fit between the rods and the helices) on all three edges are recorded as promising for assembly.« less

Mixture models in diagnostic meta-analyses--clustering summary receiver operating characteristic curves accounted for heterogeneity and correlation.

PubMed

Schlattmann, Peter; Verba, Maryna; Dewey, Marc; Walther, Mario

2015-01-01

Bivariate linear and generalized linear random effects are frequently used to perform a diagnostic meta-analysis. The objective of this article was to apply a finite mixture model of bivariate normal distributions that can be used for the construction of componentwise summary receiver operating characteristic (sROC) curves. Bivariate linear random effects and a bivariate finite mixture model are used. The latter model is developed as an extension of a univariate finite mixture model. Two examples, computed tomography (CT) angiography for ruling out coronary artery disease and procalcitonin as a diagnostic marker for sepsis, are used to estimate mean sensitivity and mean specificity and to construct sROC curves. The suggested approach of a bivariate finite mixture model identifies two latent classes of diagnostic accuracy for the CT angiography example. Both classes show high sensitivity but mainly two different levels of specificity. For the procalcitonin example, this approach identifies three latent classes of diagnostic accuracy. Here, sensitivities and specificities are quite different as such that sensitivity increases with decreasing specificity. Additionally, the model is used to construct componentwise sROC curves and to classify individual studies. The proposed method offers an alternative approach to model between-study heterogeneity in a diagnostic meta-analysis. Furthermore, it is possible to construct sROC curves even if a positive correlation between sensitivity and specificity is present. Copyright © 2015 Elsevier Inc. All rights reserved.

Intellectual Dummies

NASA Technical Reports Server (NTRS)

2002-01-01

Goddard Space Flight Center and Triangle Research & Development Corporation collaborated to create "Smart Eyes," a charge coupled device camera that, for the first time, could read and measure bar codes without the use of lasers. The camera operated in conjunction with software and algorithms created by Goddard and Triangle R&D that could track bar code position and direction with speed and precision, as well as with software that could control robotic actions based on vision system input. This accomplishment was intended for robotic assembly of the International Space Station, helping NASA to increase production while using less manpower. After successfully completing the two- phase SBIR project with Goddard, Triangle R&D was awarded a separate contract from the U.S. Department of Transportation (DOT), which was interested in using the newly developed NASA camera technology to heighten automotive safety standards. In 1990, Triangle R&D and the DOT developed a mask made from a synthetic, plastic skin covering to measure facial lacerations resulting from automobile accidents. By pairing NASA's camera technology with Triangle R&D's and the DOT's newly developed mask, a system that could provide repeatable, computerized evaluations of laceration injury was born.

Low frequency AC waveform generator

DOEpatents

Bilharz, Oscar W.

1986-01-01

Low frequency sine, cosine, triangle and square waves are synthesized in circuitry which allows variation in the waveform amplitude and frequency while exhibiting good stability and without requiring significant stabilization time. A triangle waveform is formed by a ramped integration process controlled by a saturation amplifier circuit which produces the necessary hysteresis for the triangle waveform. The output of the saturation circuit is tapped to produce the square waveform. The sine waveform is synthesized by taking the absolute value of the triangular waveform, raising this absolute value to a predetermined power, multiplying the raised absolute value of the triangle wave with the triangle wave itself and properly scaling the resultant waveform and subtracting it from the triangular waveform itself. The cosine is synthesized by squaring the triangular waveform, raising the triangular waveform to a predetermined power and adding the squared waveform raised to the predetermined power with a DC reference and subtracting the squared waveform therefrom, with all waveforms properly scaled. The resultant waveform is then multiplied with a square wave in order to correct the polarity and produce the resultant cosine waveform.

Aesthetic judgment of triangular shape: compactness and not the golden ratio determines perceived attractiveness

PubMed Central

Friedenberg, Jay

2012-01-01

Many studies over a period of more than a century have investigated the influence of the golden ratio on perceived geometric beauty. Surprisingly, very few of these studies used triangular shapes. In Experiment 1, we presented right triangles that differed in regard to their elongation determined by increasing the length of one side relative to another. Attractiveness ratings did not peak at the golden ratio, but there was a very strong influence of axis ratio overall. Participant ratings were a negative decreasing function of ratio. Triangles that pointed upward were judged as significantly more attractive than those that pointed down. We interpret these results according to a compactness hypothesis: triangles that are more compact are less likely to move or break and are thus considered more pleasing. Orientation also affects aesthetics. Upward-pointing triangles with a base parallel to the ground, regardless of their compactness, are also considered more perceptually stable and attractive. These findings were replicated across stimulus type in a second experiment with isosceles triangles and across testing procedure in a third experiment using a paired comparison technique. PMID:23145277

Developing Lesson Design to Help Students’ Triangle Conseptual Understanding

NASA Astrophysics Data System (ADS)

Prabawanto, S.; Mulyana, E.

2017-09-01

The research was aimed to develop a lesson design so that students’ triangle conceptual understanding could be achieved. The method that be used in this research was qualitative with applied didactical design research (DDR). The DDR consisted of three main stepts, namely prospective analysis, metapedadicdactic analysis, and retrospective analysis. From the three stepts above, it was gained the empirical lesson design of triangle topic. The reseach results are: (1) there were some learning obstacles of students deal with the triangle topic, namely ontogenical, epietimological, and didactical obstacles; (2) implementaion of the lesson was conducted under three main stepts, namely action, formulation, and validation. For answering weather the design can be applied to other group of students, it was recommended that it cound be investigated by doing advanced reseach.

Triangle inequalities in coherence measures and entanglement concurrence

NASA Astrophysics Data System (ADS)

Dai, Yue; You, Wenlong; Dong, Yuli; Zhang, Chengjie

2017-12-01

We provide detailed proofs of triangle inequalities in coherence measures and entanglement concurrence. If a rank-2 state ϱ can be expressed as a convex combination of two pure states, i.e., ϱ =p1| ψ1〉〈 ψ1|+ p2| ψ2〉〈 ψ2| , a triangle inequality can be established as |E (|Ψ1〉 )-E (|Ψ2〉 )|≤E (ϱ ) ≤E (|Ψ1〉 )+E (|Ψ2〉 ) , where | Ψ1〉= √{p1}|ψ1〉 and | Ψ2〉= √{p2}|ψ2〉 ; E can be considered either coherence measures or entanglement concurrence. This inequality displays mathematical beauty for its similarity to the triangle inequality in plane geometry. An illustrative example is given after the proof.

Research Triangle Park, NC Laboratory at a Glance

EPA Pesticide Factsheets

Among many other things, EPA's Research Triangle Park scientists simulate many different types of air pollution under varying meteorological conditions and study the health effects of air pollution mixtures.

Self-assembled squares and triangles by simultaneous hydrogen bonding and metal coordination.

PubMed

Marshall, Laura J; de Mendoza, Javier

2013-04-05

Through the combination of hydrogen bonding and metal-templated self-assembly, molecular squares and molecular triangles are observed in chloroform solution upon the complexation of hydrogen-bonded dimers of para-pyridyl-substituted 2-ureido-4-[1H]-pyrimidinone (UPy) and an appropriate cis-substituted palladium complex. Molecular modeling studies and NMR analysis confirmed the presence of two distinct structures in solution: the tubular structure of the molecular square and propeller-bowl structure of the molecular triangle.

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.

Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

NASA Astrophysics Data System (ADS)

Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.

2018-05-01

A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.

Finite Element Based Structural Damage Detection Using Artificial Boundary Conditions

DTIC Science & Technology

2007-09-01

C. (2005). Elementary Linear Algebra . New York: John Wiley and Sons. Avitable, Peter (2001, January) Experimental Modal Analysis, A Simple Non...variables under consideration. 3 Frequency sensitivities are the basis for a linear approximation to compute the change in the natural frequencies of a...THEORY The general problem statement for a non- linear constrained optimization problem is: To minimize ( )f x Objective Function Subject to

Switching times of nanoscale FePt: Finite size effects on the linear reversal mechanism

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

Ellis, M. O. A.; Chantrell, R. W.

2015-04-20

The linear reversal mechanism in FePt grains ranging from 2.316 nm to 5.404 nm has been simulated using atomistic spin dynamics, parametrized from ab-initio calculations. The Curie temperature and the critical temperature (T{sup *}), at which the linear reversal mechanism occurs, are observed to decrease with system size whilst the temperature window T{sup *}

Use of system identification techniques for improving airframe finite element models using test data

NASA Technical Reports Server (NTRS)

Hanagud, Sathya V.; Zhou, Weiyu; Craig, James I.; Weston, Neil J.

1991-01-01

A method for using system identification techniques to improve airframe finite element models was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

Application of the Finite Element Method to Rotary Wing Aeroelasticity

NASA Technical Reports Server (NTRS)

Straub, F. K.; Friedmann, P. P.

1982-01-01

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.

Finite-Dimensional Representations for Controlled Diffusions with Delay

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

Federico, Salvatore, E-mail: salvatore.federico@unimi.it; Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr

2015-02-15

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

Development of non-linear finite element computer code

NASA Technical Reports Server (NTRS)

Becker, E. B.; Miller, T.

1985-01-01

Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.

A discourse on sensitivity analysis for discretely-modeled structures

NASA Technical Reports Server (NTRS)

Adelman, Howard M.; Haftka, Raphael T.

1991-01-01

A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

NASA Technical Reports Server (NTRS)

Rodal, J. J. A.; Witmer, E. A.

1979-01-01

A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1982-01-01

Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.

Finite element analysis of the effect of a non-planar solid-liquid interface on the lateral solute segregation during unidirectional solidification

NASA Technical Reports Server (NTRS)

Carlson, F. M.; Chin, L.-Y.; Fripp, A. L.; Crouch, R. K.

1982-01-01

The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly nonplanar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

A finite nonlinear hyper-viscoelastic model for soft biological tissues.

PubMed

Panda, Satish Kumar; Buist, Martin Lindsay

2018-03-01

Soft tissues exhibit highly nonlinear rate and time-dependent stress-strain behaviour. Strain and strain rate dependencies are often modelled using a hyperelastic model and a discrete (standard linear solid) or continuous spectrum (quasi-linear) viscoelastic model, respectively. However, these models are unable to properly capture the materials characteristics because hyperelastic models are unsuited for time-dependent events, whereas the common viscoelastic models are insufficient for the nonlinear and finite strain viscoelastic tissue responses. The convolution integral based models can demonstrate a finite viscoelastic response; however, their derivations are not consistent with the laws of thermodynamics. The aim of this work was to develop a three-dimensional finite hyper-viscoelastic model for soft tissues using a thermodynamically consistent approach. In addition, a nonlinear function, dependent on strain and strain rate, was adopted to capture the nonlinear variation of viscosity during a loading process. To demonstrate the efficacy and versatility of this approach, the model was used to recreate the experimental results performed on different types of soft tissues. In all the cases, the simulation results were well matched (R 2 ⩾0.99) with the experimental data. Copyright © 2018 Elsevier Ltd. All rights reserved.

Points on the Path to Probability.

ERIC Educational Resources Information Center

Kiernan, James F.

2001-01-01

Presents the problem of points and the development of the binomial triangle, or Pascal's triangle. Examines various attempts to solve this problem to give students insight into the nature of mathematical discovery. (KHR)

Finding Optimal Gains In Linear-Quadratic Control Problems

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

A 3/D finite element approach for metal matrix composites based on micromechanical models

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

Svobodnik, A.J.; Boehm, H.J.; Rammerstorfer, F.G.

Based on analytical considerations by Dvorak and Bahel-El-Din, a 3/D finite element material law has been developed for the elastic-plastic analysis of unidirectional fiber-reinforced metal matrix composites. The material law described in this paper has been implemented in the finite element code ABAQUS via the user subroutine UMAT. A constitutive law is described under the assumption that the fibers are linear-elastic and the matrix is of a von Mises-type with a Prager-Ziegler kinematic hardening rule. The uniaxial effective stress-strain relationship of the matrix in the plastic range is approximated by a Ramberg-Osgood law, a linear hardening rule or a nonhardeningmore » rule. Initial yield surface of the matrix material and for the fiber reinforced composite are compared to show the effect of reinforcement. Implementation of this material law in a finite element program is shown. Furthermore, the efficiency of substepping schemes and stress corrections for the numerical integration of the elastic-plastic stress-strain relations for anisotropic materials are investigated. The results of uniaxial monotonic tests of a boron/aluminum composite are compared to some finite element analyses based on micromechanical considerations. Furthermore a complete 3/D analysis of a tensile test specimen made of a silicon-carbide/aluminum MMC and the analysis of an MMC inlet inserted in a homogenous material are shown. 12 refs.« less

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2015-12-21

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

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

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Advanced composites structural concepts and materials technologies for primary aircraft structures: Structural response and failure analysis

NASA Technical Reports Server (NTRS)

Dorris, William J.; Hairr, John W.; Huang, Jui-Tien; Ingram, J. Edward; Shah, Bharat M.

1992-01-01

Non-linear analysis methods were adapted and incorporated in a finite element based DIAL code. These methods are necessary to evaluate the global response of a stiffened structure under combined in-plane and out-of-plane loading. These methods include the Arc Length method and target point analysis procedure. A new interface material model was implemented that can model elastic-plastic behavior of the bond adhesive. Direct application of this method is in skin/stiffener interface failure assessment. Addition of the AML (angle minus longitudinal or load) failure procedure and Hasin's failure criteria provides added capability in the failure predictions. Interactive Stiffened Panel Analysis modules were developed as interactive pre-and post-processors. Each module provides the means of performing self-initiated finite elements based analysis of primary structures such as a flat or curved stiffened panel; a corrugated flat sandwich panel; and a curved geodesic fuselage panel. This module brings finite element analysis into the design of composite structures without the requirement for the user to know much about the techniques and procedures needed to actually perform a finite element analysis from scratch. An interactive finite element code was developed to predict bolted joint strength considering material and geometrical non-linearity. The developed method conducts an ultimate strength failure analysis using a set of material degradation models.

Investigation of the Influence of Shapes-Texture on Surface Deformation of UHMWPE as a Bearing Material in Static Normal Load and Rolling Contact

NASA Astrophysics Data System (ADS)

Lestari, W. D.; Ismail, R.; Jamari, J.; Bayuseno, A. P.

2017-05-01

Surface texture is a common method for improving wear properties of a tribo-pair of soft and hard bearing material. The reduction of wear rates on the contacting surface material is becoming important issues. In the present study, analysis of the contact pressure on the flat surface of UHMWPE (Ultra High Molecular Weight Polyethylene) under the static- and rolling motion with the surface of steel ball used the 3D finite element method (FEM) (the ABAQUS software version 6.12). Five shaped-texture models (square, circle, ellipse, triangle, and chevron) were presented on the flat surface for analysis. The normal load of 17, 30 and 50 N was deliberately set-up for static and rolling contact analysis. The contact pressure was determined to predict the wear behavior of the shaped-texture on the flat surface of UHMWPE. The results have shown that the static normal load yielded the lowest von-Mises stress distribution on the shaped-texture of the ellipse for all values applied a load, while the square shape experienced the highest stress distribution. Under rolling contact, however, the increasing load yielded the increasing von Mises stress distribution for the texture with a triangle shape. Moreover, the texture shapes for circle, ellipse, and chevron respectively, may undergo the lowest stress distribution for all load. The wear calculation provided that the circle and square shape may undergo the highest wear rates. Obviously, the surface texture of circle, ellipse, and chevron may experience the lowest wear rates and is potential for use in the surface engineering of bearing materials.

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

Instability, finite amplitude pulsation and mass-loss in models of massive OB-type stars

NASA Astrophysics Data System (ADS)

Yadav, Abhay Pratap; Glatzel, Wolfgang

2017-11-01

Variability and mass-loss are common phenomena in massive OB-type stars. It is argued that they are caused by violent strange mode instabilities identified in corresponding stellar models. We present a systematic linear stability analysis with respect to radial perturbations of massive OB-type stars with solar chemical composition and masses between 23 and 100 M⊙. For selected unstable stellar models, we perform non-linear simulations of the evolution of the instabilities into the non-linear regime. Finite amplitude pulsations with periods in the range between hours and 100 d are found to be the final result of the instabilities. The pulsations are associated with a mean acoustic luminosity which can be the origin of a pulsationally driven wind. Corresponding mass-loss rates lie in the range between 10-9 and 10-4 M⊙ yr-1 and may thus affect the evolution of massive stars.

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.

2018-07-01

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

Topics

ERIC Educational Resources Information Center

Mathematics Teaching, 1971

1971-01-01

Problems involving divisibility, the ten coin triangle, five times a week with 4 D, a nomogram for the lens formula, the box and ladder problem, chains of circles, tessellating hexagons, topological woggles, and numbers of triangles are discussed. (CT)

Nearly Nice Right Triangles.

ERIC Educational Resources Information Center

Reid, Bob

1989-01-01

Relationships among the sides are developed for right triangles whose sides are in the ratios 1:3, 1:4, and 1:5. The golden ratio appears in the results which can be used in secondary mathematics. (DC)

James Williamson d/b/a Golden Triangle Builders Information Sheet

EPA Pesticide Factsheets

James Williamson d/b/a Golden Triangle Builders (the Company) is located in Pittsburgh, Pennsylvania. The settlement involves renovation activities conducted at property constructed prior to 1978, located in Pittsburgh, Pennsylvania.

Status of the Cabibbo-Kobayashi-Maskawa matrix and Unitarity Triangle fits

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

Bona, M.; Ciuchini, M.; INFN, Sez. di Roma III, Rome

2007-01-12

status of the Unitarity Triangle analysis realized by the UTfit Collaboration is presented. The most recent determinations of theoretical and experimental parameters are used in order to over-constrain the apex of the Unitarity Triangle in the Standard Model. In addition, we present the analysis of the Unitarity Triangle beyond the Standard Model, by parametrizing New Physics contributions in {delta}F = 2 processes. With the new measurements from the Tevatron, namely the mass difference {delta}ms, the width difference {delta}{gamma}s and the di-muon asymmetry, it is possible to establish significant bounds on New Physics parameters also in the Bs sector. The resultsmore » and the plots presented in this paper can be found at the URL http://www.utfit.org, where they are continuously kept up-to-date.« less

Wedge sampling for computing clustering coefficients and triangle counts on large graphs

DOE PAGES

Seshadhri, C.; Pinar, Ali; Kolda, Tamara G.

2014-05-08

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social cohesion. Despite the importance of these triadic measures, algorithms to compute them can be extremely expensive. We discuss the method of wedge sampling. This versatile technique allows for the fast and accurate approximation of various types of clustering coefficients and triangle counts. Furthermore, these techniques are extensible to counting directed triangles in digraphs. Our methods come with provable andmore » practical time-approximation tradeoffs for all computations. We provide extensive results that show our methods are orders of magnitude faster than the state of the art, while providing nearly the accuracy of full enumeration.« less

Sub-Pixel Accuracy Crack Width Determination on Concrete Beams in Load Tests by Triangle Mesh Geometry Analysis

NASA Astrophysics Data System (ADS)

Liebold, F.; Maas, H.-G.

2018-05-01

This paper deals with the determination of crack widths of concrete beams during load tests from monocular image sequences. The procedure starts in a reference image of the probe with suitable surface texture under zero load, where a large number of points is defined by an interest operator. Then a triangulated irregular network is established to connect the points. Image sequences are recorded during load tests with the load increasing continuously or stepwise, or at intermittently changing load. The vertices of the triangles are tracked through the consecutive images of the sequence with sub-pixel accuracy by least squares matching. All triangles are then analyzed for changes by principal strain calculation. For each triangle showing significant strain, a crack width is computed by a thorough geometric analysis of the relative movement of the vertices.

Visual Search for Wines with a Triangle on the Label in a Virtual Store

PubMed Central

Zhao, Hui; Huang, Fuxing; Spence, Charles; Wan, Xiaoang

2017-01-01

Two experiments were conducted in a virtual reality (VR) environment in order to investigate participants’ in-store visual search for bottles of wines displaying a prominent triangular shape on their label. The experimental task involved virtually moving along a wine aisle in a virtual supermarket while searching for the wine bottle on the shelf that had a different triangle on its label from the other bottles. The results of Experiment 1 revealed that the participants identified the bottle with a downward-pointing triangle on its label more rapidly than when looking for an upward-pointing triangle on the label instead. This finding replicates the downward-pointing triangle superiority (DPTS) effect, though the magnitude of this effect was more pronounced in the first as compared to the second half of the experiment, suggesting a modulating role of practice. The results of Experiment 2 revealed that the DPTS effect was also modulated by the location of the target on the shelf. Interestingly, however, the results of a follow-up survey demonstrate that the orientation of the triangle did not influence the participants’ evaluation of the wine bottles. Taken together, these findings reveal how in-store the attention of consumers might be influenced by the design elements in product packaging. These results therefore suggest that shopping in a virtual supermarket might offer a practical means of assessing the shelf standout of product packaging, which has important implications for food marketing. PMID:29326624

Visual Search for Wines with a Triangle on the Label in a Virtual Store.

PubMed

Zhao, Hui; Huang, Fuxing; Spence, Charles; Wan, Xiaoang

2017-01-01

Two experiments were conducted in a virtual reality (VR) environment in order to investigate participants' in-store visual search for bottles of wines displaying a prominent triangular shape on their label. The experimental task involved virtually moving along a wine aisle in a virtual supermarket while searching for the wine bottle on the shelf that had a different triangle on its label from the other bottles. The results of Experiment 1 revealed that the participants identified the bottle with a downward-pointing triangle on its label more rapidly than when looking for an upward-pointing triangle on the label instead. This finding replicates the downward-pointing triangle superiority (DPTS) effect, though the magnitude of this effect was more pronounced in the first as compared to the second half of the experiment, suggesting a modulating role of practice. The results of Experiment 2 revealed that the DPTS effect was also modulated by the location of the target on the shelf. Interestingly, however, the results of a follow-up survey demonstrate that the orientation of the triangle did not influence the participants' evaluation of the wine bottles. Taken together, these findings reveal how in-store the attention of consumers might be influenced by the design elements in product packaging. These results therefore suggest that shopping in a virtual supermarket might offer a practical means of assessing the shelf standout of product packaging, which has important implications for food marketing.

Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching

NASA Technical Reports Server (NTRS)

Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven

2004-01-01

This paper analyzes the stability of hierarchical jump linear systems where the supervisor is driven by a Markovian stochastic process and by the values of the supervised jump linear system s states. The stability framework for this class of systems is developed over infinite and finite time horizons. The framework is then used to derive sufficient stability conditions for a specific class of hybrid jump linear systems with performance supervision. New sufficient stochastic stability conditions for discrete-time jump linear systems are also presented.

Optimal Estimation of Clock Values and Trends from Finite Data

NASA Technical Reports Server (NTRS)

Greenhall, Charles

2005-01-01

We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.

A users guide for A344: A program using a finite difference method to analyze transonic flow over oscillating airfoils

NASA Technical Reports Server (NTRS)

Weatherill, W. H.; Ehlers, F. E.

1979-01-01

The design and usage of a pilot program for calculating the pressure distributions over harmonically oscillating airfoils in transonic flow are described. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equations for small disturbances. The steady velocity potential which must be obtained from some other program, was required for input. The unsteady equation, as solved, is linear with spatially varying coefficients. Since sinusoidal motion was assumed, time was not a variable. The numerical solution was obtained through a finite difference formulation and either a line relaxation or an out of core direct solution method.

Shortcuts to adiabaticity from linear response theory

DOE PAGES

Acconcia, Thiago V.; Bonança, Marcus V. S.; Deffner, Sebastian

2015-10-23

A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. Moreover, with the help of phenomenological response functions, a simple expression for the excess work is found—quantifying the nonequilibrium excitations. For two specific examples, i.e., the quantum parametric oscillator and the spin 1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. We finally propose a degenerate family of protocols, which facilitates shortcuts tomore » adiabaticity for specific and very short driving times.« less

Finite linear diffusion model for design of overcharge protection for rechargeable lithium batteries

NASA Technical Reports Server (NTRS)

Narayanan, S. R.; Surampudi, S.; Attia, A. I.

1991-01-01

The overcharge condition in secondary lithium batteries employing redox additives for overcharge protection has been theoretically analyzed in terms of a finite linear diffusion model. The analysis leads to expressions relating the steady-state overcharge current density and cell voltage to the concentration, diffusion coefficient, standard reduction potential of the redox couple, and interelectrode distance. The model permits the estimation of the maximum permissible overcharge rate for any chosen set of system conditions. The model has been experimentally verified using 1,1-prime-dimethylferrocene as a redox additive. The theoretical results may be exploited in the design and optimization of overcharge protection by the redox additive approach.

Anomalous enhancement of the isospin-violating Λ (1405 ) production by a triangle singularity in Λc→π+π0π0Σ0

NASA Astrophysics Data System (ADS)

Dai, L. R.; Pavao, R.; Sakai, S.; Oset, E.

2018-06-01

The decay of Λc+ into π+π0Λ (1405 ) with the Λ (1405 ) decay into π0Σ0 through a triangle diagram is studied. This process is initiated by Λc+→π+K¯ *N , and then the K¯* decays into K ¯π and K ¯N produce the Λ (1405 ) through a triangle loop containing K¯*N K ¯ which develops a singularity around 1890 MeV. This process is prohibited by the isospin symmetry, but the decay into this channel is enhanced by the contribution of the triangle diagram, which is sensitive to the mass of the internal particles. We find a narrow peak in the π0Σ0 invariant mass distribution, which originates from the Λ (1405 ) amplitude, but is tied to the mass differences between the charged and neutral K ¯ or N states. The observation of the unavoidable peak of the triangle singularity in the isospin-violating Λ (1405 ) production would provide further support for the hadronic molecular picture of the Λ (1405 ) and further information on the K ¯N interaction.

Genetic contribution to 'theory of mind' in adolescence.

PubMed

Warrier, Varun; Baron-Cohen, Simon

2018-02-22

Difficulties in 'theory of mind' (the ability to attribute mental states to oneself or others, and to make predictions about another's behaviour based on these attributions) have been observed in several psychiatric conditions. We investigate the genetic architecture of theory of mind in 4,577 13-year-olds who completed the Emotional Triangles Task (Triangles Task), a first-order test of theory of mind. We observe a small but significant female-advantage on the Triangles Task (Cohen's d = 0.19, P < 0.01), in keeping with previous work using other tests of theory of mind. Genome-wide association analyses did not identify any significant loci, and SNP heritability was non-significant. Polygenic scores for six psychiatric conditions (ADHD, anorexia, autism, bipolar disorder, depression, and schizophrenia), and empathy were not associated with scores on the Triangles Task. However, polygenic scores of cognitive aptitude, and cognitive empathy, a term synonymous with theory of mind and measured using the "Reading the Mind in the Eyes" Test, were significantly associated with scores on the Triangles Task at multiple P-value thresholds, suggesting shared genetics between different measures of theory of mind and cognition.

Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element

NASA Technical Reports Server (NTRS)

Stapleton, Scott E.; Waas, Anthony M.; Bednarcyk, Brett A.

2010-01-01

Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Exploiting symmetries in the modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Andersen, Carl M.; Tanner, John A.

1987-01-01

A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

Draft Report for the 1994 Travel Behavior Survey

DOT National Transportation Integrated Search

1995-01-01

The Triangle Travel Behavior Survey, an essential element in the regional study of transportation activity and travel patterns, was conducted under the auspices of the Triangle Transit Authority. This report documents the design, implementation, and ...

Three-dimensional earthquake analysis of roller-compacted concrete dams

NASA Astrophysics Data System (ADS)

Kartal, M. E.

2012-07-01

Ground motion effect on a roller-compacted concrete (RCC) dams in the earthquake zone should be taken into account for the most critical conditions. This study presents three-dimensional earthquake response of a RCC dam considering geometrical non-linearity. Besides, material and connection non-linearity are also taken into consideration in the time-history analyses. Bilinear and multilinear kinematic hardening material models are utilized in the materially non-linear analyses for concrete and foundation rock respectively. The contraction joints inside the dam blocks and dam-foundation-reservoir interaction are modeled by the contact elements. The hydrostatic and hydrodynamic pressures of the reservoir water are modeled with the fluid finite elements based on the Lagrangian approach. The gravity and hydrostatic pressure effects are employed as initial condition before the strong ground motion. In the earthquake analyses, viscous dampers are defined in the finite element model to represent infinite boundary conditions. According to numerical solutions, horizontal displacements increase under hydrodynamic pressure. Besides, those also increase in the materially non-linear analyses of the dam. In addition, while the principle stress components by the hydrodynamic pressure effect the reservoir water, those decrease in the materially non-linear time-history analyses.

Non-Linear Vibroisolation Pads Design, Numerical FEM Analysis and Introductory Experimental Investigations

NASA Astrophysics Data System (ADS)

Zielnica, J.; Ziółkowski, A.; Cempel, C.

2003-03-01

Design and theoretical and experimental investigation of vibroisolation pads with non-linear static and dynamic responses is the objective of the paper. The analytical investigations are based on non-linear finite element analysis where the load-deflection response is traced against the shape and material properties of the analysed model of the vibroisolation pad. A new model of vibroisolation pad of antisymmetrical type was designed and analysed by the finite element method based on the second-order theory (large displacements and strains) with the assumption of material's non-linearities (Mooney-Rivlin model). Stability loss phenomenon was used in the design of the vibroisolators, and it was proved that it would be possible to design a model of vibroisolator in the form of a continuous pad with non-linear static and dynamic response, typical to vibroisolation purposes. The materials used for the vibroisolator are those of rubber, elastomers, and similar ones. The results of theoretical investigations were examined experimentally. A series of models made of soft rubber were designed for the test purposes. The experimental investigations of the vibroisolation models, under static and dynamic loads, confirmed the results of the FEM analysis.

The Programming Language Python In Earth System Simulations

NASA Astrophysics Data System (ADS)

Gross, L.; Imranullah, A.; Mora, P.; Saez, E.; Smillie, J.; Wang, C.

2004-12-01

Mathematical models in earth sciences base on the solution of systems of coupled, non-linear, time-dependent partial differential equations (PDEs). The spatial and time-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Cortical bone fracture analysis using XFEM - case study.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2017-04-01

We aim to achieve an accurate simulation of human cortical bone fracture using the extended finite element method within a commercial finite element software abaqus. A two-dimensional unit cell model of cortical bone is built based on a microscopy image of the mid-diaphysis of tibia of a 70-year-old human male donor. Each phase of this model, an interstitial bone, a cement line, and an osteon, are considered linear elastic and isotropic with material properties obtained by nanoindentation, taken from literature. The effect of using fracture analysis methods (cohesive segment approach versus linear elastic fracture mechanics approach), finite element type, and boundary conditions (traction, displacement, and mixed) on cortical bone crack initiation and propagation are studied. In this study cohesive segment damage evolution for a traction separation law based on energy and displacement is used. In addition, effects of the increment size and mesh density on analysis results are investigated. We find that both cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can effectively simulate cortical bone fracture. Mesh density and simulation increment size can influence analysis results when employing either approach, and using finer mesh and/or smaller increment size does not always provide more accurate results. Both approaches provide close but not identical results, and crack propagation speed is found to be slower when using the cohesive segment approach. Also, using reduced integration elements along with the cohesive segment approach decreases crack propagation speed compared with using full integration elements. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.