Artificial intelligence approach to planning the robotic assembly of large tetrahedral truss structures

NASA Technical Reports Server (NTRS)

Homemdemello, Luiz S.

1992-01-01

An assembly planner for tetrahedral truss structures is presented. To overcome the difficulties due to the large number of parts, the planner exploits the simplicity and uniformity of the shapes of the parts and the regularity of their interconnection. The planning automation is based on the computational formalism known as production system. The global data base consists of a hexagonal grid representation of the truss structure. This representation captures the regularity of tetrahedral truss structures and their multiple hierarchies. It maps into quadratic grids and can be implemented in a computer by using a two-dimensional array data structure. By maintaining the multiple hierarchies explicitly in the model, the choice of a particular hierarchy is only made when needed, thus allowing a more informed decision. Furthermore, testing the preconditions of the production rules is simple because the patterned way in which the struts are interconnected is incorporated into the topology of the hexagonal grid. A directed graph representation of assembly sequences allows the use of both graph search and backtracking control strategies.

An open source software tool to assign the material properties of bone for ABAQUS finite element simulations.

PubMed

Pegg, Elise C; Gill, Harinderjit S

2016-09-06

A new software tool to assign the material properties of bone to an ABAQUS finite element mesh was created and compared with Bonemat, a similar tool originally designed to work with Ansys finite element models. Our software tool (py_bonemat_abaqus) was written in Python, which is the chosen scripting language for ABAQUS. The purpose of this study was to compare the software packages in terms of the material assignment calculation and processing speed. Three element types were compared (linear hexahedral (C3D8), linear tetrahedral (C3D4) and quadratic tetrahedral elements (C3D10)), both individually and as part of a mesh. Comparisons were made using a CT scan of a hemi-pelvis as a test case. A small difference, of -0.05kPa on average, was found between Bonemat version 3.1 (the current version) and our Python package. Errors were found in the previous release of Bonemat (version 3.0 downloaded from www.biomedtown.org) during calculation of the quadratic tetrahedron Jacobian, and conversion of the apparent density to modulus when integrating over the Young׳s modulus field. These issues caused up to 2GPa error in the modulus assignment. For these reasons, we recommend users upgrade to the most recent release of Bonemat. Processing speeds were assessed for the three different element types. Our Python package took significantly longer (110s on average) to perform the calculations compared with the Bonemat software (10s). Nevertheless, the workflow advantages of the package and added functionality makes 'py_bonemat_abaqus' a useful tool for ABAQUS users. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Cause and Cure - Deterioration in Accuracy of CFD Simulations With Use of High-Aspect-Ratio Triangular Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Chang, Chau-Lyan; Venkatachari, Balaji Shankar

2017-01-01

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD re-searchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions and also cause numerical instability. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where triangular/tetrahedral elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identities the reason behind the difficulties in use of such high-aspect ratio triangular/tetrahedral elements is presented here. As will be shown, it turns out that the degree of accuracy deterioration of gradient computation involving a triangular element is hinged on the value of its shape factor Gamma def = sq sin Alpha1 + sq sin Alpha2 + sq sin Alpha3, where Alpha1; Alpha2 and Alpha3 are the internal angles of the element. In fact, it is shown that the degree of accuracy deterioration increases monotonically as the value of Gamma decreases monotonically from its maximal value 9/4 (attained by an equilateral triangle only) to a value much less than 1 (associated with a highly obtuse triangle). By taking advantage of the fact that a high-aspect ratio triangle is not necessarily highly obtuse, and in fact it can have a shape factor whose value is close to the maximal value 9/4, a potential solution to avoid accuracy deterioration of gradient computation associated with a high-aspect ratio triangular grid is given. Also a brief discussion on the extension of the current mathematical framework to the

Fast calculation of the sensitivity matrix in magnetic induction tomography by tetrahedral edge finite elements and the reciprocity theorem.

PubMed

Hollaus, K; Magele, C; Merwa, R; Scharfetter, H

2004-02-01

Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.

Tetrahedrality and hydrogen bonds in water

NASA Astrophysics Data System (ADS)

Székely, Eszter; Varga, Imre K.; Baranyai, András

2016-06-01

We carried out extensive calculations of liquid water at different temperatures and pressures using the BK3 model suggested recently [P. T. Kiss and A. Baranyai, J. Chem. Phys. 138, 204507 (2013)]. In particular, we were interested in undercooled regions to observe the propensity of water to form tetrahedral coordination of closest neighbors around a central molecule. We compared the found tetrahedral order with the number of hydrogen bonds and with the partial pair correlation functions unfolded as distributions of the closest, the second closest, etc. neighbors. We found that contrary to the number of hydrogen bonds, tetrahedrality changes substantially with state variables. Not only the number of tetrahedral arrangements increases with lowering the pressure, the density, and the temperature but the domain size of connecting tetrahedral structures as well. The difference in tetrahedrality is very pronounced between the two sides of the Widom line and even more so between the low density amorphous (LDA) and high density amorphous (HDA) phases. We observed that in liquid water and in HDA, the 5th water molecule, contrary to ice and LDA, is positioned between the first and the second coordination shell. We found no convincing evidence of structural heterogeneity or regions referring to structural transition.

Tetrahedral and polyhedral mesh evaluation for cerebral hemodynamic simulation--a comparison.

PubMed

Spiegel, Martin; Redel, Thomas; Zhang, Y; Struffert, Tobias; Hornegger, Joachim; Grossman, Robert G; Doerfler, Arnd; Karmonik, Christof

2009-01-01

Computational fluid dynamic (CFD) based on patient-specific medical imaging data has found widespread use for visualizing and quantifying hemodynamics in cerebrovascular disease such as cerebral aneurysms or stenotic vessels. This paper focuses on optimizing mesh parameters for CFD simulation of cerebral aneurysms. Valid blood flow simulations strongly depend on the mesh quality. Meshes with a coarse spatial resolution may lead to an inaccurate flow pattern. Meshes with a large number of elements will result in unnecessarily high computation time which is undesirable should CFD be used for planning in the interventional setting. Most CFD simulations reported for these vascular pathologies have used tetrahedral meshes. We illustrate the use of polyhedral volume elements in comparison to tetrahedral meshing on two different geometries, a sidewall aneurysm of the internal carotid artery and a basilar bifurcation aneurysm. The spatial mesh resolution ranges between 5,119 and 228,118 volume elements. The evaluation of the different meshes was based on the wall shear stress previously identified as a one possible parameter for assessing aneurysm growth. Polyhedral meshes showed better accuracy, lower memory demand, shorter computational speed and faster convergence behavior (on average 369 iterations less).

Quadratic Solid⁻Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates.

PubMed

Chalal, Hocine; Abed-Meraim, Farid

2018-06-20

In the current contribution, prismatic and hexahedral quadratic solid⁻shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.

Cause and Cure - Deterioration in Accuracy of CFD Simulations with Use of High-Aspect-Ratio Triangular/Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Chang, Chau-Lyan; Venkatachari, Balaji Shankar

2017-01-01

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD researchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where simplex elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identifies the reason behind the difficulties in use of such high-aspect ratio simplex elements is formulated using two different approaches and presented here. Drawing insights from the analysis, a potential solution to avoid that pitfall is also provided as part of this work. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, how the gradient evaluation procedures of the CESE framework can be effectively used to produce accurate and stable results on such high-aspect ratio simplex meshes is also showcased.

Streaming simplification of tetrahedral meshes.

PubMed

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

2007-01-01

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

Parallel Anisotropic Tetrahedral Adaptation

NASA Technical Reports Server (NTRS)

Park, Michael A.; Darmofal, David L.

2008-01-01

An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domain-decomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.

Marine magnetotelluric inversion with an unstructured tetrahedral mesh

NASA Astrophysics Data System (ADS)

Usui, Yoshiya; Kasaya, Takafumi; Ogawa, Yasuo; Iwamoto, Hisanori

2018-05-01

The finite element method using an unstructured tetrahedral mesh is one of the most effective methods for the three-dimensional modelling of marine magnetotelluric data which are strongly affected by bathymetry, because it enables us to incorporate both small-scale and regional-scale bathymetry into a computational mesh with a practical number of elements. The authors applied a three-dimensional inversion scheme using mesh of this type to marine magnetotelluric problems for the first time and verified its applicability. Forward calculations for two bathymetry models demonstrated that the results obtained with an unstructured tetrahedral mesh are close to the reference solutions. To evaluate the forward calculation results, we developed a general TM-mode analytical formulation for a two-dimensional sinusoidal topography. Moreover, synthetic inversion test results confirmed that a three-dimensional inversion scheme with an unstructured tetrahedral mesh enables us to recover subseafloor resistivity structure properly even for a model including a land-sea boundary as well as seafloor undulations. The verified inversion scheme was subsequently applied to a set of marine magnetotelluric data observed around the Iheya North Knoll, the middle Okinawa Trough. Three-dimensional modelling using a mesh with precise bathymetry demonstrated that the data observed around the Iheya North Knoll are strongly affected by bathymetry, especially by the sea-depth differences between the depression of the trough and the shallow East China Sea. The estimated resistivity structure under the knoll is characterized by a conductive surface layer underlain by a resistive layer. The conductive layer implies permeable pelagic/hemi-pelagic sediments, which are consistent with a previous seismological study. Furthermore, the conductive layer has a resistive part immediately below the knoll, which is regarded as the consolidated magma intrusion that formed the knoll. Furthermore, at depth of 10 km

Computing Normal Shock-Isotropic Turbulence Interaction With Tetrahedral Meshes and the Space-Time CESE Method

NASA Astrophysics Data System (ADS)

Venkatachari, Balaji Shankar; Chang, Chau-Lyan

2016-11-01

The focus of this study is scale-resolving simulations of the canonical normal shock- isotropic turbulence interaction using unstructured tetrahedral meshes and the space-time conservation element solution element (CESE) method. Despite decades of development in unstructured mesh methods and its potential benefits of ease of mesh generation around complex geometries and mesh adaptation, direct numerical or large-eddy simulations of turbulent flows are predominantly carried out using structured hexahedral meshes. This is due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for unstructured meshes that can resolve multiple physical scales and flow discontinuities simultaneously. The CESE method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to accurately simulate turbulent flows using tetrahedral meshes. As part of the study, various regimes of the shock-turbulence interaction (wrinkled and broken shock regimes) will be investigated along with a study on how adaptive refinement of tetrahedral meshes benefits this problem. The research funding for this paper has been provided by Revolutionary Computational Aerosciences (RCA) subproject under the NASA Transformative Aeronautics Concepts Program (TACP).

Hoop/column and tetrahedral truss electromagnetic tests

NASA Technical Reports Server (NTRS)

Bailey, M. C.

1987-01-01

The distortion of antennas was measured with a metric camera system at discrete target locations on the surface. Given are surface distortion for hoop column reflector antennas, for tetrahedral truss reflector antennas, and distortion contours for the tetrahedral truss reflector. Radiation patterns at 2.27-GHz, 4.26-GHz, 7.73-GHz and 11.6-GHz are given for the hoop column antenna. Also given are radiation patterns at 4.26-GHz and 7.73-GHz for the tetrahedral truss antenna.

Neutrino Mixing and the Double Tetrahedral Group

NASA Astrophysics Data System (ADS)

Bentov, Yoni; Zee, A.

2013-11-01

In the spirit of a previous study of the tetrahedral group T ≃A4, we discuss a minimalist scheme to derive the neutrino mixing matrix using the double tetrahedral group T‧, the double cover of T. The new features are three distinct two-dimensional representations and complex Clebsch-Gordan coefficients, which can result in a geometric source of CP violation in the neutrino mass matrix. In an appendix, we derive explicitly the relevant group theory for the tetrahedral group T and its double cover T‧.

ADAPTIVE TETRAHEDRAL GRID REFINEMENT AND COARSENING IN MESSAGE-PASSING ENVIRONMENTS

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

Hallberg, J.; Stagg, A.

2000-10-01

A grid refinement and coarsening scheme has been developed for tetrahedral and triangular grid-based calculations in message-passing environments. The element adaption scheme is based on an edge bisection of elements marked for refinement by an appropriate error indicator. Hash-table/linked-list data structures are used to store nodal and element formation. The grid along inter-processor boundaries is refined and coarsened consistently with the update of these data structures via MPI calls. The parallel adaption scheme has been applied to the solution of a transient, three-dimensional, nonlinear, groundwater flow problem. Timings indicate efficiency of the grid refinement process relative to the flow solvermore » calculations.« less

Updates to Multi-Dimensional Flux Reconstruction for Hypersonic Simulations on Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2010-01-01

The quality of simulated hypersonic stagnation region heating with tetrahedral meshes is investigated by using an updated three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. An earlier implementation of this algorithm provided improved symmetry characteristics on tetrahedral grids compared to conventional reconstruction methods. The original formulation however displayed quantitative differences in heating and shear that were as large as 25% compared to a benchmark, structured-grid solution. The primary cause of this discrepancy is found to be an inherent inconsistency in the formulation of the flux limiter. The inconsistency is removed by employing a Green-Gauss formulation of primitive gradients at nodes to replace the previous Gram-Schmidt algorithm. Current results are now in good agreement with benchmark solutions for two challenge problems: (1) hypersonic flow over a three-dimensional cylindrical section with special attention to the uniformity of the solution in the spanwise direction and (2) hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problems provide a sensitive indicator for algorithmic effects on heating. Additional simulations on a sharp, double cone and the shuttle orbiter are then presented to demonstrate the capabilities of the new algorithm on more geometrically complex flows with tetrahedral grids. These results provide the first indication that pure tetrahedral elements utilizing the updated, three-dimensional, upwind reconstruction algorithm may be used for the

Preliminary design of a large tetrahedral truss/hexagonal heatshield panel aerobrake

NASA Technical Reports Server (NTRS)

Dorsey, John T.; Mikulas, Martin M., Jr.

1989-01-01

An aerobrake structural concept is introduced which consists of two primary components: (1) a lightweight erectable tetrahedral support truss; and (2) sandwich hexagonal heatshield panels which, when attached to the truss, form a continuous impermeable aerobraking surface. Generic finite element models and a general analysis procedure to design tetrahedral truss/hexagonal heatshield panel aerobrakes is developed, and values of the aerobrake design parameters which minimize mass and packaging volume for a 120-foot-diameter aerobrake are determined. Sensitivity of the aerobrake design to variations in design parameters is also assessed. The results show that a 120-foot-diameter aerobrake is viable using the concept presented (i.e., the aerobrake mass is less than or equal to 15 percent of the payload spacecraft mass). Minimizing the aerobrake mass (by increasing the number of rings in the support truss) however, leads to aerobrakes with the highest part count.

Cause and Cure-Deterioration in Accuracy of CFD Simulations with Use of High-Aspect-Ratio Triangular/Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Chang, Chau-Lyan; Venkatachari, Balaji

2017-01-01

In the multi-dimensional space-time conservation element and solution element16 (CESE) method, triangles and tetrahedral mesh elements turn out to be the most natural building blocks for 2D and 3D spatial grids, respectively. As such, the CESE method is naturally compatible with the simplest 2D and 3D unstructured grids and thus can be easily applied to solve problems with complex geometries. However, because (a) accurate solution of a high-Reynolds number flow field near a solid wall requires that the grid intervals along the direction normal to the wall be much finer than those in a direction parallel to the wall and, as such, the use of grid cells with extremely high aspect ratio (103 to 106) may become mandatory, and (b) unlike quadrilateral hexahedral grids, it is well-known that accuracy of gradient computations involving triangular tetrahedral grids tends to deteriorate rapidly as cell aspect ratio increases. As a result, the use of triangular tetrahedral grid cells near a solid wall has long been deemed impractical by CFD researchers. In view of (a) the critical role played by triangular tetrahedral grids in the CESE development, and (b) the importance of accurate resolution of high-Reynolds number flow field near a solid wall, as will be presented in the main paper, a comprehensive and rigorous mathematical framework that clearly identifies the reasons behind the accuracy deterioration as described above has been developed for the 2D case involving triangular cells. By avoiding the pitfalls identified by the 2D framework, and its 3D extension, it has been shown numerically.

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.

2015-01-01

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the

Evaluation of a Kinematically-Driven Finite Element Footstrike Model.

PubMed

Hannah, Iain; Harland, Andy; Price, Dan; Schlarb, Heiko; Lucas, Tim

2016-06-01

A dynamic finite element model of a shod running footstrike was developed and driven with 6 degree of freedom foot segment kinematics determined from a motion capture running trial. Quadratic tetrahedral elements were used to mesh the footwear components with material models determined from appropriate mechanical tests. Model outputs were compared with experimental high-speed video (HSV) footage, vertical ground reaction force (GRF), and center of pressure (COP) excursion to determine whether such an approach is appropriate for the development of athletic footwear. Although unquantified, good visual agreement to the HSV footage was observed but significant discrepancies were found between the model and experimental GRF and COP readings (9% and 61% of model readings outside of the mean experimental reading ± 2 standard deviations, respectively). Model output was also found to be highly sensitive to input kinematics with a 120% increase in maximum GRF observed when translating the force platform 2 mm vertically. While representing an alternative approach to existing dynamic finite element footstrike models, loading highly representative of an experimental trial was not found to be achievable when employing exclusively kinematic boundary conditions. This significantly limits the usefulness of employing such an approach in the footwear development process.

Video Vectorization via Tetrahedral Remeshing.

PubMed

Wang, Chuan; Zhu, Jie; Guo, Yanwen; Wang, Wenping

2017-02-09

We present a video vectorization method that generates a video in vector representation from an input video in raster representation. A vector-based video representation offers the benefits of vector graphics, such as compactness and scalability. The vector video we generate is represented by a simplified tetrahedral control mesh over the spatial-temporal video volume, with color attributes defined at the mesh vertices. We present novel techniques for simplification and subdivision of a tetrahedral mesh to achieve high simplification ratio while preserving features and ensuring color fidelity. From an input raster video, our method is capable of generating a compact video in vector representation that allows a faithful reconstruction with low reconstruction errors.

Finite-element design and optimization of a three-dimensional tetrahedral porous titanium scaffold for the reconstruction of mandibular defects.

PubMed

Luo, Danmei; Rong, Qiguo; Chen, Quan

2017-09-01

Reconstruction of segmental defects in the mandible remains a challenge for maxillofacial surgery. The use of porous scaffolds is a potential method for repairing these defects. Now, additive manufacturing techniques provide a solution for the fabrication of porous scaffolds with specific geometrical shapes and complex structures. The goal of this study was to design and optimize a three-dimensional tetrahedral titanium scaffold for the reconstruction of mandibular defects. With a fixed strut diameter of 0.45mm and a mean cell size of 2.2mm, a tetrahedral structural porous scaffold was designed for a simulated anatomical defect derived from computed tomography (CT) data of a human mandible. An optimization method based on the concept of uniform stress was performed on the initial scaffold to realize a minimal-weight design. Geometric and mechanical comparisons between the initial and optimized scaffold show that the optimized scaffold exhibits a larger porosity, 81.90%, as well as a more homogeneous stress distribution. These results demonstrate that tetrahedral structural titanium scaffolds are feasible structures for repairing mandibular defects, and that the proposed optimization scheme has the ability to produce superior scaffolds for mandibular reconstruction with better stability, higher porosity, and less weight. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Vibrational Spectra of Tetrahedral Fullerenes.

PubMed

Cheng; Li; Tang

1999-01-01

From the topological structures of the following classes of tetrahedral fullerenes-(1) Cn(h, h; -i, i), Cn(h, 0; -i, 2i), Cn(2h + i, -h + i; i, i), Cn(h - i, h + 2i; -i, 2i), and Cn(h, i; 0, i) for Td symmetry; (2) Cn(h, k; k, h), Cn(h, k; -h - k, k), and Cn(h, k; -h, h + k) for Th symmetry; (3) Cn(h, k; i, j) for T symmetry-we have obtained theoretically the formulas for the numbers of their IR and Raman active modes for all of the tetrahedral fullerenes through the decomposition of their nuclear motions into irreducible representations by means of group theory. Copyright 1999 Academic Press.

Boundary Recovery For Delaunay Tetrahedral Meshes Using Local Topological Transformations

PubMed Central

Ghadyani, Hamid; Sullivan, John; Wu, Ziji

2009-01-01

Numerous high-quality, volume mesh-generation systems exist. However, no strategy can address all geometry situations without some element qualities being compromised. Many 3D mesh generation algorithms are based on Delaunay tetrahedralization which frequently fails to preserve the input boundary surface topology. For biomedical applications, this surface preservation can be critical as they usually contain multiple material regions of interest coherently connected. In this paper we present an algorithm as a post-processing method that optimizes local regions of compromised element quality and recovers the original boundary surface facets (triangles) regardless of the original mesh generation strategy. The algorithm carves out a small sub-volume in the vicinity of the missing boundary facet or compromised element, creating a cavity. If the task is to recover a surface boundary facet, a natural exit hole in the cavity will be present. This hole is patched with the missing boundary surface face first followed by other patches to seal the cavity. If the task was to improve a compromised region, then the cavity is already sealed. Every triangular facet of the cavity shell is classified as an active face and can be connected to another shell node creating a tetrahedron. In the process the base of the tetrahedron is removed from the active face list and potentially 3 new active faces are created. This methodology is the underpinnings of our last resort method. Each active face can be viewed as the trunk of a tree. An exhaustive breath and depth search will identify all possible tetrahedral combinations to uniquely fill the cavity. We have streamlined this recursive process reducing the time complexity by orders of magnitude. The original surfaces boundaries (internal and external) are fully restored and the quality of compromised regions improved. PMID:20305743

Tetrahedral bonding in amorphous carbon

NASA Astrophysics Data System (ADS)

McKenzie, D. R.

1996-12-01

Electron configurations close to the tetrahedral 0034-4885/59/12/002/img1 hybridization are found in pure amorphous carbon at a concentration which depends on preparation conditions. Tetrahedral bonding at levels of approximately 80% is found in amorphous carbons formed from beams of carbon ions with energies in a `window' between 20 eV and approximately 500 eV. Suitable techniques for its formation include cathodic arc deposition, ion beam deposition and laser ablation. Similar material appears to be formed by pressure treatment of fullerene precursors and by displacement damage in diamond. Highly tetrahedral forms of amorphous carbon (ta-C) show electronic, optical and mechanical properties which approach those of diamond and are quite different from amorphous carbons with low 0034-4885/59/12/002/img1 content. Useful techniques for determining the 0034-4885/59/12/002/img1 content include electron energy loss spectroscopy, electron and neutron diffraction and Raman spectroscopy. Considerable progress has been made in the understanding of this material by simulating its structure in the computer with a range of techniques from empirical potentials to ab initio quantum mechanics. The structure shows departures from an idealized glassy state of diamond which would have a random tetrahedral network structure as used to describe amorphous silicon and germanium. A surprising feature of the structure simulated using ab initio methods is the presence of small rings containing three or four 0034-4885/59/12/002/img1 carbon atoms. The electronic and optical properties are strongly influenced by the residual of 0034-4885/59/12/002/img5 carbon. Applications to electronic devices are at an early stage with the demonstration of photoconductivity and some simple junction devices. Applications as a wear resistant coating are promising, since the theoretically predicted high values of elastic constants, comparable to but less than those of diamond, are achieved experimentally

Methods for prismatic/tetrahedral grid generation and adaptation

NASA Technical Reports Server (NTRS)

Kallinderis, Y.

1995-01-01

The present work involves generation of hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is a method for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A High Speed Civil Transport (HSCT) type of aircraft geometry is considered. The generated hybrid grid required only 170 K tetrahedra instead of an estimated two million had a tetrahedral mesh been used in the prisms region as well. A solution adaptive scheme for viscous computations on hybrid grids is also presented. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples 3-D, isotropic division of tetrahedra and 2-D, directional division of prisms.

Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1979-01-01

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

Quadratic Optimisation with One Quadratic Equality Constraint

DTIC Science & Technology

2010-06-01

This report presents a theoretical framework for minimising a quadratic objective function subject to a quadratic equality constraint. The first part of the report gives a detailed algorithm which computes the global minimiser without calling special nonlinear optimisation solvers. The second part of the report shows how the developed theory can be applied to solve the time of arrival geolocation problem.

Self-Replicating Quadratics

ERIC Educational Resources Information Center

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

A bicontinuous tetrahedral structure in a liquid-crystalline lipid

NASA Astrophysics Data System (ADS)

Longley, William; McIntosh, Thomas J.

1983-06-01

The structure of most lipid-water phases can be visualized as an ordered distribution of two liquid media, water and hydrocarbons, separated by a continuous surface covered by the polar groups of the lipid molecules1. In the cubic phases in particular, rod-like elements are linked into three-dimensional networks1,2. Two of these phases (space groups Ia3d and Pn3m) contain two such three-dimensional networks mutually inter-woven and unconnected. Under the constraints of energy minimization3, the interface between the components in certain of these `porous fluids' may well resemble one of the periodic minimal surface structures of the type described mathematically by Schwarz4,5. A structure of this sort has been proposed for the viscous isotropic (cubic) form of glycerol monooleate (GMO) by Larsson et al.6 who suggested that the X-ray diagrams of Lindblom et al.7 indicated a body-centred crystal structure in which lipid bilayers might be arranged as in Schwarz's octahedral surface4. We have now found that at high water contents, a primitive cubic lattice better fits the X-ray evidence with the material in the crystal arranged in a tetrahedral way. The lipid appears to form a single bilayer, continuous in three dimensions, separating two continuous interlinked networks of water. Each of the water networks has the symmetry of the diamond crystal structure and the bilayer lies in the space between them following a surface resembling Schwarz's tetrahedral surface4.

Quadratic Damping

ERIC Educational Resources Information Center

Fay, Temple H.

2012-01-01

Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

Tetrahedrality and structural order for hydrophobic interactions in a coarse-grained water model

NASA Astrophysics Data System (ADS)

Chaimovich, Aviel; Shell, M. Scott

2014-02-01

The hydrophobic interaction manifests two separate regimes in terms of size: Small nonpolar bodies exhibit a weak oscillatory force (versus distance) while large nonpolar surfaces exhibit a strong monotonic one. This crossover in hydrophobic behavior is typically explained in terms of water's tetrahedral structure: Its tetrahedrality is enhanced near small solutes and diminished near large planar ones. Here, we demonstrate that water's tetrahedral correlations signal this switch even in a highly simplified, isotropic, "core-softened" water model. For this task, we introduce measures of tetrahedrality based on the angular distribution of water's nearest neighbors. On a quantitative basis, the coarse-grained model of course is only approximate: (1) While greater than simple Lennard-Jones liquids, its bulk tetrahedrality remains lower than that of fully atomic models; and (2) the decay length of the large-scale hydrophobic interaction is less than has been found in experiments. Even so, the qualitative behavior of the model is surprisingly rich and exhibits numerous waterlike hydrophobic behaviors, despite its simplicity. We offer several arguments for the manner in which it should be able to (at least partially) reproduce tetrahedral correlations underlying these effects.

Tetrahedrality and structural order for hydrophobic interactions in a coarse-grained water model.

PubMed

Chaimovich, Aviel; Shell, M Scott

2014-02-01

The hydrophobic interaction manifests two separate regimes in terms of size: Small nonpolar bodies exhibit a weak oscillatory force (versus distance) while large nonpolar surfaces exhibit a strong monotonic one. This crossover in hydrophobic behavior is typically explained in terms of water's tetrahedral structure: Its tetrahedrality is enhanced near small solutes and diminished near large planar ones. Here, we demonstrate that water's tetrahedral correlations signal this switch even in a highly simplified, isotropic, "core-softened" water model. For this task, we introduce measures of tetrahedrality based on the angular distribution of water's nearest neighbors. On a quantitative basis, the coarse-grained model of course is only approximate: (1) While greater than simple Lennard-Jones liquids, its bulk tetrahedrality remains lower than that of fully atomic models; and (2) the decay length of the large-scale hydrophobic interaction is less than has been found in experiments. Even so, the qualitative behavior of the model is surprisingly rich and exhibits numerous waterlike hydrophobic behaviors, despite its simplicity. We offer several arguments for the manner in which it should be able to (at least partially) reproduce tetrahedral correlations underlying these effects.

Quadratic soliton self-reflection at a quadratically nonlinear interface

NASA Astrophysics Data System (ADS)

Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

2003-11-01

The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

Modulation of chondrocyte motility by tetrahedral DNA nanostructures.

PubMed

Shi, Sirong; Lin, Shiyu; Shao, Xiaoru; Li, Qianshun; Tao, Zhang; Lin, Yunfeng

2017-10-01

Contemporarily, a highly increasing attention was paid to nanoconstructs, particularly DNA nanostructures possessing precise organization, functional manipulation, biocompatibility and biodegradability. Amongst these DNA nanomaterials, tetrahedral DNA nanostructures (TDNs) are a significantly ideal bionanomaterials with focusing on the property that can be internalized into cytoplasm in the absence of transfection. Therefore, the focus of this study was on investigating the influence of TDNs on the chondrocytes locomotion. Tetrahedral DNA nanostructures was confirmed by 6% polyacrylamide gel electrophoresis (PAGE) and dynamic light scattering (DLS). Subsequently, the effect of TDNs on chondrocyte locomotion was investigated by real-time cell analysis (RTCA) and wound healing assay. The variation of relevant genes and proteins was detected by quantitative polymerase chain reaction (qPCR), western blotting and immunofluorescence respectively. We demonstrated that tetrahedral DNA nanostructures have positive influence on chondrocytes locomotion and promoted the expression of RhoA, ROCK2 and vinculin. Additionally, upon exposure to TDNs with the concentration of 250 nmol L -1 , the chondrocytes were showed the highest motility via both RTCA and wound healing assay. Meanwhile, the mRNA and protein expression of RhoA, ROCK2 and vinculin were also significantly enhanced with the same concentration. It can be concluded that the TDNs with the optimal concentration of 250 nmol L -1 could extremely promoted the chondrocytes locomotion through facilitating the expression of RhoA, ROCK2 and vinculin. These results seemed to reveal that this special three-dimensional DNA tetrahedral nanostructures may be applied to cartilage repair and treatment in the future. © 2017 John Wiley & Sons Ltd.

The Space-Time Conservative Schemes for Large-Scale, Time-Accurate Flow Simulations with Tetrahedral Meshes

NASA Technical Reports Server (NTRS)

Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung

2016-01-01

Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity elements have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

Structural stiffness, strength and dynamic characteristics of large tetrahedral space truss structures

NASA Technical Reports Server (NTRS)

Mikulas, M. M., Jr.; Bush, H. G.; Card, M. F.

1977-01-01

Physical characteristics of large skeletal frameworks for space applications are investigated by analyzing one concept: the tetrahedral truss, which is idealized as a sandwich plate with isotropic faces. Appropriate analytical relations are presented in terms of the truss column element properties which for calculations were taken as slender graphite/epoxy tubes. Column loads, resulting from gravity gradient control and orbital transfer, are found to be small for the class structure investigated. Fundamental frequencies of large truss structures are shown to be an order of magnitude lower than large earth based structures. Permissible loads are shown to result in small lateral deflections of the truss due to low-strain at Euler buckling of the slender graphite/epoxy truss column elements. Lateral thermal deflections are found to be a fraction of the truss depth using graphite/epoxy columns.

Quantum superintegrable system with a novel chain structure of quadratic algebras

NASA Astrophysics Data System (ADS)

Liao, Yidong; Marquette, Ian; Zhang, Yao-Zhong

2018-06-01

We analyse the n-dimensional superintegrable Kepler–Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure and obtain the algebra relations satisfied by them and the corresponding Casimir operators. These quadratic sub-algebras are realized in terms of a chain of deformed oscillators with factorized structure functions. We construct the finite-dimensional unitary representations of the deformed oscillators, and give an algebraic derivation of the energy spectrum of the superintegrable system.

Implementation of tetrahedral-mesh geometry in Monte Carlo radiation transport code PHITS

NASA Astrophysics Data System (ADS)

Furuta, Takuya; Sato, Tatsuhiko; Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Brown, Justin L.; Bolch, Wesley E.

2017-06-01

A new function to treat tetrahedral-mesh geometry was implemented in the particle and heavy ion transport code systems. To accelerate the computational speed in the transport process, an original algorithm was introduced to initially prepare decomposition maps for the container box of the tetrahedral-mesh geometry. The computational performance was tested by conducting radiation transport simulations of 100 MeV protons and 1 MeV photons in a water phantom represented by tetrahedral mesh. The simulation was repeated with varying number of meshes and the required computational times were then compared with those of the conventional voxel representation. Our results show that the computational costs for each boundary crossing of the region mesh are essentially equivalent for both representations. This study suggests that the tetrahedral-mesh representation offers not only a flexible description of the transport geometry but also improvement of computational efficiency for the radiation transport. Due to the adaptability of tetrahedrons in both size and shape, dosimetrically equivalent objects can be represented by tetrahedrons with a much fewer number of meshes as compared its voxelized representation. Our study additionally included dosimetric calculations using a computational human phantom. A significant acceleration of the computational speed, about 4 times, was confirmed by the adoption of a tetrahedral mesh over the traditional voxel mesh geometry.

Implementation of tetrahedral-mesh geometry in Monte Carlo radiation transport code PHITS.

PubMed

Furuta, Takuya; Sato, Tatsuhiko; Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Brown, Justin L; Bolch, Wesley E

2017-06-21

A new function to treat tetrahedral-mesh geometry was implemented in the particle and heavy ion transport code systems. To accelerate the computational speed in the transport process, an original algorithm was introduced to initially prepare decomposition maps for the container box of the tetrahedral-mesh geometry. The computational performance was tested by conducting radiation transport simulations of 100 MeV protons and 1 MeV photons in a water phantom represented by tetrahedral mesh. The simulation was repeated with varying number of meshes and the required computational times were then compared with those of the conventional voxel representation. Our results show that the computational costs for each boundary crossing of the region mesh are essentially equivalent for both representations. This study suggests that the tetrahedral-mesh representation offers not only a flexible description of the transport geometry but also improvement of computational efficiency for the radiation transport. Due to the adaptability of tetrahedrons in both size and shape, dosimetrically equivalent objects can be represented by tetrahedrons with a much fewer number of meshes as compared its voxelized representation. Our study additionally included dosimetric calculations using a computational human phantom. A significant acceleration of the computational speed, about 4 times, was confirmed by the adoption of a tetrahedral mesh over the traditional voxel mesh geometry.

Quadratic RK shooting solution for a environmental parameter prediction boundary value problem

NASA Astrophysics Data System (ADS)

Famelis, Ioannis Th.; Tsitouras, Ch.

2014-10-01

Using tools of Information Geometry, the minimum distance between two elements of a statistical manifold is defined by the corresponding geodesic, e.g. the minimum length curve that connects them. Such a curve, where the probability distribution functions in the case of our meteorological data are two parameter Weibull distributions, satisfies a 2nd order Boundary Value (BV) system. We study the numerical treatment of the resulting special quadratic form system using Shooting method. We compare the solutions of the problem when we employ a classical Singly Diagonally Implicit Runge Kutta (SDIRK) 4(3) pair of methods and a quadratic SDIRK 5(3) pair . Both pairs have the same computational costs whereas the second one attains higher order as it is specially constructed for quadratic problems.

Numerical solution of quadratic matrix equations for free vibration analysis of structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

A review of defects and disorder in multinary tetrahedrally bonded semiconductors [Defects and disorder in multinary tetrahedrally bonded semiconductors studied by experiment and theory

DOE PAGES

Baranowski, Lauryn L.; Zawadzki, Pawel; Lany, Stephan; ...

2016-11-10

Defects are critical to understanding the electronic properties of semiconducting compounds, for applications such as light-emitting diodes, transistors, photovoltaics, and thermoelectrics. In this review, we describe our work investigating defects in tetrahedrally bonded, multinary semiconductors, and discuss the place of our research within the context of publications by other groups. We applied experimental and theory techniques to understand point defects, structural disorder, and extended antisite defects in one semiconductor of interest for photovoltaic applications, Cu 2SnS 3. We contrast our findings on Cu 2SnS 3 with other chemically related Cu-Sn-S compounds, as well as structurally related compounds such as Cumore » 2ZnSnS 4 and Cu(In,Ga)Se 2. We find that evaluation of point defects alone is not sufficient to understand defect behavior in multinary tetrahedrally bonded semiconductors. In the case of Cu 2SnS 3 and Cu 2ZnSnS 4, structural disorder and entropy-driven cation clustering can result in nanoscale compositional inhomogeneities which detrimentally impact the electronic transport. Therefore, it is not sufficient to assess only the point defect behavior of new multinary tetrahedrally bonded compounds; effects such as structural disorder and extended antisite defects must also be considered. Altogether, this review provides a framework for evaluating tetrahedrally bonded semiconducting compounds with respect to their defect behavior for photovoltaic and other applications, and suggests new materials that may not be as prone to such imperfections.« less

A review of defects and disorder in multinary tetrahedrally bonded semiconductors [Defects and disorder in multinary tetrahedrally bonded semiconductors studied by experiment and theory

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

Baranowski, Lauryn L.; Zawadzki, Pawel; Lany, Stephan

Defects are critical to understanding the electronic properties of semiconducting compounds, for applications such as light-emitting diodes, transistors, photovoltaics, and thermoelectrics. In this review, we describe our work investigating defects in tetrahedrally bonded, multinary semiconductors, and discuss the place of our research within the context of publications by other groups. We applied experimental and theory techniques to understand point defects, structural disorder, and extended antisite defects in one semiconductor of interest for photovoltaic applications, Cu 2SnS 3. We contrast our findings on Cu 2SnS 3 with other chemically related Cu-Sn-S compounds, as well as structurally related compounds such as Cumore » 2ZnSnS 4 and Cu(In,Ga)Se 2. We find that evaluation of point defects alone is not sufficient to understand defect behavior in multinary tetrahedrally bonded semiconductors. In the case of Cu 2SnS 3 and Cu 2ZnSnS 4, structural disorder and entropy-driven cation clustering can result in nanoscale compositional inhomogeneities which detrimentally impact the electronic transport. Therefore, it is not sufficient to assess only the point defect behavior of new multinary tetrahedrally bonded compounds; effects such as structural disorder and extended antisite defects must also be considered. Altogether, this review provides a framework for evaluating tetrahedrally bonded semiconducting compounds with respect to their defect behavior for photovoltaic and other applications, and suggests new materials that may not be as prone to such imperfections.« less

Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

NASA Astrophysics Data System (ADS)

Bick, Christian; Sebek, Michael; Kiss, István Z.

2017-10-01

We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.

Quadrat Data for Fermilab Prairie Plant Survey

Science.gov Websites

Quadrat Data 2012 Quadrat Data 2013 Quadrat Data None taken by volunteers in 2014 due to weather problems . 2015 Quadrat Data 2016 Quadrat Data None taken by volunteers in 2017 due to weather and other problems

Tetrahedral 4 α and 12C+α cluster structures in 16O

NASA Astrophysics Data System (ADS)

Kanada-En'yo, Yoshiko

2017-09-01

I have investigated structures of the ground and excited states of 16O with the method of variation after spin-parity projection in the antisymmetrized molecular dynamics model combined with the generator coordinate method of 12C+α cluster. The calculation reasonably reproduces the experimental energy spectra; E 2 , E 3 , E 4 , and I S 1 transitions; and α -decay properties. The formation of 4 α clusters has been confirmed from nucleon degrees of freedom in the AMD model without assuming the existence of any clusters. They form "tetrahedral" 4 α - and 12C+α cluster structures. The 12C+α structure constructs the Kπ=0+ band consisting of the 02+, 21+, and 41+ states and the Kπ=0- band of the 12-, 32-, and 51- states. The 01+, 31-, and 42+ states are assigned to the ground band constructed from the tetrahedral 4 α structure. The 01+ and 31- are approximately interpreted as Td band members with the ideal tetrahedral configuration. The ground-state 4 α correlation plays an important role in the enhancement of the E 3 transition strength to the 31-. The 42+ state is not the ideal Td member but constructed from a distorted tetrahedral 4 α structure. Moreover, significant state mixing of the tetrahedral 4 α and 12C+α cluster structures occurs between 41+ and 42+ states, indicating that the Td configuration of 4 α is rather fragile at Jπ=4+ .

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

Self-assembly of a tetrahedral 58-nuclear barium vanadium oxide cluster.

PubMed

Kastner, Katharina; Puscher, Bianka; Streb, Carsten

2013-01-07

We report the synthesis and characterization of a molecular barium vanadium oxide cluster featuring high nuclearity and high symmetry. The tetrameric, 2.3 nm cluster H(5)[Ba(10)(NMP)(14)(H(2)O)(8)[V(12)O(33)](4)Br] is based on a bromide-centred, octahedral barium scaffold which is capped by four previously unknown [V(12)O(33)](6-) clusters in a tetrahedral fashion. The compound represents the largest polyoxovanadate-based heterometallic cluster known to date. The cluster is formed in organic solution and it is suggested that the bulky N-methyl-2-pyrrolidone (NMP) solvent ligands allow the isolation of this giant molecule and prevent further condensation to a solid-state metal oxide. The cluster is fully characterized using single-crystal XRD, elemental analysis, ESI mass spectrometry and other spectroscopic techniques.

Single-laser, one beam, tetrahedral magneto-optical trap.

PubMed

Vangeleyn, Matthieu; Griffin, Paul F; Riis, Erling; Arnold, Aidan S

2009-08-03

We have realized a 4-beam pyramidal magneto-optical trap ideally suited for future microfabrication. Three mirrors split and steer a single incoming beam into a tripod of reflected beams, allowing trapping in the four-beam overlap volume. We discuss the influence of mirror angle on cooling and trapping, finding optimum efficiency in a tetrahedral configuration. We demonstrate the technique using an ex-vacuo mirror system to illustrate the previously inaccessible supra-plane pyramid MOT configuration. Unlike standard pyramidal MOTs both the pyramid apex and its mirror angle are non-critical and our MOT offers improved molasses free from atomic shadows in the laser beams. The MOT scheme naturally extends to a 2-beam refractive version with high optical access. For quantum gas experiments, the mirror system could also be used for a stable 3D tetrahedral optical lattice.

Why Is the Tetrahedral Bond Angle 109 Degrees? The Tetrahedron-in-a-Cube

ERIC Educational Resources Information Center

Lim, Kieran F.

2012-01-01

The common question of why the tetrahedral angle is 109.471 degrees can be answered using a tetrahedron-in-a-cube, along with some Year 10 level mathematics. The tetrahedron-in-a-cube can also be used to demonstrate the non-polarity of tetrahedral molecules, the relationship between different types of lattice structures, and to demonstrate that…

The Kontsevich tetrahedral flow revisited

NASA Astrophysics Data System (ADS)

Bouisaghouane, A.; Buring, R.; Kiselev, A.

2017-09-01

We prove that the Kontsevich tetrahedral flow P ˙ =Qa:b(P) , the right-hand side of which is a linear combination of two differential monomials of degree four in a bi-vector P on an affine real Poisson manifold Nn, does infinitesimally preserve the space of Poisson bi-vectors on Nn if and only if the two monomials in Qa:b(P) are balanced by the ratio a : b = 1 : 6. The proof is explicit; it is written in the language of Kontsevich graphs.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation

PubMed Central

Gao, Zhanheng; Yu, Zeyun; Holst, Michael

2012-01-01

Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522

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

DNA tetrahedral scaffolds-based platform for the construction of electrochemiluminescence biosensor.

PubMed

Feng, Qiu-Mei; Zhou, Zhen; Li, Mei-Xing; Zhao, Wei; Xu, Jing-Juan; Chen, Hong-Yuan

2017-04-15

Proximal metallic nanoparticles (NPs) could quench the electrochemiluminescence (ECL) emission of semiconductor quantum dots (QDs) due to Förster energy transfer (FRET), but at a certain distance, the coupling of light-emission with surface plasmon resonance (SPR) result in enhanced ECL. Thus, the modification strategies and distances control between QDs and metallic NPs are critical for the ECL intensity of QDs. In this strategy, a SPR enhanced ECL sensor based on DNA tetrahedral scaffolds modified platform was reported for the detection of telomerase activity. Due to the rigid three-dimensional structure, DNA tetrahedral scaffolds grafting on the electrode surface could accurately modulate the distance between CdS QDs and luminol labelled gold nanoparticles (L-Au NPs), meanwhile provide an enhanced spatial dimension and accessibility for the assembly of multiple L-Au NPs. The ECL intensities of both CdS QDs (-1.25V vs. SCE) and luminol (+0.33V vs. SCE) gradually increased along with the formation of multiple L-Au NPs at the vertex of DNA tetrahedral scaffolds induced by telomerase, bringing in a dual-potential ECL analysis. The proposed method showed high sensitivity for the identification of telomerase and was successfully applied for the differentiation of cancer cells from normal cells. This work suggests that DNA tetrahedral scaffolds could serve as an excellent choice for the construction of SPR-ECL system. Copyright © 2016 Elsevier B.V. All rights reserved.

Quadratic spline subroutine package

USGS Publications Warehouse

Rasmussen, Lowell A.

1982-01-01

A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)

LiBSi2: a tetrahedral semiconductor framework from boron and silicon atoms bearing lithium atoms in the channels.

PubMed

Zeilinger, Michael; van Wüllen, Leo; Benson, Daryn; Kranak, Verina F; Konar, Sumit; Fässler, Thomas F; Häussermann, Ulrich

2013-06-03

Silicon swallows up boron: The novel open tetrahedral framework structure (OTF) of the Zintl phase LiBSi2 was made by applying high pressure to a mixture of LiB and elemental silicon. The compound represents a new topology in the B-Si net (called tum), which hosts Li atoms in the channels (see picture). LiBSi2 is the first example where B and Si atoms form an ordered common framework structure with B engaged exclusively in heteronuclear B-Si contacts.

Coarse-grained theory of a realistic tetrahedral liquid model

NASA Astrophysics Data System (ADS)

Procaccia, I.; Regev, I.

2012-02-01

Tetrahedral liquids such as water and silica-melt show unusual thermodynamic behavior such as a density maximum and an increase in specific heat when cooled to low temperatures. Previous work had shown that Monte Carlo and mean-field solutions of a lattice model can exhibit these anomalous properties with or without a phase transition, depending on the values of the different terms in the Hamiltonian. Here we use a somewhat different approach, where we start from a very popular empirical model of tetrahedral liquids —the Stillinger-Weber model— and construct a coarse-grained theory which directly quantifies the local structure of the liquid as a function of volume and temperature. We compare the theory to molecular-dynamics simulations and show that the theory can rationalize the simulation results and the anomalous behavior.

Simulation of Stagnation Region Heating in Hypersonic Flow on Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2007-01-01

Hypersonic flow simulations using the node based, unstructured grid code FUN3D are presented. Applications include simple (cylinder) and complex (towed ballute) configurations. Emphasis throughout is on computation of stagnation region heating in hypersonic flow on tetrahedral grids. Hypersonic flow over a cylinder provides a simple test problem for exposing any flaws in a simulation algorithm with regard to its ability to compute accurate heating on such grids. Such flaws predominantly derive from the quality of the captured shock. The importance of pure tetrahedral formulations are discussed. Algorithm adjustments for the baseline Roe / Symmetric, Total-Variation-Diminishing (STVD) formulation to deal with simulation accuracy are presented. Formulations of surface normal gradients to compute heating and diffusion to the surface as needed for a radiative equilibrium wall boundary condition and finite catalytic wall boundary in the node-based unstructured environment are developed. A satisfactory resolution of the heating problem on tetrahedral grids is not realized here; however, a definition of a test problem, and discussion of observed algorithm behaviors to date are presented in order to promote further research on this important problem.

The Effect of Titanium Tetrahedral Coordination of Silica-Titania Catalyst on the Physical Properties of Biodiesel

NASA Astrophysics Data System (ADS)

Nizar, U. K.; Hidayatul, J.; Sundari, R.; Bahrizal, B.; Amran, A.; Putra, A.; Latisma DJ, L.; Dewata, I.

2018-04-01

This study investigates the correlation of the number of titanium tetrahedral coordination and biodiesel production. The solid-state method has been used to synthesis of silica-titania catalyst for biodiesel production, which the precursors, i.e. silica and titania commercials were heated in the temperature range of 450 - 550°C. The characterization of the prepared silica-titania has been studied by FTIR and DR UV-Vis in order to identify and calculate the presence of titanium tetrahedral coordination in silica-titania catalyst. A very small peak at around 950 cm-1 indicated the presence of titanium tetrahedral coordination through Si–O–Ti bonds. Deconvolution of DR UV-Vis spectra showed the coordination of titanium in silica-titania is more octahedral. However, the number of titanium tetrahedral coordination of the prepared silica-titania is found higher than that of TiO2 commercial. The increasing of titanium tetrahedral fraction in silica-titania affects the physical properties of biodiesel in terms of boiling point, viscosity and density, which is produced by the reaction of methanol and palm oil.

Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1980-01-01

Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.

RELATIONSHIP BETWEEN RIGIDITY OF EXTERNAL FIXATOR AND NUMBER OF PINS: COMPUTER ANALYSIS USING FINITE ELEMENTS

PubMed Central

Sternick, Marcelo Back; Dallacosta, Darlan; Bento, Daniela Águida; do Reis, Marcelo Lemos

2015-01-01

Objective: To analyze the rigidity of a platform-type external fixator assembly, according to different numbers of pins on each clamp. Methods: Computer simulation on a large-sized Cromus dynamic external fixator (Baumer SA) was performed using a finite element method, in accordance with the standard ASTM F1541. The models were generated with approximately 450,000 quadratic tetrahedral elements. Assemblies with two, three and four Schanz pins of 5.5 mm in diameter in each clamp were compared. Every model was subjected to a maximum force of 200 N, divided into 10 sub-steps. For the components, the behavior of the material was assumed to be linear, elastic, isotropic and homogeneous. For each model, the rigidity of the assembly and the Von Mises stress distribution were evaluated. Results: The rigidity of the system was 307.6 N/mm for two pins, 369.0 N/mm for three and 437.9 N/mm for four. Conclusion: The results showed that four Schanz pins in each clamp promoted rigidity that was 19% greater than in the configuration with three pins and 42% greater than with two pins. Higher tension occurred in configurations with fewer pins. In the models analyzed, the maximum tension occurred on the surface of the pin, close to the fixation area. PMID:27047879

An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA

NASA Technical Reports Server (NTRS)

Djomehri, M. Jahed; Erickson, Larry L.

1994-01-01

A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.

Hinge specification for a square-faceted tetrahedral truss

NASA Technical Reports Server (NTRS)

Adams, L. R.

1984-01-01

A square-faceted tetrahedral truss is geometrically analyzed. Expressions are developed for single degree of freedom hinges which allow packaging of the structure into a configuration in which all members are parallel and closely packed in a square pattern. Deployment is sequential, thus providing control over the structure during deployment.

New approach based on tetrahedral-mesh geometry for accurate 4D Monte Carlo patient-dose calculation

NASA Astrophysics Data System (ADS)

Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Kim, Seonghoon; Sohn, Jason W.

2015-02-01

In the present study, to achieve accurate 4D Monte Carlo dose calculation in radiation therapy, we devised a new approach that combines (1) modeling of the patient body using tetrahedral-mesh geometry based on the patient’s 4D CT data, (2) continuous movement/deformation of the tetrahedral patient model by interpolation of deformation vector fields acquired through deformable image registration, and (3) direct transportation of radiation particles during the movement and deformation of the tetrahedral patient model. The results of our feasibility study show that it is certainly possible to construct 4D patient models (= phantoms) with sufficient accuracy using the tetrahedral-mesh geometry and to directly transport radiation particles during continuous movement and deformation of the tetrahedral patient model. This new approach not only produces more accurate dose distribution in the patient but also replaces the current practice of using multiple 3D voxel phantoms and combining multiple dose distributions after Monte Carlo simulations. For routine clinical application of our new approach, the use of fast automatic segmentation algorithms is a must. In order to achieve, simultaneously, both dose accuracy and computation speed, the number of tetrahedrons for the lungs should be optimized. Although the current computation speed of our new 4D Monte Carlo simulation approach is slow (i.e. ~40 times slower than that of the conventional dose accumulation approach), this problem is resolvable by developing, in Geant4, a dedicated navigation class optimized for particle transportation in tetrahedral-mesh geometry.

Tetrahedral Models of Learning: Application to College Reading.

ERIC Educational Resources Information Center

Nist, Sherrie L.

J. D. Bransford's tetrahedral model of learning considers four variables: (1) learning activities, (2) characteristics of the learner, (3) criterial tasks, and (4) the nature of the materials. Bransford's model provides a research-based theoretical framework that can be used to teach, model, and have students apply a variety of study strategies to…

The Factorability of Quadratics: Motivation for More Techniques

ERIC Educational Resources Information Center

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

2005-01-01

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

Self-assembled DNA tetrahedral optofluidic lasers with precise and tunable gain control.

PubMed

Chen, Qiushu; Liu, Huajie; Lee, Wonsuk; Sun, Yuze; Zhu, Dan; Pei, Hao; Fan, Chunhai; Fan, Xudong

2013-09-07

We have applied self-assembled DNA tetrahedral nanostructures for the precise and tunable control of the gain in an optofluidic fluorescence resonance energy transfer (FRET) laser. By adjusting the ratio of the donor and the acceptor attached to the tetrahedral vertices, 3.8 times reduction in the lasing threshold and 28-fold enhancement in the lasing efficiency were demonstrated. This work takes advantage of the self-recognition and self-assembly capabilities of biomolecules with well-defined structures and addressability, enabling nano-engineering of the laser down to the molecular level.

Practical implementation of tetrahedral mesh reconstruction in emission tomography

PubMed Central

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

2014-01-01

This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio

Practical implementation of tetrahedral mesh reconstruction in emission tomography

NASA Astrophysics Data System (ADS)

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

2013-05-01

This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio

Students' Understanding of Quadratic Equations

ERIC Educational Resources Information Center

López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

2016-01-01

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

Tetrahedral hydrocarbon nanoparticles in space: X-ray spectra

NASA Astrophysics Data System (ADS)

Bilalbegović, G.; Maksimović, A.; Valencic, L. A.

2018-06-01

It has been proposed, or confirmed, that diamond nanoparticles exist in various environments in space: close to active galactic nuclei, in the vicinity of supernovae and pulsars, in the interior of several planets in the Solar system, in carbon planets, and other exoplanets, carbon-rich stars, meteorites, in X-ray active Herbig Ae/Be stars, and in the interstellar medium. Using density functional theory methods, we calculate the carbon K-edge X-ray absorption spectrum of two large tetrahedral nanodiamonds: C26H32 and C51H52. We also study and test our methods on the astrophysical molecule CH4, the smallest C-H tetrahedral structure. A possible detection of nanodiamonds from X-ray spectra by future telescopes, such as the project Arcus, is proposed. Simulated spectra of the diffuse interstellar medium using Cyg X-2 as a source show that nanodiamonds studied in this work can be detected by Arcus, a high-resolution X-ray spectrometer mission selected by NASA for a Phase A concept study.

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

NASA Technical Reports Server (NTRS)

Frink, Neal T.; Pirzadeh, Shahyar Z.

1998-01-01

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Multi-Dimensional, Inviscid Flux Reconstruction for Simulation of Hypersonic Heating on Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2009-01-01

The quality of simulated hypersonic stagnation region heating on tetrahedral meshes is investigated by using a three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. Two test problems are investigated: hypersonic flow over a three-dimensional cylinder with special attention to the uniformity of the solution in the spanwise direction and hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problem provides a sensitive test for algorithmic effects on heating. This investigation is believed to be unique in its focus on three-dimensional, rotated upwind schemes for the simulation of hypersonic heating on tetrahedral grids. This study attempts to fill the void left by the inability of conventional (quasi-one-dimensional) approaches to accurately simulate heating in a tetrahedral grid system. Results show significant improvement in spanwise uniformity of heating with some penalty of ringing at the captured shock. Issues with accuracy near the peak shear location are identified and require further study.

Exact solutions to quadratic gravity

NASA Astrophysics Data System (ADS)

Pravda, V.; Pravdová, A.; Podolský, J.; Švarc, R.

2017-04-01

Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime. Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one nonlinear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

Orthogonality preserving infinite dimensional quadratic stochastic operators

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

Akın, Hasan; Mukhamedov, Farrukh

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

Robust linear quadratic designs with respect to parameter uncertainty

NASA Technical Reports Server (NTRS)

Douglas, Joel; Athans, Michael

1992-01-01

The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.

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.

On the influence of tetrahedral covalent-hybridization on electronic band structure of topological insulators from first principles

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

Zhang, X. M.; Xu, G. Z.; Liu, E. K.

Based on first-principles calculations, we investigate the influence of tetrahedral covalent-hybridization between main-group and transition-metal atoms on the topological band structures of binary HgTe and ternary half-Heusler compounds, respectively. Results show that, for the binary HgTe, when its zinc-blend structure is artificially changed to rock-salt one, the tetrahedral covalent-hybridization will be removed and correspondingly the topologically insulating band character lost. While for the ternary half-Heusler system, the strength of covalent-hybridization can be tuned by varying both chemical compositions and atomic arrangements, and the competition between tetrahedral and octahedral covalent-hybridization has been discussed in details. As a result, we found thatmore » a proper strength of tetrahedral covalent-hybridization is probably in favor to realizing the topologically insulating state with band inversion occurring at the Γ point of the Brillouin zone.« less

Comprehensive understanding of mole concept subject matter according to the tetrahedral chemistry education (empirical study on the first-year chemistry students of Technische Universität Dresden)

NASA Astrophysics Data System (ADS)

Prabowo, D. W.; Mulyani, S.; van Pée, K.-H.; Indriyanti, N. Y.

2018-05-01

This research aims to apprehend: (1) the shape of tetrahedral chemistry education which is called the future of chemistry education, (2) comprehensive understanding of chemistry first-year students of Technische Universität Dresden according to the chemistry education’s tetrahedral shape on mole concept subject matter. This research used quantitative and qualitative; paper and pencil test and interview. The former was conducted in the form of test containing objective test instrument. The results of this study are (1) learning based on tetrahedral shape of chemistry education put the chemical substance (macroscopic), symbolic representation (symbol), and its process (molecular) in the context of human beings (human element) by integrating content and context, without emphasis on one thing and weaken another, (2) first-year chemistry students of Technische Universität Dresden have comprehensively understood the mole concept associated with the context of everyday life, whereby students are able to find out macroscopic information from statements that are contextual to human life and then by using symbols and formulas are able to comprehend the molecular components as well as to interpret and analyse problems effectively.

EVA assembly of large space structure element

NASA Technical Reports Server (NTRS)

Bement, L. J.; Bush, H. G.; Heard, W. L., Jr.; Stokes, J. W., Jr.

1981-01-01

The results of a test program to assess the potential of manned extravehicular activity (EVA) assembly of erectable space trusses are described. Seventeen tests were conducted in which six "space-weight" columns were assembled into a regular tetrahedral cell by a team of two "space"-suited test subjects. This cell represents the fundamental "element" of a tetrahedral truss structure. The tests were conducted under simulated zero-gravity conditions. Both manual and simulated remote manipulator system modes were evaluated. Articulation limits of the pressure suit and zero gravity could be accommodated by work stations with foot restraints. The results of this study have confirmed that astronaut EVA assembly of large, erectable space structures is well within man's capabilities.

Parallel Higher-order Finite Element Method for Accurate Field Computations in Wakefield and PIC Simulations

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

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

Over the past years, SLAC's Advanced Computations Department (ACD), under SciDAC sponsorship, has developed a suite of 3D (2D) parallel higher-order finite element (FE) codes, T3P (T2P) and Pic3P (Pic2P), aimed at accurate, large-scale simulation of wakefields and particle-field interactions in radio-frequency (RF) cavities of complex shape. The codes are built on the FE infrastructure that supports SLAC's frequency domain codes, Omega3P and S3P, to utilize conformal tetrahedral (triangular)meshes, higher-order basis functions and quadratic geometry approximation. For time integration, they adopt an unconditionally stable implicit scheme. Pic3P (Pic2P) extends T3P (T2P) to treat charged-particle dynamics self-consistently using the PIC (particle-in-cell)more » approach, the first such implementation on a conformal, unstructured grid using Whitney basis functions. Examples from applications to the International Linear Collider (ILC), Positron Electron Project-II (PEP-II), Linac Coherent Light Source (LCLS) and other accelerators will be presented to compare the accuracy and computational efficiency of these codes versus their counterparts using structured grids.« less

An Unexpected Influence on a Quadratic

ERIC Educational Resources Information Center

Davis, Jon D.

2013-01-01

Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

Mesh quality control for multiply-refined tetrahedral grids

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Strawn, Roger

1994-01-01

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

Seven Wonders of the Ancient and Modern Quadratic World.

ERIC Educational Resources Information Center

Taylor, Sharon E.; Mittag, Kathleen Cage

2001-01-01

Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

Ultrahigh-resolution γ-ray spectroscopy of 156Gd: a test of tetrahedral symmetry.

PubMed

Jentschel, M; Urban, W; Krempel, J; Tonev, D; Dudek, J; Curien, D; Lauss, B; de Angelis, G; Petkov, P

2010-06-04

Tetrahedral symmetry in strongly interacting systems would establish a new class of quantum effects at subatomic scale. Excited states in 156Gd that could carry the information about the tetrahedral symmetry were populated in the 155Gd(n,γ)156Gd reaction and studied using the GAMS4/5 Bragg spectrometers at the Institut Laue-Langevin. We have identified the 5(1)- → 3(1)- transition of 131.983(12) keV in 156Gd and determined its intensity to be 1.9(3)x10(-6) per neutron capture. The lifetime τ=220(-30)(+180) fs of the 5(1)- state in 156Gd has been measured using the GRID technique. The resulting B(E2)=293(-134)(+6) Weisskopf unit rate of the 131.983 keV transition provides the intrinsic quadrupole moment of the 5(1)- state in 156Gd to be Q0=7.1(-1.6)(+0.7) b. This large value, comparable to the quadrupole moment of the ground state in 156Gd, gives strong evidence against tetrahedral symmetry in the lowest odd-spin, negative-parity band of 156Gd.

A tetrapyridine ligand with a rigid tetrahedral core forms metal-organic frameworks with PtS type architecture.

PubMed

Caputo, Christopher B; Vukotic, V Nicholas; Sirizzotti, Natalie M; Loeb, Stephen J

2011-08-14

A new tetradentate, pyridine ligand with a rigid tetrahedral core can be prepared in good yield by a cross-coupling methodology. Two metal organic framework structures of Cu(II) with PtS-type topology having a carbon atom as the tetrahedral node have been characterized utilising this ligand. This journal is © The Royal Society of Chemistry 2011

THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

EPA Science Inventory

Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

Quadratic correlation filters for optical correlators

NASA Astrophysics Data System (ADS)

Mahalanobis, Abhijit; Muise, Robert R.; Vijaya Kumar, Bhagavatula V. K.

2003-08-01

Linear correlation filters have been implemented in optical correlators and successfully used for a variety of applications. The output of an optical correlator is usually sensed using a square law device (such as a CCD array) which forces the output to be the squared magnitude of the desired correlation. It is however not a traditional practice to factor the effect of the square-law detector in the design of the linear correlation filters. In fact, the input-output relationship of an optical correlator is more accurately modeled as a quadratic operation than a linear operation. Quadratic correlation filters (QCFs) operate directly on the image data without the need for feature extraction or segmentation. In this sense, the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required to detect peaks in the outputs of multiple linear filters, but choosing a winner among them is an error prone task. In contrast, all channels in a QCF work together to optimize the same performance metric and produce a combined output that leads to considerable simplification of the post-processing. In this paper, we propose a novel approach to the design of quadratic correlation based on the Fukunaga Koontz transform. Although quadratic filters are known to be optimum when the data is Gaussian, it is expected that they will perform as well as or better than linear filters in general. Preliminary performance results are provided that show that quadratic correlation filters perform better than their linear counterparts.

Synthesis, evaluation and defect compensation of tetrahedral glasses as possible solar cell materials. Final report, February 1, 1979-April 30, 1980

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

Rauh, R.D.; Rose, T.L.; Scoville, A.N.

1980-04-01

The work reported was directed towards evaluation of new amorphous compounds for application in solar cells. The ternary A/sup II/B/sup IV/C/sub 2//sup V/ chalcopyrite systems were selected because of their inexpensive constituent elements and tetrahedral geometry. Polycrystalline samples of the ternary arsenides with Cd and Zn as the group II element and Ge, Si, Sn as the group IV element were synthesized. Thin films were deposited by vacuum evaporation of the bulk ternary arsenides. The stoichiometries of the films were irreproducible and were usually deficient in the lower vapor pressure group IV element. Films made by evaporating polycrystalline ZnAs/sub 2/,more » which also has a tetrahedral bonding structure, had stoichiometries generally in the range from Zn/sub 3/As/sub 2/ to ZnAs/sub 2/. The former compound is formed by the decomposition of ZnAs/sub 2/ to Zn/sub 3/As/sub 2/ and As/sub 4/. The intermediate stoichiometries are thought to be mixtures of the decomposition products. Preliminary results from annealing of the films indicate that heat treatment produces the stoichiometries expected for one of the two forms of zinc arsenide. The as-deposited films are amorphous when the substrate temperature is kept below 100/sup 0/C. The a-ZnAs/sub x/ films were characterized. EDAX and Auger analysis showed that films were homogeneous in the plane of the substrate, but that some variation occurred in the depth profile of the films. This change in composition is consistent with the sample decomposition which occurs during the evaporation. The as-prepared films were p-type with room temperature resistivities on the order of 10/sup 2/-10/sup 4/..cap omega..-cm. Optical absorption measurements gave optical band gap values of 1.2 eV for a-Zn/sub 3/As/sub 2/ and 1.5 eV for a-ZnAs/sub 2/. The ZnAs/sub x/ films were photoconductive.« less

Extended orientational correlation study for molecular liquids containing distorted tetrahedral molecules: Application to methylene halides

NASA Astrophysics Data System (ADS)

Pothoczki, Szilvia; Temleitner, László; Pusztai, László

2010-04-01

The method of Rey [Rey, J. Chem. Phys. 126, 164506 (2007)] for describing how molecules orient toward each other in systems with perfect tetrahedral molecules is extended to the case of distorted tetrahedral molecules of c2v symmetry by means of introducing 28 subgroups. Additionally, the original analysis developed for perfect tetrahedral molecules, based on six groups, is adapted for molecules with imperfect tetrahedral shape. Deriving orientational correlation functions have been complemented with detailed analyses of dipole-dipole correlations. This way, (up to now) the most complete structure determination can be carried out for such molecular systems. In the present work, these calculations have been applied for particle configurations resulting from reverse Monte Carlo computer modeling. These particle arrangements are fully consistent with structure factors from neutron and x-ray diffraction measurements. Here we present a complex structural study for methylene halide (chloride, bromide, and iodide) molecular liquids, as possibly the best representative examples. It has been found that the most frequent orientations of molecules are of the 2:2 type over the entire distance range in these liquids. Focusing on the short range orientation, neighboring molecules turn toward each other with there "H,Y"-"H,Y" (Y: Cl, Br, I) edges, apart from CH2Cl2 where the H,H-H,Cl arrangement is the most frequent. In general, the structure of methylene chloride appears to be different from the structure of the other two liquids.

On the time-weighted quadratic sum of linear discrete systems

NASA Technical Reports Server (NTRS)

Jury, E. I.; Gutman, S.

1975-01-01

A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.

A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TETRAHEDRAL DOMAINS

PubMed Central

Fu, Zhisong; Kirby, Robert M.; Whitaker, Ross T.

2014-01-01

Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper presents a parallel algorithm for solving the eikonal equation on fully unstructured tetrahedral meshes. The method is appropriate for the type of fine-grained parallelism found on modern massively-SIMD architectures such as graphics processors and takes into account the particular constraints and capabilities of these computing platforms. This work builds on previous work for solving these equations on triangle meshes; in this paper we adapt and extend previous two-dimensional strategies to accommodate three-dimensional, unstructured, tetrahedralized domains. These new developments include a local update strategy with data compaction for tetrahedral meshes that provides solutions on both serial and parallel architectures, with a generalization to inhomogeneous, anisotropic speed functions. We also propose two new update schemes, specialized to mitigate the natural data increase observed when moving to three dimensions, and the data structures necessary for efficiently mapping data to parallel SIMD processors in a way that maintains computational density. Finally, we present descriptions of the implementations for a single CPU, as well as multicore CPUs with shared memory and SIMD architectures, with comparative results against state-of-the-art eikonal solvers. PMID:25221418

Toward Verification of USM3D Extensions for Mixed Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Frink, Neal T.; Ding, Ejiang; Parlette, Edward B.

2013-01-01

The unstructured tetrahedral grid cell-centered finite volume flow solver USM3D has been recently extended to handle mixed element grids composed of hexahedral, prismatic, pyramidal, and tetrahedral cells. Presently, two turbulence models, namely, baseline Spalart-Allmaras (SA) and Menter Shear Stress Transport (SST), support mixed element grids. This paper provides an overview of the various numerical discretization options available in the newly enhanced USM3D. Using the SA model, the flow solver extensions are verified on three two-dimensional test cases available on the Turbulence Modeling Resource website at the NASA Langley Research Center. The test cases are zero pressure gradient flat plate, planar shear, and bump-inchannel. The effect of cell topologies on the flow solution is also investigated using the planar shear case. Finally, the assessment of various cell and face gradient options is performed on the zero pressure gradient flat plate case.

Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme

PubMed Central

Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; Nguyen, Manh Cuong; Wang, Cai-Zhuang; Lin, Zijing; Zhu, Zi-Zhong; Ho, Kai-Ming

2015-01-01

Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A2MSiO4 with A = Li or Na and M = Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. These structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs. PMID:26497381

Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme

DOE PAGES

Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; ...

2015-10-26

Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A 2MSiO 4 with A = Li or Na and M = Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. In addition, these structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which havemore » been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs.« less

An analysis of spectral envelope-reduction via quadratic assignment problems

NASA Technical Reports Server (NTRS)

George, Alan; Pothen, Alex

1994-01-01

A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper, we provide an analysis of the spectral envelope reduction algorithm. We described related 1- and 2-sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work involved in an envelope Cholesky factorization scheme. We formulate the latter two problems as quadratic assignment problems, and then study the 2-sum problem in more detail. We obtain lower bounds on the 2-sum by considering a projected quadratic assignment problem, and then show that finding a permutation matrix closest to an orthogonal matrix attaining one of the lower bounds justifies the spectral envelope reduction algorithm. The lower bound on the 2-sum is seen to be tight for reasonably 'uniform' finite element meshes. We also obtain asymptotically tight lower bounds for the envelope size for certain classes of meshes.

Simultaneous travel time tomography for updating both velocity and reflector geometry in triangular/tetrahedral cell model

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; He, Lei-yu; Li, Xing-wang; Sun, Jia-yu

2018-05-01

To conduct forward and simultaneous inversion in a complex geological model, including an irregular topography (or irregular reflector or velocity anomaly), we in this paper combined our previous multiphase arrival tracking method (referred as triangular shortest-path method, TSPM) in triangular (2D) or tetrahedral (3D) cell model and a linearized inversion solver (referred to as damped minimum norms and constrained least squares problem solved using the conjugate gradient method, DMNCLS-CG) to formulate a simultaneous travel time inversion method for updating both velocity and reflector geometry by using multiphase arrival times. In the triangular/tetrahedral cells, we deduced the partial derivative of velocity variation with respective to the depth change of reflector. The numerical simulation results show that the computational accuracy can be tuned to a high precision in forward modeling and the irregular velocity anomaly and reflector geometry can be accurately captured in the simultaneous inversion, because the triangular/tetrahedral cell can be easily used to stitch the irregular topography or subsurface interface.

Simultaneous travel time tomography for updating both velocity and reflector geometry in triangular/tetrahedral cell model

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; He, Lei-yu; Li, Xing-wang; Sun, Jia-yu

2017-12-01

To conduct forward and simultaneous inversion in a complex geological model, including an irregular topography (or irregular reflector or velocity anomaly), we in this paper combined our previous multiphase arrival tracking method (referred as triangular shortest-path method, TSPM) in triangular (2D) or tetrahedral (3D) cell model and a linearized inversion solver (referred to as damped minimum norms and constrained least squares problem solved using the conjugate gradient method, DMNCLS-CG) to formulate a simultaneous travel time inversion method for updating both velocity and reflector geometry by using multiphase arrival times. In the triangular/tetrahedral cells, we deduced the partial derivative of velocity variation with respective to the depth change of reflector. The numerical simulation results show that the computational accuracy can be tuned to a high precision in forward modeling and the irregular velocity anomaly and reflector geometry can be accurately captured in the simultaneous inversion, because the triangular/tetrahedral cell can be easily used to stitch the irregular topography or subsurface interface.

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

DOE PAGES

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

2015-02-24

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

An Algebraic Approach for Solving Quadratic Inequalities

ERIC Educational Resources Information Center

Mahmood, Munir; Al-Mirbati, Rudaina

2017-01-01

In recent years most text books utilise either the sign chart or graphing functions in order to solve a quadratic inequality of the form ax[superscript 2] + bx + c < 0 This article demonstrates an algebraic approach to solve the above inequality. To solve a quadratic inequality in the form of ax[superscript 2] + bx + c < 0 or in the…

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

NASA Astrophysics Data System (ADS)

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

2011-02-01

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

Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

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

Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis

This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

ERIC Educational Resources Information Center

Laine, A. D.

2015-01-01

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

Four-Coordinate Iron(II) Diaryl Compounds with Monodentate N-Heterocyclic Carbene Ligation: Synthesis, Characterization, and Their Tetrahedral-Square Planar Isomerization in Solution.

PubMed

Liu, Yuesheng; Luo, Lun; Xiao, Jie; Wang, Lei; Song, You; Qu, Jingping; Luo, Yi; Deng, Liang

2015-05-18

The salt elimination reactions of (IPr2Me2)2FeCl2 (IPr2Me2 = 1,3-diisopropyl-4,5-dimethylimidazol-2-ylidene) with the corresponding aryl Grignard reagents afford [(IPr2Me2)2FeAr2] (Ar = Ph, 3; C6H4-p-Me, 4; C6H4-p-(t)Bu, 5; C6H3-3,5-(CF3)2, 6) in good yields. X-ray crystallographic studies revealed the presence of both tetrahedral and trans square planar isomers for 3 and 6 and the tetrahedral structures for 4 and 5. Magnetic susceptibility and (57)Fe Mössbauer spectrum measurements on the solid samples indicated the high-spin (S = 2) and intermediate-spin (S = 1) nature of the tetrahedral and square planar structures, respectively. Solution property studies, including solution magnetic susceptibility measurement, variable-temperature (1)H and (19)F NMR, and absorption spectroscopy, on 3-6, as well as an (57)Fe Mössbauer spectrum study on a frozen tetrahydrofuran solution of tetrahedral [(IPr2Me2)2(57)FePh2] suggest the coexistence of tetrahedral and trans square planar structures in solution phase. Density functional theory calculations on (IPr2Me2)2FePh2 disclosed that the tetrahedral and trans square planar isomers are close in energy and that the geometry isomerization can occur by spin-change-coupled geometric transformation on four-coordinate iron(II) center.

Platelet adhesion on phosphorus-incorporated tetrahedral amorphous carbon films

NASA Astrophysics Data System (ADS)

Liu, Aiping; Zhu, Jiaqi; Liu, Meng; Dai, Zhifei; Han, Xiao; Han, Jiecai

2008-11-01

The haemocompatibility of phosphorus-incorporated tetrahedral amorphous carbon (ta-C:P) films, synthesized by filtered cathodic vacuum arc technique with PH 3 as the dopant source, was assessed by in vitro platelet adhesion tests. Results based on scanning electron microscopy and contact angle measurements reveal that phosphorus incorporation improves the wettability and blood compatibility of ta-C film. Our studies may provide a novel approach for the design and synthesis of doped ta-C films to repel platelet adhesion and reduce thrombosis risk.

The stability of quadratic-reciprocal functional equation

NASA Astrophysics Data System (ADS)

Song, Aimin; Song, Minwei

2018-04-01

A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

Test spaces and characterizations of quadratic spaces

NASA Astrophysics Data System (ADS)

Dvurečenskij, Anatolij

1996-10-01

We show that a test space consisting of nonzero vectors of a quadratic space E and of the set all maximal orthogonal systems in E is algebraic iff E is Dacey or, equivalently, iff E is orthomodular. In addition, we present another orthomodularity criteria of quadratic spaces, and using the result of Solèr, we show that they can imply that E is a real, complex, or quaternionic Hilbert space.

Geometric quadratic stochastic operator on countable infinite set

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

Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

2015-02-03

In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

Analytical and Photogrammetric Characterization of a Planar Tetrahedral Truss

NASA Technical Reports Server (NTRS)

Wu, K. Chauncey; Adams, Richard R.; Rhodes, Marvin D.

1990-01-01

Future space science missions are likely to require near-optical quality reflectors which are supported by a stiff truss structure. This support truss should conform closely with its intended shape to minimize its contribution to the overall surface error of the reflector. The current investigation was conducted to evaluate the planar surface accuracy of a regular tetrahedral truss structure by comparing the results of predicted and measured node locations. The truss is a 2-ring hexagonal structure composed of 102 equal-length truss members. Each truss member is nominally 2 meters in length between node centers and is comprised of a graphite/epoxy tube with aluminum nodes and joints. The axial stiffness and the length variation of the truss components were determined experimentally and incorporated into a static finite element analysis of the truss. From this analysis, the root mean square (RMS) surface error of the truss was predicted to be 0.11 mm (0004 in). Photogrammetry tests were performed on the assembled truss to measure the normal displacements of the upper surface nodes and to determine if the truss would maintain its intended shape when subjected to repeated assembly. Considering the variation in the truss component lengths, the measures rms error of 0.14 mm (0.006 in) in the assembled truss is relatively small. The test results also indicate that a repeatable truss surface is achievable. Several potential sources of error were identified and discussed.

Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Chang, Chau-Lyan; Yen, Joseph C.

2013-01-01

In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.

Quadratic Programming for Allocating Control Effort

NASA Technical Reports Server (NTRS)

Singh, Gurkirpal

2005-01-01

A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

Some Paradoxical Results for the Quadratically Weighted Kappa

ERIC Educational Resources Information Center

Warrens, Matthijs J.

2012-01-01

The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories "n" it is shown that if one of the raters uses the same…

Automated Tetrahedral Mesh Generation for CFD Analysis of Aircraft in Conceptual Design

NASA Technical Reports Server (NTRS)

Ordaz, Irian; Li, Wu; Campbell, Richard L.

2014-01-01

The paper introduces an automation process of generating a tetrahedral mesh for computational fluid dynamics (CFD) analysis of aircraft configurations in early conceptual design. The method was developed for CFD-based sonic boom analysis of supersonic configurations, but can be applied to aerodynamic analysis of aircraft configurations in any flight regime.

Fostering Teacher Development to a Tetrahedral Orientation in the Teaching of Chemistry

ERIC Educational Resources Information Center

Lewthwaite, Brian; Wiebe, Rick

2011-01-01

This paper reports on the initial outcomes from the end of the fourth year of a 5 year research and professional development project to improve chemistry teaching among three cohorts of chemistry teachers in Manitoba, Canada. The project responds to a new curriculum introduction advocating a tetrahedral orientation (Mahaffy, "Journal of…

Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra

NASA Astrophysics Data System (ADS)

Yates, L. A.; Jarvis, P. D.

2018-04-01

We analyze the structure of the family of quadratic superalgebras, introduced in Jarvis et al (2011 J. Phys. A: Math. Theor. 44 235205), for the quadratic deformations of N  =  1 space-time conformal supersymmetry. We characterize in particular the ‘zero-step’ modules for this case. In such modules, the odd generators vanish identically, and the quadratic superalgebra is realized on a single irreducible representation of the even subalgebra (which is a Lie algebra). In the case under study, the quadratic deformations of N  =  1 space-time conformal supersymmetry, it is shown that each massless positive energy unitary irreducible representation (in the standard classification of Mack), forms such a zero-step module, for an appropriate parameter choice amongst the quadratic family (with vanishing central charge). For these massless particle multiplets therefore, quadratic supersymmetry is unbroken, in that the supersymmetry generators annihilate all physical states (including the vacuum state), while at the same time, superpartners do not exist.

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

PubMed

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

A Quadratic Spring Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2010-01-01

Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

On orthogonality preserving quadratic stochastic operators

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

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-05-15

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

Chemically Realistic Tetrahedral Lattice Models for Polymer Chains: Application to Polyethylene Oxide.

PubMed

Dietschreit, Johannes C B; Diestler, Dennis J; Knapp, Ernst W

2016-05-10

To speed up the generation of an ensemble of poly(ethylene oxide) (PEO) polymer chains in solution, a tetrahedral lattice model possessing the appropriate bond angles is used. The distance between noncovalently bonded atoms is maintained at realistic values by generating chains with an enhanced degree of self-avoidance by a very efficient Monte Carlo (MC) algorithm. Potential energy parameters characterizing this lattice model are adjusted so as to mimic realistic PEO polymer chains in water simulated by molecular dynamics (MD), which serves as a benchmark. The MD data show that PEO chains have a fractal dimension of about two, in contrast to self-avoiding walk lattice models, which exhibit the fractal dimension of 1.7. The potential energy accounts for a mild hydrophobic effect (HYEF) of PEO and for a proper setting of the distribution between trans and gauche conformers. The potential energy parameters are determined by matching the Flory radius, the radius of gyration, and the fraction of trans torsion angles in the chain. A gratifying result is the excellent agreement of the pair distribution function and the angular correlation for the lattice model with the benchmark distribution. The lattice model allows for the precise computation of the torsional entropy of the chain. The generation of polymer conformations of the adjusted lattice model is at least 2 orders of magnitude more efficient than MD simulations of the PEO chain in explicit water. This method of generating chain conformations on a tetrahedral lattice can also be applied to other types of polymers with appropriate adjustment of the potential energy function. The efficient MC algorithm for generating chain conformations on a tetrahedral lattice is available for download at https://github.com/Roulattice/Roulattice .

Sandia Higher Order Elements (SHOE) v 0.5 alpha

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

2013-09-24

SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likelymore » exist.« less

The Mystical "Quadratic Formula."

ERIC Educational Resources Information Center

March, Robert H.

1993-01-01

Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

Linear quadratic optimization for positive LTI system

NASA Astrophysics Data System (ADS)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

Determining the Optimal Solution for Quadratically Constrained Quadratic Programming (QCQP) on Energy-Saving Generation Dispatch Problem

NASA Astrophysics Data System (ADS)

Lesmana, E.; Chaerani, D.; Khansa, H. N.

2018-03-01

Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method

3D level set methods for evolving fronts on tetrahedral meshes with adaptive mesh refinement

DOE PAGES

Morgan, Nathaniel Ray; Waltz, Jacob I.

2017-03-02

The level set method is commonly used to model dynamically evolving fronts and interfaces. In this work, we present new methods for evolving fronts with a specified velocity field or in the surface normal direction on 3D unstructured tetrahedral meshes with adaptive mesh refinement (AMR). The level set field is located at the nodes of the tetrahedral cells and is evolved using new upwind discretizations of Hamilton–Jacobi equations combined with a Runge–Kutta method for temporal integration. The level set field is periodically reinitialized to a signed distance function using an iterative approach with a new upwind gradient. We discuss themore » details of these level set and reinitialization methods. Results from a range of numerical test problems are presented.« less

PSQP: Puzzle Solving by Quadratic Programming.

PubMed

Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

2017-02-01

In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

The important role of tetrahedral Ti{sup 4+} sites in the phase transformation and photocatalytic activity of TiO{sub 2} nanocomposites.

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

Li, G.; Dimitrijevic, N. M.; Chen, L.

Highly photoactive, tetrahedral Ti{sup 4+} sites can be created, other than in zeolite cavities and on silica substrate, in mixed-phase TiO{sub 2} nanocomposites. The tetrahedral Ti{sup 4+} species was shown to be an intermediate formed during the thermally driven phase transformation from anatase to rutile.

Visualising the Roots of Quadratic Equations with Complex Coefficients

ERIC Educational Resources Information Center

Bardell, Nicholas S.

2014-01-01

This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

NASA Astrophysics Data System (ADS)

Leonenko, N. N.; Ruiz-Medina, M. D.

2006-07-01

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

Evolution of stacking fault tetrahedral and work hardening effect in copper single crystals

NASA Astrophysics Data System (ADS)

Liu, Hai Tao; Zhu, Xiu Fu; Sun, Ya Zhou; Xie, Wen Kun

2017-11-01

Stacking fault tetrahedral (SFT), generated in machining of copper single crystal as one type of subsurface defects, has significant influence on the performance of workpiece. In this study, molecular dynamics (MD) simulation is used to investigate the evolution of stacking fault tetrahedral in nano-cutting of copper single crystal. The result shows that SFT is nucleated at the intersection of differently oriented stacking fault (SF) planes and SFT evolves from the preform only containing incomplete surfaces into a solid defect. The evolution of SFT contains several stress fluctuations until the complete formation. Nano-indentation simulation is then employed on the machined workpiece from nano-cutting, through which the interaction between SFT and later-formed dislocations in subsurface is studied. In the meanwhile, force-depth curves obtained from nano-indentation on pristine and machined workpieces are compared to analyze the mechanical properties. By simulation of nano-cutting and nano-indentation, it is verified that SFT is a reason of the work hardening effect.

Investigation of negative-parity states in Dy 156 : Search for evidence of tetrahedral symmetry

DOE PAGES

Hartley, D. J.; Riedinger, L. L.; Janssens, R. V. F.; ...

2017-01-01

An experiment populating low/medium-spin states in 156Dy was performed to investigate the possibility of tetrahedral symmetry in this nucleus. In particular, focus was placed on the low-spin, negative-parity states since recent theoretical studies suggest that these may be good candidates for this high-rank symmetry. The states were produced in the 148Nd( 12C,4 n) reaction and the Gammasphere array was utilized to detect the emitted rays. B(E 2) /B(E1) ratios of transition probabilities from the low-spin, negative-parity bands were determined and used to interpret whether these structures are best associated with tetrahedral symmetry or, as previously assigned, to octupole vibrations. Additionally,more » several other negative-parity structures were observed to higher spin and two new sequences were established« less

Investigation of negative-parity states in Dy 156 : Search for evidence of tetrahedral symmetry

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

Hartley, D. J.; Riedinger, L. L.; Janssens, R. V. F.

2017-01-01

An experiment populating low/medium-spin states in 156 Dy was performed to investigate the possibility of tetrahedral symmetry in this nucleus. In particular, focus was placed on the low-spin, negative-parity states since recent theoretical studies suggest that these may be good candidates for this high-rank symmetry. The states were produced in the 148 Nd ( 12 C , 4 n ) reaction and the Gammasphere array was utilized to detect the emitted γ rays. B ( E 2 ) / B ( E 1 ) ratios of transition probabilities from the low-spin, negative-parity bands were determined and used to interpret whethermore » these structures are best associated with tetrahedral symmetry or, as previously assigned, to octupole vibrations. In addition, several other negative-parity structures were observed to higher spin and two new sequences were established.« less

Adinkras from ordered quartets of BC4 Coxeter group elements and regarding 1,358,954,496 matrix elements of the Gadget

NASA Astrophysics Data System (ADS)

Gates, S. James; Guyton, Forrest; Harmalkar, Siddhartha; Kessler, David S.; Korotkikh, Vadim; Meszaros, Victor A.

2017-06-01

We examine values of the Adinkra Holoraumy-induced Gadget representation space metric over all possible four-color, four-open node, and four-closed node adinkras. Of the 1,358,954,496 gadget matrix elements, only 226,492,416 are non-vanishing and take on one of three values: -1/3, 1/3, or 1 and thus a subspace isomorphic to a description of a body-centered tetrahedral molecule emerges.

Self-Assembled DNA Tetrahedral Scaffolds for the Construction of Electrochemiluminescence Biosensor with Programmable DNA Cyclic Amplification.

PubMed

Feng, Qiu-Mei; Guo, Yue-Hua; Xu, Jing-Juan; Chen, Hong-Yuan

2017-05-24

A novel DNA tetrahedron-structured electrochemiluminescence (ECL) platform for bioanalysis with programmable DNA cyclic amplification was developed. In this work, glucose oxidase (GOD) was labeled to a DNA sequence (S) as functional conjugation (GOD-S), which could hybridize with other DNA sequences (L and P) to form GOD-S:L:P probe. In the presence of target DNA and a help DNA (A), the programmable DNA cyclic amplification was activated and released GOD-S via toehold-mediated strand displacement. Then, the obtained GOD-S was further immobilized on the DNA tetrahedral scaffolds with a pendant capture DNA and Ru(bpy) 3 2+ -conjugated silica nanoparticles (RuSi NPs) decorated on the electrode surface. Thus, the amount of GOD-S assembled on the electrode surface depended on the concentration of target DNA and GOD could catalyze glucose to generate H 2 O 2 in situ. The ECL signal of Ru(bpy) 3 2+ -TPrA system was quenched by the presence of H 2 O 2 . By integrating the programmable DNA cyclic amplification and in situ generating H 2 O 2 as Ru(bpy) 3 2+ ECL quencher, a sensitive DNA tetrahedron-structured ECL sensing platform was proposed for DNA detection. Under optimized conditions, this biosensor showed a wide linear range from 100 aM to 10 pM with a detection limit of 40 aM, indicating a promising application in DNA analysis. Furthermore, by labeling GOD to different recognition elements, the proposed strategy could be used for the detection of various targets. Thus, this programmable cascade amplification strategy not only retains the high selectivity and good capturing efficiency of tetrahedral-decorated electrode surface but also provides potential applications in the construction of ECL biosensor.

Geometric Approaches to Quadratic Equations from Other Times and Places.

ERIC Educational Resources Information Center

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Analysis of Students' Error in Learning of Quadratic Equations

ERIC Educational Resources Information Center

Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

2010-01-01

The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

Tetrahedral Hohlraum Visualization and Pointings

NASA Astrophysics Data System (ADS)

Klare, K. A.; Wallace, J. M.; Drake, D.

1997-11-01

In designing experiments for Omega, the tetrahedral hohlraum (a sphere with four holes) can make full use of all 60 beams. There are some complications: the beams must clear the laser entrance hole (LEH), must miss a central capsule, absolutely must not go out the other LEHs, and should distribute in the interior of the hohlraum to maximize the uniformity of irradiation on the capsule while keeping reasonable laser spot sizes. We created a 15-offset coordinate system with which an IDL program computes clearances, writes a file for QuickDraw 3D (QD3D) visualization, and writes input for the viewfactor code RAYNA IV. Visualizing and adjusting the parameters by eye gave more reliable results than computer optimization. QD3D images permitted quick live rotations to determine offsets. The clearances obtained insured safe operation and good physics. The viewfactor code computes the initial irradiation of the hohlraum and capsule or of a uniform hohlraum source with the loss through the four LEHs and shows a high degree of uniformity with both, better for lasers because this deposits more energy near the LEHs to compensate for the holes.

Self-accelerating parabolic beams in quadratic nonlinear media

NASA Astrophysics Data System (ADS)

Dolev, Ido; Libster, Ana; Arie, Ady

2012-09-01

We present experimental observation of self-accelerating parabolic beams in quadratic nonlinear media. We show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another in the two transverse coordinates. In addition, the two coupled harmonics have the same acceleration within and after the nonlinear medium. We also study the evolution of second harmonic accelerating beams inside the quadratic media and their correlation with theoretical beams.

Binary Inspiral in Quadratic Gravity

NASA Astrophysics Data System (ADS)

Yagi, Kent

2015-01-01

Quadratic gravity is a general class of quantum-gravity-inspired theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to a scalar field. In this article, we focus on the scalar Gauss- Bonnet (sGB) theory and consider the black hole binary inspiral in this theory. By applying the post-Newtonian (PN) formalism, we found that there is a scalar dipole radiation which leads to -1PN correction in the energy flux relative to gravitational radiation in general relativity. From the orbital decay rate of a low-mass X-ray binary A0600-20, we obtain the bound that is six orders of magnitude stronger than the current solar system bound. Furthermore, we show that the excess in the orbital decay rate of XTE J1118+480 can be explained by the scalar radiation in sGB theory.

Tangent Lines without Derivatives for Quadratic and Cubic Equations

ERIC Educational Resources Information Center

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

Sketching the General Quadratic Equation Using Dynamic Geometry Software

ERIC Educational Resources Information Center

Stols, G. H.

2005-01-01

This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

MurD ligase from E. coli: Tetrahedral intermediate formation study by hybrid quantum mechanical/molecular mechanical replica path method.

PubMed

Perdih, Andrej; Hodoscek, Milan; Solmajer, Tom

2009-02-15

MurD (UDP-N-acetylmuramoyl-L-alanine:D-glutamate ligase), a three-domain bacterial protein, catalyses a highly specific incorporation of D-glutamate to the cytoplasmic intermediate UDP-N-acetyl-muramoyl-L-alanine (UMA) utilizing ATP hydrolysis to ADP and P(i). This reaction is part of a biosynthetic path yielding bacterial peptidoglycan. On the basis of structural studies of MurD complexes, a stepwise catalytic mechanism was proposed that commences with a formation of the acyl-phosphate intermediate, followed by a nucleophilic attack of D-glutamate that, through the formation of a tetrahedral reaction intermediate and subsequent phosphate dissociation, affords the final product, UDP-N-acetyl-muramoyl-L-alanine-D-glutamate (UMAG). A hybrid quantum mechanical/molecular mechanical (QM/MM) molecular modeling approach was utilized, combining the B3LYP QM level of theory with empirical force field simulations to evaluate three possible reaction pathways leading to tetrahedral intermediate formation. Geometries of the starting structures based on crystallographic experimental data and tetrahedral intermediates were carefully examined together with a role of crucial amino acids and water molecules. The replica path method was used to generate the reaction pathways between the starting structures and the corresponding tetrahedral reaction intermediates, offering direct comparisons with a sequential kinetic mechanism and the available structural data for this enzyme. The acquired knowledge represents new and valuable information to assist in the ongoing efforts leading toward novel inhibitors of MurD as potential antibacterial drugs. (c) 2008 Wiley-Liss, Inc.

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

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

Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar

2016-06-15

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators aremore » useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.« less

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.

High-pressure NaCl-phase of tetrahedral compounds

NASA Astrophysics Data System (ADS)

Soma, T.; -Matsuo Kagaya, H.

1984-04-01

The phase transition of tetrahedral compounds such as GaP, InP, ZnS, ZnSe, ZnTe and CdTe under pressure is investigated from the electronic theory of solids by using our recently presented binding force, which includes mainly covalent interactions in the pseudopotential formalism and partially ionic interactions. The partially ionic forces give the important contributions to the high-pressure phase and stabilize the NaCl-type structure for the high-pressure phase of these compounds, although not reported for GaP experimentally. Then, the numerical results such as the transition pressure, the volume-discontinuity, the transition heat with respect to the pressure-induced phase transition from the zinc-blende-to the NaCl-type lattice are obtained theoretically.

Nuclear tetrahedral symmetry: possibly present throughout the periodic table.

PubMed

Dudek, J; Goźdź, A; Schunck, N; Miśkiewicz, M

2002-06-24

More than half a century after the fundamental, spherical shell structure in nuclei had been established, theoretical predictions indicated that the shell gaps comparable or even stronger than those at spherical shapes may exist. Group-theoretical analysis supported by realistic mean-field calculations indicate that the corresponding nuclei are characterized by the TD(d) ("double-tetrahedral") symmetry group. Strong shell-gap structure is enhanced by the existence of the four-dimensional irreducible representations of TD(d); it can be seen as a geometrical effect that does not depend on a particular realization of the mean field. Possibilities of discovering the TD(d) symmetry in experiment are discussed.

Electromagnetic tracking system with reduced distortion using quadratic excitation.

PubMed

Bien, Tomasz; Li, Mengfei; Salah, Zein; Rose, Georg

2014-03-01

Electromagnetic tracking systems, frequently used in minimally invasive surgery, are affected by conductive distorters. The influence of conductive distorters on electromagnetic tracking system accuracy can be reduced through magnetic field modifications. This approach was developed and tested. The voltage induced directly by the emitting coil in the sensing coil without additional influence by the conductive distorter depends on the first derivative of the voltage on the emitting coil. The voltage which is induced indirectly by the emitting coil across the conductive distorter in the sensing coil, however, depends on the second derivative of the voltage on the emitting coil. The electromagnetic tracking system takes advantage of this difference by supplying the emitting coil with a quadratic excitation voltage. The method is adaptive relative to the amount of distortion cause by the conductive distorters. This approach is evaluated with an experimental setup of the electromagnetic tracking system. In vitro testing showed that the maximal error decreased from 10.9 to 3.8 mm when the quadratic voltage was used to excite the emitting coil instead of the sinusoidal voltage. Furthermore, the root mean square error in the proximity of the aluminum disk used as a conductive distorter was reduced from 3.5 to 1.6 mm when the electromagnetic tracking system used the quadratic instead of sinusoidal excitation. Electromagnetic tracking with quadratic excitation is immune to the effects of a conductive distorter, especially compared with sinusoidal excitation of the emitting coil. Quadratic excitation of electromagnetic tracking for computer-assisted surgery is promising for clinical applications.

Online Quadrat Study - Site Index

Science.gov Websites

Study Project - Prairie Advocates Project ) Background Information - Data Collection and Entry - Data Data Entry Data Summaries and Graphs Quadrat Study Poster for your classroom. Directions for Looking at by Prairie Study Prairie Experts For Non-Fermilab Prairie researchers: Complete step-by-step

Modeling 3D PCMI using the Extended Finite Element Method with higher order elements

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

Jiang, W.; Spencer, Benjamin W.

2017-03-31

This report documents the recent development to enable XFEM to work with higher order elements. It also demonstrates the application of higher order (quadratic) elements to both 2D and 3D models of PCMI problems, where discrete fractures in the fuel are represented using XFEM. The modeling results demonstrate the ability of the higher order XFEM to accurately capture the effects of a crack on the response in the vicinity of the intersecting surfaces of cracked fuel and cladding, as well as represent smooth responses in the regions away from the crack.

Use of edge-based finite elements for solving three dimensional scattering problems

NASA Technical Reports Server (NTRS)

Chatterjee, A.; Jin, J. M.; Volakis, John L.

1991-01-01

Edge based finite elements are free from drawbacks associated with node based vectorial finite elements and are, therefore, ideal for solving 3-D scattering problems. The finite element discretization using edge elements is checked by solving for the resonant frequencies of a closed inhomogeneously filled metallic cavity. Great improvements in accuracy are observed when compared to the classical node based approach with no penalty in terms of computational time and with the expected absence of spurious modes. A performance comparison between the edge based tetrahedra and rectangular brick elements is carried out and tetrahedral elements are found to be more accurate than rectangular bricks for a given storage intensity. A detailed formulation for the scattering problem with various approaches for terminating the finite element mesh is also presented.

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

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

Manzini, Gianmarco; Gyrya, Vitaliy

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

Atomic Scale Picture of the Ion Conduction Mechanism in Tetrahedral Network of Lanthanum Barium Gallate

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

Jalarvo, Niina H; Gourdon, Olivier; Bi, Zhonghe

2013-01-01

Combined experimental study of impedance spectroscopy, neutron powder diffraction and quasielastic neutron scattering was performed to shed light into the atomic scale ion migration processes in proton and oxide ion conductor; La0.8Ba1.2GaO3.9 . This material consist of tetrahedral GaO4 units, which are rather flexible and rocking motion of these units promotes the ionic migration process. The oxide ion (vacancy) conduction takes place on channels along c axis, involving a single elementary step, which occurs between adjacent tetrahedron (inter-tetrahedron jump). The proton conduction mechanism consists of intra-tetrahedron and inter-tetrahedron elementary processes. The intra-tetrahedron proton transport is the rate-limiting process, with activationmore » energy of 0.44 eV. The rocking motion of the GaO4 tetrahedron aids the inter-tetrahedral proton transport, which has the activation energy of 0.068 eV.« less

A voxel-based finite element model for the prediction of bladder deformation

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

Chai Xiangfei; Herk, Marcel van; Hulshof, Maarten C. C. M.

2012-01-15

Purpose: A finite element (FE) bladder model was previously developed to predict bladder deformation caused by bladder filling change. However, two factors prevent a wide application of FE models: (1) the labor required to construct a FE model with high quality mesh and (2) long computation time needed to construct the FE model and solve the FE equations. In this work, we address these issues by constructing a low-resolution voxel-based FE bladder model directly from the binary segmentation images and compare the accuracy and computational efficiency of the voxel-based model used to simulate bladder deformation with those of a classicalmore » FE model with a tetrahedral mesh. Methods: For ten healthy volunteers, a series of MRI scans of the pelvic region was recorded at regular intervals of 10 min over 1 h. For this series of scans, the bladder volume gradually increased while rectal volume remained constant. All pelvic structures were defined from a reference image for each volunteer, including bladder wall, small bowel, prostate (male), uterus (female), rectum, pelvic bone, spine, and the rest of the body. Four separate FE models were constructed from these structures: one with a tetrahedral mesh (used in previous study), one with a uniform hexahedral mesh, one with a nonuniform hexahedral mesh, and one with a low-resolution nonuniform hexahedral mesh. Appropriate material properties were assigned to all structures and uniform pressure was applied to the inner bladder wall to simulate bladder deformation from urine inflow. Performance of the hexahedral meshes was evaluated against the performance of the standard tetrahedral mesh by comparing the accuracy of bladder shape prediction and computational efficiency. Results: FE model with a hexahedral mesh can be quickly and automatically constructed. No substantial differences were observed between the simulation results of the tetrahedral mesh and hexahedral meshes (<1% difference in mean dice similarity

Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

ERIC Educational Resources Information Center

Vaiyavutjamai, Pongchawee; Clements, M. A.

2006-01-01

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows

PubMed Central

Wang, Di; Kleinberg, Robert D.

2009-01-01

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C2, C3, C4,…. It is known that C2 can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing Ck (k > 2) require solving a linear program. In this paper we prove that C3 can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}n, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

PubMed

Wang, Di; Kleinberg, Robert D

2009-11-28

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

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

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1997-01-01

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

The generalized quadratic knapsack problem. A neuronal network approach.

PubMed

Talaván, Pedro M; Yáñez, Javier

2006-05-01

The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

Tetrahedral aminopeptidase: a novel large protease complex from archaea

PubMed Central

Franzetti, B.; Schoehn, G.; Hernandez, J.-F.; Jaquinod, M.; Ruigrok, R.W.H.; Zaccai, G.

2002-01-01

A dodecameric protease complex with a tetrahedral shape (TET) was isolated from Haloarcula marismortui, a salt-loving archaeon. The 42 kDa monomers in the complex are homologous to metal-binding, bacterial aminopeptidases. TET has a broad aminopeptidase activity and can process peptides of up to 30–35 amino acids in length. TET has a central cavity that is accessible through four narrow channels (<17 Å wide) and through four wider channels (21 Å wide). This architecture is different from that of all the proteolytic complexes described to date that are made up by rings or barrels with a single central channel and only two openings. PMID:11980710

Exploring Quadratic Functions with Logger "Pro"

ERIC Educational Resources Information Center

Pope, Derek

2018-01-01

The author shares the lesson that he used to introduce the quadratic unit to students in an extended second-year algebra class, demonstrate why it was appropriate for his struggling learners, and discuss possible future modifications to this lesson.

Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

ERIC Educational Resources Information Center

Pathak, H. K.; Grewal, A. S.

2002-01-01

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

Geometrical and Graphical Solutions of Quadratic Equations.

ERIC Educational Resources Information Center

Hornsby, E. John, Jr.

1990-01-01

Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

Synthesis and Catalytic Activity of Pt Monolayer on Pd Tetrahedral Nanocrystals with CO-adsorption-induced Removal of Surfactants

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

Gong K.; Vukmirovic M.B.; Ma C.

2011-11-01

We synthesized the Pt monolayer shell-Pd tetrahedral core electrocatalysts that are notable for their high activity and stable performance. A small number of low-coordination sites and defects, and high content of the (1 1 1)-oriented facets on Pd tetrahedron makes them a suitable support for a Pt monolayer to obtain an active O{sub 2} reduction reaction (ORR) electrocatalyst. The surfactants, used to control size and shape of Pd tetrahedral nanoparticles, are difficult to remove and cause adverse effects on the ORR. We describe a simple and noninvasive method to synthesize high-purity tetrahedral Pd nanocrystals (TH Pd) by combining a hydrothermalmore » route and CO adsorption-induced removal of surfactants. Poly(vinylpyrrolidone) (PVP), used as a protecting and reducing agent in hydrothermal reactions, is strongly bonded to the surface of the resulting nanocrystals. We demonstrate that PVP was displaced efficiently by adsorbed CO. A clean surface was achieved upon CO stripping at a high potential (1.0 V vs RHE). It played a decisive role in improving the activity of the Pt monolayer/TH Pd electrocatalyst for the ORR. Furthermore, the results demonstrate a versatile method for removal of surfactants from various nanoparticles that severely limited their applications.« less

Homotopy approach to optimal, linear quadratic, fixed architecture compensation

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1991-01-01

Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

Quadratic spatial soliton interactions

NASA Astrophysics Data System (ADS)

Jankovic, Ladislav

Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30

Unraveling the Voltage-Fade Mechanism in High-Energy-Density Lithium-Ion Batteries: Origin of the Tetrahedral Cations for Spinel Conversion

DOE PAGES

Mohanty, Debasish; Li, Jianlin; Abraham, Daniel P.; ...

2014-09-30

Discovery of high-voltage layered lithium-and manganese-rich (LMR) composite oxide electrode has dramatically enhanced the energy density of current Li-ion energy storage systems. However, practical usage of these materials is currently not viable because of their inability to maintain a consistent voltage profile (voltage fading) during subsequent charge-discharge cycles. This report rationalizes the cause of this voltage fade by providing the evidence of layer to spinel-like (LSL) structural evolution pathways in the host Li 1.2Mn 0.55Ni 0.15Co 0.1O 2 LMR composite oxide. By employing neutron powder diffraction, and temperature dependent magnetic susceptibility, we show that LSL structural rearrangement in LMR oxidemore » occurs through a tetrahedral cation intermediate via: i) diffusion of lithium atoms from octahedral to tetrahedral sites of the lithium layer [(Li Lioct →Li Litet] which is followed by the dispersal of the lithium ions from the adjacent octahedral site of the metal layer to the tetrahedral sites of lithium layer [Li TM oct → Li Litet]; and ii) migration of Mn from the octahedral sites of the transition metal layer to the permanent octahedral site of lithium layer via tetrahedral site of lithium layer [Mn TMoct Mn Litet Mn Lioct)]. The findings opens the door to the potential routes to mitigate this atomic restructuring in the high-voltage LMR composite oxide cathodes by manipulating the composition/structure for practical use in high-energy-density lithium-ion batteries.« less

Genetic training of network using chaos concept: application to QSAR studies of vibration modes of tetrahedral halides.

PubMed

Lu, Qingzhang; Shen, Guoli; Yu, Ruqin

2002-11-15

The chaotic dynamical system is introduced in genetic algorithm to train ANN to formulate the CGANN algorithm. Logistic mapping as one of the most important chaotic dynamic mappings provides each new generation a high chance to hold GA's population diversity. This enhances the ability to overcome overfitting in training an ANN. The proposed CGANN has been used for QSAR studies to predict the tetrahedral modes (nu(1)(A1) and nu(2)(E)) of halides [MX(4)](epsilon). The frequencies predicted by QSAR were compared with those calculated by quantum chemistry methods including PM3, AM1, and MNDO/d. The possibility of improving the predictive ability of QSAR by including quantum chemistry parameters as feature variables has been investigated using tetrahedral tetrahalide examples. Copyright 2002 Wiley Periodicals, Inc.

Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2012-01-01

A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

On Volterra quadratic stochastic operators with continual state space

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

Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

2015-05-15

Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on themore » segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.« less

Schur Stability Regions for Complex Quadratic Polynomials

ERIC Educational Resources Information Center

Cheng, Sui Sun; Huang, Shao Yuan

2010-01-01

Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

C1 finite elements on non-tensor-product 2d and 3d manifolds

PubMed Central

Nguyen, Thien; Karčiauskas, Kęstutis; Peters, Jörg

2015-01-01

Geometrically continuous (Gk) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are Ck also for non-tensor-product layout. This paper describes and analyzes one such concrete C1 geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed G1 surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Remarkably, for Poisson’s equation on the disk using interior vertices of valence 3 and symmetric layout, we observe O(h3) convergence in the L∞ norm for this family of elements. Numerical experiments confirm the elements to be effective for solving the trivariate Poisson equation on the solid cylinder, deformations thereof (a turbine blade), modeling and computing geodesics on smooth free-form surfaces via the heat equation, for solving the biharmonic equation on the disk and for Koiter-type thin-shell analysis. PMID:26594070

C1 finite elements on non-tensor-product 2d and 3d manifolds.

PubMed

Nguyen, Thien; Karčiauskas, Kęstutis; Peters, Jörg

2016-01-01

Geometrically continuous ( G k ) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are C k also for non-tensor-product layout. This paper describes and analyzes one such concrete C 1 geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed G 1 surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Remarkably, for Poisson's equation on the disk using interior vertices of valence 3 and symmetric layout, we observe O ( h 3 ) convergence in the L ∞ norm for this family of elements. Numerical experiments confirm the elements to be effective for solving the trivariate Poisson equation on the solid cylinder, deformations thereof (a turbine blade), modeling and computing geodesics on smooth free-form surfaces via the heat equation, for solving the biharmonic equation on the disk and for Koiter-type thin-shell analysis.

Boundary element analysis of post-tensioned slabs

NASA Astrophysics Data System (ADS)

Rashed, Youssef F.

2015-06-01

In this paper, the boundary element method is applied to carry out the structural analysis of post-tensioned flat slabs. The shear-deformable plate-bending model is employed. The effect of the pre-stressing cables is taken into account via the equivalent load method. The formulation is automated using a computer program, which uses quadratic boundary elements. Verification samples are presented, and finally a practical application is analyzed where results are compared against those obtained from the finite element method. The proposed method is efficient in terms of computer storage and processing time as well as the ease in data input and modifications.

Linear and quadratic static response functions and structure functions in Yukawa liquids.

PubMed

Magyar, Péter; Donkó, Zoltán; Kalman, Gabor J; Golden, Kenneth I

2014-08-01

We compute linear and quadratic static density response functions of three-dimensional Yukawa liquids by applying an external perturbation potential in molecular dynamics simulations. The response functions are also obtained from the equilibrium fluctuations (static structure factors) in the system via the fluctuation-dissipation theorems. The good agreement of the quadratic response functions, obtained in the two different ways, confirms the quadratic fluctuation-dissipation theorem. We also find that the three-point structure function may be factorizable into two-point structure functions, leading to a cluster representation of the equilibrium triplet correlation function.

Arsenic Incorporation in Pyrite at Ambient Temperature at Both Tetrahedral S-I and Octahedral FeII Sites: Evidence from EXAFS-DFT Analysis.

PubMed

Le Pape, Pierre; Blanchard, Marc; Brest, Jessica; Boulliard, Jean-Claude; Ikogou, Maya; Stetten, Lucie; Wang, Shuaitao; Landrot, Gautier; Morin, Guillaume

2017-01-03

Pyrite is a ubiquitous mineral in reducing environments and is well-known to incorporate trace elements such as Co, Ni, Se, Au, and commonly As. Indeed, As-bearing pyrite is observed in a wide variety of sedimentary environments, making it a major sink for this toxic metalloid. Based on the observation of natural hydrothermal pyrites, As -I is usually assigned to the occupation of tetrahedral S -I sites, with the same oxidation state as in arsenopyrite (FeAsS), although rare occurrences of As III and As II have been reported. However, the modes of As incorporation into pyrite during its crystallization under low-temperature diagenetic conditions have not yet been elucidated because arsenic acts as an inhibitor for pyrite nucleation at ambient temperature. Here, we provide evidence from X-ray absorption spectroscopy for As II,III incorporation into pyrite at octahedral Fe II sites and for As -I at tetrahedral S -I sites during crystallization at ambient temperature. Extended X-ray absorption fine structure (EXAFS) spectra of these As-bearing pyrites are explained by local structure models obtained using density functional theory (DFT), assuming incorporation of As at the Fe and S sites, as well as local clustering of arsenic. Such observations of As -I incorporation at ambient temperature can aid in the understanding of the early formation of authigenic arsenian pyrite in subsurface sediments. Moreover, evidence for substitution of As II,III for Fe in our synthetic samples raises questions about both the possible occurrence and the geochemical reactivity of such As-bearing pyrites in low-temperature subsurface environments.

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.

Geometrical Solutions of Quadratic Equations.

ERIC Educational Resources Information Center

Grewal, A. S.; Godloza, L.

1999-01-01

Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

The non-avian theropod quadrate I: standardized terminology with an overview of the anatomy and function

PubMed Central

Araújo, Ricardo; Mateus, Octávio

2015-01-01

The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber—invaded by the quadrate diverticulum of the mandibular arch pneumatic system—was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455

A study of pH-dependence of shrink and stretch of tetrahedral DNA nanostructures.

PubMed

Wang, Ping; Xia, Zhiwei; Yan, Juan; Liu, Xunwei; Yao, Guangbao; Pei, Hao; Zuo, Xiaolei; Sun, Gang; He, Dannong

2015-04-21

We monitored the shrink and stretch of the tetrahedral DNA nanostructure (TDN) and the i-motif connected TDN structure at pH 8.5 and pH 4.5, and we found that not only the i-motif can change its structure when the pH changes, but also the TDN and the DNA double helix change their structures when the pH changes.

Mixed Element Type Unstructured Grid Generation for Viscous Flow Applications

NASA Technical Reports Server (NTRS)

Marcum, David L.; Gaither, J. Adam

2000-01-01

A procedure is presented for efficient generation of high-quality unstructured grids suitable for CFD simulation of high Reynolds number viscous flow fields. Layers of anisotropic elements are generated by advancing along prescribed normals from solid boundaries. The points are generated such that either pentahedral or tetrahedral elements with an implied connectivity can be be directly recovered. As points are generated they are temporarily attached to a volume triangulation of the boundary points. This triangulation allows efficient local search algorithms to be used when checking merging layers, The existing advancing-front/local-reconnection procedure is used to generate isotropic elements outside of the anisotropic region. Results are presented for a variety of applications. The results demonstrate that high-quality anisotropic unstructured grids can be efficiently and consistently generated for complex configurations.

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

PubMed Central

Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

2014-01-01

The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

On Some Algebraic and Combinatorial Properties of Dunkl Elements

NASA Astrophysics Data System (ADS)

Kirillov, Anatol N.

2013-06-01

We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.

On Some Algebraic and Combinatorial Properties of Dunkl Elements

NASA Astrophysics Data System (ADS)

Kirillov, Anatol N.

2012-11-01

We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.

Photonuclear sum rules and the tetrahedral configuration of He4

NASA Astrophysics Data System (ADS)

Gazit, Doron; Barnea, Nir; Bacca, Sonia; Leidemann, Winfried; Orlandini, Giuseppina

2006-12-01

Three well-known photonuclear sum rules (SR), i.e., the Thomas-Reiche-Kuhn, the bremsstrahlungs and the polarizability SR are calculated for He4 with the realistic nucleon-nucleon potential Argonne V18 and the three-nucleon force Urbana IX. The relation between these sum rules and the corresponding energy weighted integrals of the cross section is discussed. Two additional equivalences for the bremsstrahlungs SR are given, which connect it to the proton-neutron and neutron-neutron distances. Using them, together with our result for the bremsstrahlungs SR, we find a deviation from the tetrahedral symmetry of the spatial configuration of He4. The possibility to access this deviation experimentally is discussed.

Lattice vibrational contribution to equation of state for tetrahedral compounds

NASA Astrophysics Data System (ADS)

Kagaya, H.-Matsuo; Kotoku, H.; Soma, T.

1989-02-01

The lattice vibrational contributions to the Helmholtz free energy and the thermal pressure of tetrahedral compounds such as GaP, InP, ZnS, ZnSe, ZnTe and CdTe are investigated from the electronic theory of solids in the dynamical treatment based on our presented binding force. The temperature dependence of Helmholtz free energy and thermal pressure from lattice vibrational term are quantitatively obtained, and vibrational contributions to free energy are small compared with the static crystal energy. The influence of the thermal pressure is important to the equation of state in high temperatures, and the reformulation of the volume scale for the pressure-volume relation is given by considering the thermal pressure.

Quadratic canonical transformation theory and higher order density matrices.

PubMed

Neuscamman, Eric; Yanai, Takeshi; Chan, Garnet Kin-Lic

2009-03-28

Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H(2)O and N(2) binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

NASA Astrophysics Data System (ADS)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

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 dual boundary element formulation for elastoplastic fracture mechanics

NASA Astrophysics Data System (ADS)

Leitao, V.; Aliabadi, M. H.; Rooke, D. P.

1993-08-01

The extension of the dual boundary element method (DBEM) to the analysis of elastoplastic fracture mechanics (EPFM) problems is presented. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied to one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. In order to avoid collocation at crack tips, crack kinks, and crack-edge corners, both crack surfaces are discretized with discontinuous quadratic boundary elements. The elastoplastic behavior is modeled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral, and/or triangular cells. A center-cracked plate and a slant edge-cracked plate subjected to tensile load are analyzed and the results are compared with others available in the literature. J-type integrals are calculated.

Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

NASA Astrophysics Data System (ADS)

Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu

2018-03-01

A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.

Estimating factors influencing the detection probability of semiaquatic freshwater snails using quadrat survey methods

USGS Publications Warehouse

Roesler, Elizabeth L.; Grabowski, Timothy B.

2018-01-01

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts.

Evaluation of a 3D point cloud tetrahedral tomographic reconstruction method

PubMed Central

Pereira, N F; Sitek, A

2011-01-01

Tomographic reconstruction on an irregular grid may be superior to reconstruction on a regular grid. This is achieved through an appropriate choice of the image space model, the selection of an optimal set of points and the use of any available prior information during the reconstruction process. Accordingly, a number of reconstruction-related parameters must be optimized for best performance. In this work, a 3D point cloud tetrahedral mesh reconstruction method is evaluated for quantitative tasks. A linear image model is employed to obtain the reconstruction system matrix and five point generation strategies are studied. The evaluation is performed using the recovery coefficient, as well as voxel- and template-based estimates of bias and variance measures, computed over specific regions in the reconstructed image. A similar analysis is performed for regular grid reconstructions that use voxel basis functions. The maximum likelihood expectation maximization reconstruction algorithm is used. For the tetrahedral reconstructions, of the five point generation methods that are evaluated, three use image priors. For evaluation purposes, an object consisting of overlapping spheres with varying activity is simulated. The exact parallel projection data of this object are obtained analytically using a parallel projector, and multiple Poisson noise realizations of these exact data are generated and reconstructed using the different point generation strategies. The unconstrained nature of point placement in some of the irregular mesh-based reconstruction strategies has superior activity recovery for small, low-contrast image regions. The results show that, with an appropriately generated set of mesh points, the irregular grid reconstruction methods can out-perform reconstructions on a regular grid for mathematical phantoms, in terms of the performance measures evaluated. PMID:20736496

Evaluation of a 3D point cloud tetrahedral tomographic reconstruction method

NASA Astrophysics Data System (ADS)

Pereira, N. F.; Sitek, A.

2010-09-01

Tomographic reconstruction on an irregular grid may be superior to reconstruction on a regular grid. This is achieved through an appropriate choice of the image space model, the selection of an optimal set of points and the use of any available prior information during the reconstruction process. Accordingly, a number of reconstruction-related parameters must be optimized for best performance. In this work, a 3D point cloud tetrahedral mesh reconstruction method is evaluated for quantitative tasks. A linear image model is employed to obtain the reconstruction system matrix and five point generation strategies are studied. The evaluation is performed using the recovery coefficient, as well as voxel- and template-based estimates of bias and variance measures, computed over specific regions in the reconstructed image. A similar analysis is performed for regular grid reconstructions that use voxel basis functions. The maximum likelihood expectation maximization reconstruction algorithm is used. For the tetrahedral reconstructions, of the five point generation methods that are evaluated, three use image priors. For evaluation purposes, an object consisting of overlapping spheres with varying activity is simulated. The exact parallel projection data of this object are obtained analytically using a parallel projector, and multiple Poisson noise realizations of these exact data are generated and reconstructed using the different point generation strategies. The unconstrained nature of point placement in some of the irregular mesh-based reconstruction strategies has superior activity recovery for small, low-contrast image regions. The results show that, with an appropriately generated set of mesh points, the irregular grid reconstruction methods can out-perform reconstructions on a regular grid for mathematical phantoms, in terms of the performance measures evaluated.

Photon-phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator

NASA Astrophysics Data System (ADS)

Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping

2017-07-01

A direct photon-phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field.

Membrane triangles with corner drilling freedoms. I - The EFF element

NASA Technical Reports Server (NTRS)

Alvin, Ken; De La Fuente, Horacio M.; Haugen, Bjorn; Felippa, Carlos A.

1992-01-01

The formulation of 3-node 9-DOF membrane elements with normal-to-element-plane rotations (drilling freedoms) is examined in the context of parametrized variational principles. In particular, attention is given to the application of the extended free formulation (EFF) to the construction of a triangular membrane element with drilling freedoms that initially has complete quadratic polynomial expansions in each displacement component. The main advantage of the EFF over the free formulation triangle is that an explicit form is obtained for the higher-order stiffness.

Curious Consequences of a Miscopied Quadratic

ERIC Educational Resources Information Center

Poet, Jeffrey L.; Vestal, Donald L., Jr.

2005-01-01

The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

2017-12-01

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

Chiral transcription in self-assembled tetrahedral Eu 4L 6 chiral cages displaying sizable circularly polarized luminescence

DOE PAGES

Yeung, Chi -Tung; Yim, King -Him; Wong, Ho -Yin; ...

2017-10-24

Predictable stereoselective formation of supramolecular assembly is generally believed to be an important but complicated process. Here, we show that point chirality of a ligand decisively influences its supramolecular assembly behavior. We designed three closely related chiral ligands with different point chiralities, and observe their self-assembly into europium (Eu) tetrametallic tetrahedral cages. One ligand exhibits a highly diastereoselective assembly into homochiral (either ΔΔΔΔ or ΛΛΛΛ) Eu tetrahedral cages whereas the two other ligands, with two different approaches of loosened point chirality, lead to a significant breakdown of the diastereoselectivity to generate a mixture of (ΔΔΔΔ and ΛΛΛΛ) isomers. The cagesmore » are highly emissive (luminescence quantum yields of 16(1) to 18(1)%) and exhibit impressive circularly polarized luminescence properties (|g lum |: up to 0.16). With in-depth studies, we present an example that correlates the nonlinear enhancement of the chiroptical response to the nonlinearity dependence on point chirality.« less

Discrete Element Method Simulation of a Boulder Extraction From an Asteroid

NASA Technical Reports Server (NTRS)

Kulchitsky, Anton K.; Johnson, Jerome B.; Reeves, David M.; Wilkinson, Allen

2014-01-01

The force required to pull 7t and 40t polyhedral boulders from the surface of an asteroid is simulated using the discrete element method considering the effects of microgravity, regolith cohesion and boulder acceleration. The connection between particle surface energy and regolith cohesion is estimated by simulating a cohesion sample tearing test. An optimal constant acceleration is found where the peak net force from inertia and cohesion is a minimum. Peak pulling forces can be further reduced by using linear and quadratic acceleration functions with up to a 40% reduction in force for quadratic acceleration.

Symmetric tridiagonal structure preserving finite element model updating problem for the quadratic model

NASA Astrophysics Data System (ADS)

Rakshit, Suman; Khare, Swanand R.; Datta, Biswa Nath

2018-07-01

One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-diagonal, etc.). Though a large number of papers have been published in recent years on various aspects of solutions of this problem, papers dealing with structure preservation almost do not exist. A novel optimization based approach that preserves the symmetric tridiagonal structures of the stiffness and damping matrices is proposed in this paper. An analytical expression for the global minimum solution of the associated optimization problem along with the results of numerical experiments obtained by both the analytical expressions and by an appropriate numerical optimization algorithm are presented. The results of numerical experiments support the validity of the proposed method.

Using Linear and Quadratic Functions to Teach Number Patterns in Secondary School

ERIC Educational Resources Information Center

Kenan, Kok Xiao-Feng

2017-01-01

This paper outlines an approach to definitively find the general term in a number pattern, of either a linear or quadratic form, by using the general equation of a linear or quadratic function. This approach is governed by four principles: (1) identifying the position of the term (input) and the term itself (output); (2) recognising that each…

Exponential Thurston maps and limits of quadratic differentials

NASA Astrophysics Data System (ADS)

Hubbard, John; Schleicher, Dierk; Shishikura, Mitsuhiro

2009-01-01

We give a topological characterization of postsingularly finite topological exponential maps, i.e., universal covers g\\colon{C}to{C}setminus\\{0\\} such that 0 has a finite orbit. Such a map either is Thurston equivalent to a unique holomorphic exponential map λ e^z or it has a topological obstruction called a degenerate Levy cycle. This is the first analog of Thurston's topological characterization theorem of rational maps, as published by Douady and Hubbard, for the case of infinite degree. One main tool is a theorem about the distribution of mass of an integrable quadratic differential with a given number of poles, providing an almost compact space of models for the entire mass of quadratic differentials. This theorem is given for arbitrary Riemann surfaces of finite type in a uniform way.

Toward efficient biomechanical-based deformable image registration of lungs for image-guided radiotherapy

NASA Astrophysics Data System (ADS)

Al-Mayah, Adil; Moseley, Joanne; Velec, Mike; Brock, Kristy

2011-08-01

Both accuracy and efficiency are critical for the implementation of biomechanical model-based deformable registration in clinical practice. The focus of this investigation is to evaluate the potential of improving the efficiency of the deformable image registration of the human lungs without loss of accuracy. Three-dimensional finite element models have been developed using image data of 14 lung cancer patients. Each model consists of two lungs, tumor and external body. Sliding of the lungs inside the chest cavity is modeled using a frictionless surface-based contact model. The effect of the type of element, finite deformation and elasticity on the accuracy and computing time is investigated. Linear and quadrilateral tetrahedral elements are used with linear and nonlinear geometric analysis. Two types of material properties are applied namely: elastic and hyperelastic. The accuracy of each of the four models is examined using a number of anatomical landmarks representing the vessels bifurcation points distributed across the lungs. The registration error is not significantly affected by the element type or linearity of analysis, with an average vector error of around 2.8 mm. The displacement differences between linear and nonlinear analysis methods are calculated for all lungs nodes and a maximum value of 3.6 mm is found in one of the nodes near the entrance of the bronchial tree into the lungs. The 95 percentile of displacement difference ranges between 0.4 and 0.8 mm. However, the time required for the analysis is reduced from 95 min in the quadratic elements nonlinear geometry model to 3.4 min in the linear element linear geometry model. Therefore using linear tetrahedral elements with linear elastic materials and linear geometry is preferable for modeling the breathing motion of lungs for image-guided radiotherapy applications.

Optimization of Time-Dependent Particle Tracing Using Tetrahedral Decomposition

NASA Technical Reports Server (NTRS)

Kenwright, David; Lane, David

1995-01-01

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation and step-size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations or expensive matrix inversions. Integration accuracy is maintained using an adaptive step-size control scheme which is regulated by the path line curvature. The problem of cell-searching, point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells yet produces almost identical particle trajectories.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Extended Decentralized Linear-Quadratic-Gaussian Control

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2000-01-01

A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.

Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

NASA Astrophysics Data System (ADS)

Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin

2017-10-01

We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.

Supported Tetrahedral Oxo-Sn Catalyst: Single Site, Two Modes of Catalysis

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

Beletskiy, Evgeny V.; Hou, Xianliang; Shen, Zhongliang

2016-03-17

Mild calcination in ozone of a (POSS)-Sn- (POSS) complex grafted on silica generated a heterogenized catalyst that mostly retained the tetrahedral coordination of its homogeneous precursor, as evidenced by spectroscopic characterizations using EXAFS, NMR, UV-vis, and DRIFT. The Sn centers are accessible and uniform and can be quantified by stoichiometric pyridine poisoning. This Sn-catalyst is active in hydride transfer reactions as a typical solid Lewis acid. However, the Sn centers can also create Brønsted acidity with alcohol by binding the alcohol strongly as alkoxide and transferring the hydroxyl H to the neighboring Sn-O-Si bond. The resulting acidic silanol is activemore » in epoxide ring opening and acetalization reactions.« less

Pressure-volume relations and bulk modulus under pressure of tetrahedral compounds

NASA Astrophysics Data System (ADS)

Soma, T.; Takahashi, Y.; Kagaya, H.-M.

1985-03-01

The pressure-volume relation and the compression effect on the bulk modulus of tetrahedral compounds such as GaP, InP, ZnS, ZnSe, ZnTe and CdTe are investigated from the electronic theory of solids by using a recently presented binding force, which includes mainly covalent interactions in the pseudopotential formalism and partially ionic interactions. The calculated results of the pressure-volume relations involving the pressure-induced phase transition are useful when comparing with the experimental data under high pressure. The calculated bulk modulus of these compounds increases as the crystal volume decreases. Further, the pressure derivative of bulk modulus is not constant and decreases with the reduction of the crystal volume.

Investigating Students' Mathematical Difficulties with Quadratic Equations

ERIC Educational Resources Information Center

O'Connor, Bronwyn Reid; Norton, Stephen

2016-01-01

This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar

1989-01-01

A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

Factorization method of quadratic template

NASA Astrophysics Data System (ADS)

Kotyrba, Martin

2017-07-01

Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

Dental application of novel finite element analysis software for three-dimensional finite element modeling of a dentulous mandible from its computed tomography images.

PubMed

Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich

2013-12-01

This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.

Quadratic forms involving Green's and Robin functions

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

Dubinin, Vladimir N

2009-10-31

General inequalities for quadratic forms with coefficients depending on the values of Green's and Robin functions are obtained. These inequalities cover also the reduced moduli of strips and half-strips. Some applications of the results obtained to extremal partitioning problems and related questions of geometric function theory are discussed. Bibliography: 29 titles.

Spectroscopic criteria for identification of nuclear tetrahedral and octahedral symmetries: Illustration on a rare earth nucleus

NASA Astrophysics Data System (ADS)

Dudek, J.; Curien, D.; Dedes, I.; Mazurek, K.; Tagami, S.; Shimizu, Y. R.; Bhattacharjee, T.

2018-02-01

We formulate criteria for identification of the nuclear tetrahedral and octahedral symmetries and illustrate for the first time their possible realization in a rare earth nucleus 152Sm. We use realistic nuclear mean-field theory calculations with the phenomenological macroscopic-microscopic method, the Gogny-Hartree-Fock-Bogoliubov approach, and general point-group theory considerations to guide the experimental identification method as illustrated on published experimental data. Following group theory the examined symmetries imply the existence of exotic rotational bands on whose properties the spectroscopic identification criteria are based. These bands may contain simultaneously states of even and odd spins, of both parities and parity doublets at well-defined spins. In the exact-symmetry limit those bands involve no E 2 transitions. We show that coexistence of tetrahedral and octahedral deformations is essential when calculating the corresponding energy minima and surrounding barriers, and that it has a characteristic impact on the rotational bands. The symmetries in question imply the existence of long-lived shape isomers and, possibly, new waiting point nuclei—impacting the nucleosynthesis processes in astrophysics—and an existence of 16-fold degenerate particle-hole excitations. Specifically designed experiments which aim at strengthening the identification arguments are briefly discussed.

Dual boundary element formulation for elastoplastic fracture mechanics

NASA Astrophysics Data System (ADS)

Leitao, V.; Aliabadi, M. H.; Rooke, D. P.

1995-01-01

In this paper the extension of the dual boundary element method (DBEM) to the analysis of elastoplastic fracture mechanics (EPFM) problems is presented. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. In order to avoid collocation at crack tips, crack kinks and crack-edge corners, both crack surfaces are discretized with discontinuous quadratic boundary elements. The elasto-plastic behavior is modelled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral and/or triangular cells. This formulation was implemented for two-dimensional domains only, although there is no theoretical or numerical limitation to its application to three-dimensional ones. A center-cracked plate and a slant edge-cracked plate subjected to tensile load are analysed and the results are compared with others available in the literature. J-type integrals are calculated.

Quadratic electroabsorption studies of molecular motion in dye-doped polymers

NASA Astrophysics Data System (ADS)

Poga, Constantina; Kuzyk, Mark G.; Dirk, Carl W.

1993-02-01

This paper reports on quadratic electroabsorption studies of thin-film solid solutions of squarylium dye molecules in poly(methylmethacrylate) polymer with the aim of understanding the role of electronic and reorientational mechanisms in the third-order nonlinear-optical susceptibility. We present a generalized theory of the quadratic electrooptic response that includes both electronic mechanisms and molecular reorientation and show that the ratio of two independent third-order susceptibility tensor components, namely (chi) (3)3333/(chi) (3)1133, determines the relative contribution of each mechanism. Based on these theoretical results, we have designed and built an experiment that determines this ratio as a function of temperature and wavelength. Results show that at room temperature and near the first electronic transition wavelength, the response is dominated by the electronic mechanism, and that the reorientational contribution dominates when the sample is heated above its glass transition temperature. Furthermore, results show that, off-resonance, the sign of the imaginary part of the third-order susceptibility is positive. Quadratic electroabsorption is thus shown to be a versatile tool for measuring the imaginary part of the third-order nonlinear-optical susceptibility which yields information about the interaction of polymer and dopant molecule.

Integration of the Quadratic Function and Generalization

ERIC Educational Resources Information Center

Mitsuma, Kunio

2011-01-01

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

Relative Positioning Evaluation of a Tetrahedral Flight Formation’s Satellites

NASA Astrophysics Data System (ADS)

Mahler, W. F. C.; Rocco, E. M.; Santos, D. P. S.

2017-10-01

This paper presents a study about the tetrahedral layout of four satellites in a way that every half-orbital period this set groups together while flying in formation. The formation is calculated analyzing the problem from a geometrical perspective and disposed by precisely adjusting the orbital parameters of each satellite. The dynamic modelling considers the orbital motion equations. The results are analyzed, compared and discussed. A detection algorithm is used as flag to signal the regular tetrahedron’s exact moments of occurrence. To do so, the volume calculated during the simulation is compared to the real volume, based on the initial conditions of the exact moment of formation and respecting a tolerance. This tolerance value is stablished arbitrarily depending on the mission and the formation’s geometrical parameters. The simulations will run on a computational environment.

Strong spin-orbit effects in transition metal oxides with tetrahedral coordination

NASA Astrophysics Data System (ADS)

Forte, Filomena; Guerra, Delia; Autieri, Carmine; Romano, Alfonso; Noce, Canio; Avella, Adolfo

2018-05-01

To prove that spin-orbit coupling can play a relevant role in determining the magnetic structure of transition metal oxides with tetrahedral coordination, we investigate the d1 Mott insulator KOsO4, combining density functional theory calculations and the exact diagonalization approach. We find that the interplay between crystal field, strong spin-orbit coupling, electronic correlations and structural distortions brings the system towards an antiferromagnetic phase, characterized by a non-vanishing orbital angular momentum and anisotropy among the in-plane and the out-of-plane antiferromagnetic correlations. We also show that, due to the peculiar interplay between spin-orbit coupling, Hund's coupling and hopping connectivity the system is on the verge of developing short range ferromagnetic correlations marked by strong directionality.

Linear quadratic regulators with eigenvalue placement in a specified region

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar

1988-01-01

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at + or - pi/2k (k = 2 or 3) from the negative real axis with a sector angle of pi/2 or less, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. The design method is mainly based on the solution of a linear matrix Liapunov equation, and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.

Tuning a fuzzy controller using quadratic response surfaces

NASA Technical Reports Server (NTRS)

Schott, Brian; Whalen, Thomas

1992-01-01

Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

NASA Technical Reports Server (NTRS)

Toda, M.; Patel, R.; Sridhar, B.

1976-01-01

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations

NASA Astrophysics Data System (ADS)

Gomez, Humberto; Lopez-Arcos, Cristhiam; Talavera, Pedro

2017-10-01

In this paper we reconsider the Cachazo-He-Yuan construction (CHY) of the so called scattering amplitudes at one-loop, in order to obtain quadratic propagators. In theories with colour ordering the key ingredient is the redefinition of the Parke-Taylor factors. After classifying all the possible one-loop CHY-integrands we conjecture a new one-loop amplitude for the massless Bi-adjoint Φ3 theory. The prescription directly reproduces the quadratic propagators of the traditional Feynman approach.

Characterization of a Quadratic Function in Rn

ERIC Educational Resources Information Center

Xu, Conway

2010-01-01

It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

Emotion suppression moderates the quadratic association between RSA and executive function.

PubMed

Spangler, Derek P; Bell, Martha Ann; Deater-Deckard, Kirby

2015-09-01

There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated (a) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (b) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a 2-min resting period during which electrocardiogram (ECG) was continually assessed. In the next phase, the women completed an array of executive function and nonexecutive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. © 2015 Society for Psychophysiological Research.

Emotion suppression moderates the quadratic association between RSA and executive function

PubMed Central

Spangler, Derek P.; Bell, Martha Ann; Deater-Deckard, Kirby

2016-01-01

There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated: (1) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (2) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a two-minute resting period during which ECG was continually assessed. In the next phase, the women completed an array of executive function and non-executive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. PMID:26018941

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.

Mixed-mode high-power impulse magnetron sputter deposition of tetrahedral amorphous carbon with pulse-length control of ionization

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

Tucker, M. D.; Marks, N. A.; Ganesan, R.

2016-04-21

High-power impulse magnetron sputtering (HiPIMS) is used to deposit amorphous carbon thin films with sp{sup 3} fractions of 13% to 82%. Increasing the pulse length results in a transition from conventional HiPIMS deposition to a “mixed-mode” in which an arc triggers on the target surface, resulting in a large flux of carbon ions. The films are characterized using X-ray photoelectron spectroscopy, Raman spectroscopy, ellipsometry, nanoindentation, elastic recoil detection analysis, and measurements of stress and contact angle. All properties vary in a consistent manner, showing a high tetrahedral character only for long pulses, demonstrating that mixed-mode deposition is the source ofmore » the high carbon ion flux. Varying the substrate bias reveals an “energy window” effect, where the sp{sup 3} fraction of the films is greatest for a substrate bias around −100 V and decreases for higher or lower bias values. In the absence of bias, the films' properties show little dependence on the pulse length, showing that energetic ions are the origin of the highly tetrahedral character.« less

Finite Element Analysis of Osteosynthesis Screw Fixation in the Bone Stock: An Appropriate Method for Automatic Screw Modelling

PubMed Central

Wieding, Jan; Souffrant, Robert; Fritsche, Andreas; Mittelmeier, Wolfram; Bader, Rainer

2012-01-01

The use of finite element analysis (FEA) has grown to a more and more important method in the field of biomedical engineering and biomechanics. Although increased computational performance allows new ways to generate more complex biomechanical models, in the area of orthopaedic surgery, solid modelling of screws and drill holes represent a limitation of their use for individual cases and an increase of computational costs. To cope with these requirements, different methods for numerical screw modelling have therefore been investigated to improve its application diversity. Exemplarily, fixation was performed for stabilization of a large segmental femoral bone defect by an osteosynthesis plate. Three different numerical modelling techniques for implant fixation were used in this study, i.e. without screw modelling, screws as solid elements as well as screws as structural elements. The latter one offers the possibility to implement automatically generated screws with variable geometry on arbitrary FE models. Structural screws were parametrically generated by a Python script for the automatic generation in the FE-software Abaqus/CAE on both a tetrahedral and a hexahedral meshed femur. Accuracy of the FE models was confirmed by experimental testing using a composite femur with a segmental defect and an identical osteosynthesis plate for primary stabilisation with titanium screws. Both deflection of the femoral head and the gap alteration were measured with an optical measuring system with an accuracy of approximately 3 µm. For both screw modelling techniques a sufficient correlation of approximately 95% between numerical and experimental analysis was found. Furthermore, using structural elements for screw modelling the computational time could be reduced by 85% using hexahedral elements instead of tetrahedral elements for femur meshing. The automatically generated screw modelling offers a realistic simulation of the osteosynthesis fixation with screws in the adjacent

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre

2014-07-01

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

A Deep Penetration Problem Calculation Using AETIUS:An Easy Modeling Discrete Ordinates Transport Code UsIng Unstructured Tetrahedral Mesh, Shared Memory Parallel

NASA Astrophysics Data System (ADS)

KIM, Jong Woon; LEE, Young-Ouk

2017-09-01

As computing power gets better and better, computer codes that use a deterministic method seem to be less useful than those using the Monte Carlo method. In addition, users do not like to think about space, angles, and energy discretization for deterministic codes. However, a deterministic method is still powerful in that we can obtain a solution of the flux throughout the problem, particularly as when particles can barely penetrate, such as in a deep penetration problem with small detection volumes. Recently, a new state-of-the-art discrete-ordinates code, ATTILA, was developed and has been widely used in several applications. ATTILA provides the capabilities to solve geometrically complex 3-D transport problems by using an unstructured tetrahedral mesh. Since 2009, we have been developing our own code by benchmarking ATTILA. AETIUS is a discrete ordinates code that uses an unstructured tetrahedral mesh such as ATTILA. For pre- and post- processing, Gmsh is used to generate an unstructured tetrahedral mesh by importing a CAD file (*.step) and visualizing the calculation results of AETIUS. Using a CAD tool, the geometry can be modeled very easily. In this paper, we describe a brief overview of AETIUS and provide numerical results from both AETIUS and a Monte Carlo code, MCNP5, in a deep penetration problem with small detection volumes. The results demonstrate the effectiveness and efficiency of AETIUS for such calculations.

Unravelling Student Challenges with Quadratics: A Cognitive Approach

ERIC Educational Resources Information Center

Kotsopoulos, Donna

2007-01-01

The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

An optimal consumption and investment problem with quadratic utility and negative wealth constraints.

PubMed

Roh, Kum-Hwan; Kim, Ji Yeoun; Shin, Yong Hyun

2017-01-01

In this paper, we investigate the optimal consumption and portfolio selection problem with negative wealth constraints for an economic agent who has a quadratic utility function of consumption and receives a constant labor income. Due to the property of the quadratic utility function, we separate our problem into two cases and derive the closed-form solutions for each case. We also illustrate some numerical implications of the optimal consumption and portfolio.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

NASA Astrophysics Data System (ADS)

Szederkényi, Gábor; Hangos, Katalin M.

2004-04-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

Communications circuit including a linear quadratic estimator

DOEpatents

Ferguson, Dennis D.

2015-07-07

A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.

On a 3-D singularity element for computation of combined mode stress intensities

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Kathiresan, K.

1976-01-01

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

Morphofunctional Analysis of the Quadrate of Spinosauridae (Dinosauria: Theropoda) and the Presence of Spinosaurus and a Second Spinosaurine Taxon in the Cenomanian of North Africa.

PubMed Central

Hendrickx, Christophe; Mateus, Octávio; Buffetaut, Eric

2016-01-01

Six quadrate bones, of which two almost certainly come from the Kem Kem beds (Cenomanian, Upper Cretaceous) of south-eastern Morocco, are determined to be from juvenile and adult individuals of Spinosaurinae based on phylogenetic, geometric morphometric, and phylogenetic morphometric analyses. Their morphology indicates two morphotypes evidencing the presence of two spinosaurine taxa ascribed to Spinosaurus aegyptiacus and? Sigilmassasaurus brevicollis in the Cenomanian of North Africa, casting doubt on the accuracy of some recent skeletal reconstructions which may be based on elements from several distinct species. Morphofunctional analysis of the mandibular articulation of the quadrate has shown that the jaw mechanics was peculiar in Spinosauridae. In mature spinosaurids, the posterior parts of the two mandibular rami displaced laterally when the jaw was depressed due to a lateromedially oriented intercondylar sulcus of the quadrate. Such lateral movement of the mandibular ramus was possible due to a movable mandibular symphysis in spinosaurids, allowing the pharynx to be widened. Similar jaw mechanics also occur in some pterosaurs and living pelecanids which are both adapted to capture and swallow large prey items. Spinosauridae, which were engaged, at least partially, in a piscivorous lifestyle, were able to consume large fish and may have occasionally fed on other prey such as pterosaurs and juvenile dinosaurs. PMID:26734729

A Unified Approach to Teaching Quadratic and Cubic Equations.

ERIC Educational Resources Information Center

Ward, A. J. B.

2003-01-01

Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

Optimization of structures to satisfy a flutter velocity constraint by use of quadratic equation fitting. M.S. Thesis

NASA Technical Reports Server (NTRS)

Motiwalla, S. K.

1973-01-01

Using the first and the second derivative of flutter velocity with respect to the parameters, the velocity hypersurface is made quadratic. This greatly simplifies the numerical procedure developed for determining the values of the design parameters such that a specified flutter velocity constraint is satisfied and the total structural mass is near a relative minimum. A search procedure is presented utilizing two gradient search methods and a gradient projection method. The procedure is applied to the design of a box beam, using finite-element representation. The results indicate that the procedure developed yields substantial design improvement satisfying the specified constraint and does converge to near a local optimum.

Finding the Best Quadratic Approximation of a Function

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

Fast parallel DNA-based algorithms for molecular computation: quadratic congruence and factoring integers.

PubMed

Chang, Weng-Long

2012-03-01

Assume that n is a positive integer. If there is an integer such that M (2) ≡ C (mod n), i.e., the congruence has a solution, then C is said to be a quadratic congruence (mod n). If the congruence does not have a solution, then C is said to be a quadratic noncongruence (mod n). The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithm's submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.

Dark-bright quadratic solitons with a focusing effective Kerr nonlinearity

NASA Astrophysics Data System (ADS)

Chen, Manna; Ping, Xiaorou; Liang, Guo; Guo, Qi; Lu, Daquan; Hu, Wei

2018-01-01

Dark solitons are traditionally considered to exist in defocusing Kerr nonlinearity media. We investigate dark quadratic solitons with a focusing effective Kerr nonlinearity and a sine-oscillatory nonlocal response. A nonlinear refractive index with a focusing sine-oscillatory response leads to a defocusing effect with a strong degree of nonlocality, which causes the formation of dark solitons. By analyzing the modulational instability, we determine the parameter domain for dark quadratic solitons with a stable background and numerically obtain dark-bright soliton solutions in the form of pairs, which avoid radiative phenomena. Based on a numerical simulation, we find that all dark-bright soliton pairs are unstable after a relatively long propagation distance, and their stabilities are affected by the soliton interval and the degree of nonlocality.

Directional passability and quadratic steering logic for pyramid-type single gimbal control moment gyros

NASA Astrophysics Data System (ADS)

Yamada, Katsuhiko; Jikuya, Ichiro

2014-09-01

Singularity analysis and the steering logic of pyramid-type single gimbal control moment gyros are studied. First, a new concept of directional passability in a specified direction is introduced to investigate the structure of an elliptic singular surface. The differences between passability and directional passability are discussed in detail and are visualized for 0H, 2H, and 4H singular surfaces. Second, quadratic steering logic (QSL), a new steering logic for passing the singular surface, is investigated. The algorithm is based on the quadratic constrained quadratic optimization problem and is reduced to the Newton method by using Gröbner bases. The proposed steering logic is demonstrated through numerical simulations for both constant torque maneuvering examples and attitude control examples.

Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.

PubMed

McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T

2013-12-13

Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model.

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

Linear quadratic stochastic control of atomic hydrogen masers.

PubMed

Koppang, P; Leland, R

1999-01-01

Data are given showing the results of using the linear quadratic Gaussian (LQG) technique to steer remote hydrogen masers to Coordinated Universal Time (UTC) as given by the United States Naval Observatory (USNO) via two-way satellite time transfer and the Global Positioning System (GPS). Data also are shown from the results of steering a hydrogen maser to the real-time USNO mean. A general overview of the theory behind the LQG technique also is given. The LQG control is a technique that uses Kalman filtering to estimate time and frequency errors used as input into a control calculation. A discrete frequency steer is calculated by minimizing a quadratic cost function that is dependent on both the time and frequency errors and the control effort. Different penalties, chosen by the designer, are assessed by the controller as the time and frequency errors and control effort vary from zero. With this feature, controllers can be designed to force the time and frequency differences between two standards to zero, either more or less aggressively depending on the application.

Epitaxially stabilized iridium spinel oxide without cations in the tetrahedral site

NASA Astrophysics Data System (ADS)

Kuriyama, Hiromichi; Matsuno, Jobu; Niitaka, Seiji; Uchida, Masaya; Hashizume, Daisuke; Nakao, Aiko; Sugimoto, Kunihisa; Ohsumi, Hiroyuki; Takata, Masaki; Takagi, Hidenori

2010-05-01

Single-crystalline thin film of an iridium dioxide polymorph Ir2O4 has been fabricated by the pulsed laser deposition of LixIr2O4 precursor and the subsequent Li-deintercalation using soft chemistry. Ir2O4 crystallizes in a spinel (AB2O4) without A cations in the tetrahedral site, which is isostructural to λ-MnO2. Ir ions form a pyrochlore sublattice, which is known to give rise to a strong geometrical frustration. This Ir spinel was found to be a narrow gap insulator, in remarkable contrast to the metallic ground state of rutile-type IrO2. We argue that an interplay of a strong spin-orbit coupling and a Coulomb repulsion gives rise to an insulating ground state as in a layered perovskite Sr2IrO4.

Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

STARS: A general-purpose finite element computer program for analysis of engineering structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1984-01-01

STARS (Structural Analysis Routines) is primarily an interactive, graphics-oriented, finite-element computer program for analyzing the static, stability, free vibration, and dynamic responses of damped and undamped structures, including rotating systems. The element library consists of one-dimensional (1-D) line elements, two-dimensional (2-D) triangular and quadrilateral shell elements, and three-dimensional (3-D) tetrahedral and hexahedral solid elements. These elements enable the solution of structural problems that include truss, beam, space frame, plane, plate, shell, and solid structures, or any combination thereof. Zero, finite, and interdependent deflection boundary conditions can be implemented by the program. The associated dynamic response analysis capability provides for initial deformation and velocity inputs, whereas the transient excitation may be either forces or accelerations. An effective in-core or out-of-core solution strategy is automatically employed by the program, depending on the size of the problem. Data input may be at random within a data set, and the program offers certain automatic data-generation features. Input data are formatted as an optimal combination of free and fixed formats. Interactive graphics capabilities enable convenient display of nodal deformations, mode shapes, and element stresses.

Spatial Convergence of Three Dimensional Turbulent Flows

NASA Technical Reports Server (NTRS)

Park, Michael A.; Anderson, W. Kyle

2016-01-01

Finite-volume and finite-element schemes, both implemented within the FUN3D flow solver, are evaluated for several test cases described on the Turbulence-Modeling Resource (TMR) web site. The cases include subsonic flow over a hemisphere cylinder, subsonic flow over a swept bump configuration, and supersonic flow in a square duct. The finite- volume and finite-element schemes are both used to obtain solutions for the first two cases, whereas only the finite-volume scheme is used for the supersonic duct. For the hemisphere cylinder, finite-element solutions obtained on tetrahedral meshes are compared with finite- volume solutions on mixed-element meshes. For the swept bump, finite-volume solutions have been obtained for both hexahedral and tetrahedral meshes and are compared with finite-element solutions obtained on tetrahedral meshes. For the hemisphere cylinder and the swept bump, solutions are obtained on a series of meshes with varying grid density and comparisons are made between drag coefficients, pressure distributions, velocity profiles, and profiles of the turbulence working variable. The square duct shows small variation due to element type or the spatial accuracy of turbulence model convection. It is demonstrated that the finite-element scheme on tetrahedral meshes yields similar accuracy as the finite- volume scheme on mixed-element and hexahedral grids, and demonstrates less sensitivity to the mesh topology (biased tetrahedral grids) than the finite-volume scheme.

Solving the Integral of Quadratic Forms of Covariance Matrices for Applications in Polarimetric Radar Imagery

NASA Astrophysics Data System (ADS)

Marino, Armando; Hajnsek, Irena

2015-04-01

In this work, the solution of quadratic forms with special application to polarimetric and interferometric covariance matrices is investigated. An analytical solution for the integral of a single quadratic form is derived. Additionally, the integral of the Pol-InSAR coherence (expressed as combination of quadratic forms) is investigated. An approximation for such integral is proposed and defined as Trace coherence. Such approximation is tested on real data to verify that the error is acceptable. The trace coherence can be used for tackle problems related to change detection. Moreover, the use of the Trace coherence in model inversion (as for the RVoG three stage inversion) will be investigated in the future.

Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity.

PubMed

Li, Feilong; Zhao, Youxuan; Cao, Peng; Hu, Ning

2018-07-01

This paper investigates the propagation of Lamb waves in thin plates with quadratic nonlinearity by one-way mixing method using numerical simulations. It is shown that an A 0 -mode wave can be generated by a pair of S 0 and A 0 mode waves only when mixing condition is satisfied, and mixing wave signals are capable of locating the damage zone. Additionally, it is manifested that the acoustic nonlinear parameter increases linearly with quadratic nonlinearity but monotonously with the size of mixing zone. Furthermore, because of frequency deviation, the waveform of the mixing wave changes significantly from a regular diamond shape to toneburst trains. Copyright © 2018 Elsevier B.V. All rights reserved.

Design of linear quadratic regulators with eigenvalue placement in a specified region

NASA Technical Reports Server (NTRS)

Shieh, Leang-San; Zhen, Liu; Coleman, Norman P.

1990-01-01

Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.

Consistent linearization of the element-independent corotational formulation for the structural analysis of general shells

NASA Technical Reports Server (NTRS)

Rankin, C. C.

1988-01-01

A consistent linearization is provided for the element-dependent corotational formulation, providing the proper first and second variation of the strain energy. As a result, the warping problem that has plagued flat elements has been overcome, with beneficial effects carried over to linear solutions. True Newton quadratic convergence has been restored to the Structural Analysis of General Shells (STAGS) code for conservative loading using the full corotational implementation. Some implications for general finite element analysis are discussed, including what effect the automatic frame invariance provided by this work might have on the development of new, improved elements.

Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions

ERIC Educational Resources Information Center

Leyendekkers, J. V.; Shannon, A. G.

2004-01-01

An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

Polyamorphism in tetrahedral substances: Similarities between silicon and ice

NASA Astrophysics Data System (ADS)

Garcez, K. M. S.; Antonelli, A.

2015-07-01

Tetrahedral substances, such as silicon, water, germanium, and silica, share various unusual phase behaviors. Among them, the so-called polyamorphism, i.e., the existence of more than one amorphous form, has been intensively investigated in the last three decades. In this work, we study the metastable relations between amorphous states of silicon in a wide range of pressures, using Monte Carlo simulations. Our results indicate that the two amorphous forms of silicon at high pressures, the high density amorphous (HDA) and the very high density amorphous (VHDA), can be decompressed from high pressure (˜20 GPa) down to the tensile regime, where both convert into the same low density amorphous. Such behavior is also observed in ice. While at high pressure (˜20 GPa), HDA is less stable than VHDA, at the pressure of 10 GPa both forms exhibit similar stability. On the other hand, at much lower pressure (˜5 GPa), HDA and VHDA are no longer the most stable forms, and, upon isobaric annealing, an even less dense form of amorphous silicon emerges, the expanded high density amorphous, again in close similarity to what occurs in ice.

Hyers-Ulam stability of a generalized Apollonius type quadratic mapping

NASA Astrophysics Data System (ADS)

Park, Chun-Gil; Rassias, Themistocles M.

2006-10-01

Let X,Y be linear spaces. It is shown that if a mapping satisfies the following functional equation: then the mapping is quadratic. We moreover prove the Hyers-Ulam stability of the functional equation (0.1) in Banach spaces.

Quadratic Expressions by Means of "Summing All the Matchsticks"

ERIC Educational Resources Information Center

Gierdien, M. Faaiz

2012-01-01

This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such "matchstick" problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are…

Sequential Quadratic Programming Algorithms for Optimization

DTIC Science & Technology

1989-08-01

quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the

Tetrahedrally Coordinated Fe3+ in Silicate Glasses: A Mossbauer, Iron K-edge XANES and Raman Spectroscopies Study

NASA Astrophysics Data System (ADS)

Cochain, B.; Neuville, D. R.; McCammon, C.; Henderson, G. S.; de Ligny, D.; Pinet, O.; Richet, P.

2009-05-01

In natural or industrial glasses, iron is the most abundant transition metal. A good knowledge of its redox equilibrium is important to better understand the chemical and structural evolution of magmas (crystallization, viscosity), and also to optimize vitrification processes and properties of iron-bearing glasses. To study the role of iron in silicate glasses and melts, we have used in a consistent manner the Mössbauer, iron K-edge XANES and Raman spectroscopies to investigate several series of silicate glasses as a function of redox state. The samples were selected to cover a wide composition range and to investigate the interactions of iron with two network forming cations, namely, Al3+ and B3+. The glasses investigated were synthesized at high temperature under various conditions of oxygen fugacity to achieve different redox ratios for each composition. Therefore, the iron redox state was varied from the most oxidized to the most reduced. Iron redox ratios were first determined by wet chemical analysis and in some cases by room temperature Mossbauer spectroscopy. This experimental method was also used to determine the local structure of iron of some of the investigated glasses. These results where compared to iron K-edge XANES/EXAFS spectroscopy results, which lead to the iron redox state and indicate that Fe2+ is in octahedral coordination whereas Fe3+ is in tetrahedral coordination. In addition, Raman spectroscopy gave us information on the network polymerization of glasses. Clearly changes in Raman spectra are visible with the evolution of iron redox ratio. For a given composition, we observed systematically, in the 800-1200 cm-1 envelope, which is sensitive to the environment of tetrahedrally coordinated cations, the growth of a band with the iron content and the oxidation state of the sample. The peak area of this band, which we attribute to vibrational modes involving tetrahedrally coordinated Fe3+, increases with the oxidation of the sample. This

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

NASA Astrophysics Data System (ADS)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

The algebraic decoding of the (41, 21, 9) quadratic residue code

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Truong, T. K.; Chen, Xuemin; Yin, Xiaowei

1992-01-01

A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.

Optomechanically induced opacity and amplification in a quadratically coupled optomechanical system

NASA Astrophysics Data System (ADS)

Si, Liu-Gang; Xiong, Hao; Zubairy, M. Suhail; Wu, Ying

2017-03-01

We analyze theoretically the features of the output field of a quadratically coupled optomechanical system, which is driven by a strong coupling field and a weak signal field, and in which the membrane (treated as a mechanical resonator) is excited by a weak coherent driving field with two-phonon resonance. We show that the system exhibits complex quantum coherent and interference effects resulting in transmission of the signal field from opacity to remarkable amplification. We also find that the total phase of the applied fields can significantly adjust the signal field's transmission spectrum. The study of the propagation of the signal field in such a quadratically coupled optomechanical system proves that the proposed device can operate as an optical transistor.

Contractions and deformations of quasiclassical Lie algebras preserving a nondegenerate quadratic Casimir operator

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

Campoamor-Stursberg, R., E-mail: rutwig@mat.ucm.e

2008-05-15

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasiclassical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from noncompact real simple algebras with nonsimple complexification, where we impose that a nondegenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem and obtain sufficient conditions on integrable cocycles of quasiclassical Lie algebras in order to preserve nondegenerate quadratic Casimir operators by the associated linear deformations.

Output-Adaptive Tetrahedral Cut-Cell Validation for Sonic Boom Prediction

NASA Technical Reports Server (NTRS)

Park, Michael A.; Darmofal, David L.

2008-01-01

A cut-cell approach to Computational Fluid Dynamics (CFD) that utilizes the median dual of a tetrahedral background grid is described. The discrete adjoint is also calculated, which permits adaptation based on improving the calculation of a specified output (off-body pressure signature) in supersonic inviscid flow. These predicted signatures are compared to wind tunnel measurements on and off the configuration centerline 10 body lengths below the model to validate the method for sonic boom prediction. Accurate mid-field sonic boom pressure signatures are calculated with the Euler equations without the use of hybrid grid or signature propagation methods. Highly-refined, shock-aligned anisotropic grids were produced by this method from coarse isotropic grids created without prior knowledge of shock locations. A heuristic reconstruction limiter provided stable flow and adjoint solution schemes while producing similar signatures to Barth-Jespersen and Venkatakrishnan limiters. The use of cut-cells with an output-based adaptive scheme completely automated this accurate prediction capability after a triangular mesh is generated for the cut surface. This automation drastically reduces the manual intervention required by existing methods.

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

PubMed

Gorban, A N; Mirkes, E M; Zinovyev, A

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize arbitrary sub-quadratic error potentials using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.

A meta-model analysis of a finite element simulation for defining poroelastic properties of intervertebral discs.

PubMed

Nikkhoo, Mohammad; Hsu, Yu-Chun; Haghpanahi, Mohammad; Parnianpour, Mohamad; Wang, Jaw-Lin

2013-06-01

Finite element analysis is an effective tool to evaluate the material properties of living tissue. For an interactive optimization procedure, the finite element analysis usually needs many simulations to reach a reasonable solution. The meta-model analysis of finite element simulation can be used to reduce the computation of a structure with complex geometry or a material with composite constitutive equations. The intervertebral disc is a complex, heterogeneous, and hydrated porous structure. A poroelastic finite element model can be used to observe the fluid transferring, pressure deviation, and other properties within the disc. Defining reasonable poroelastic material properties of the anulus fibrosus and nucleus pulposus is critical for the quality of the simulation. We developed a material property updating protocol, which is basically a fitting algorithm consisted of finite element simulations and a quadratic response surface regression. This protocol was used to find the material properties, such as the hydraulic permeability, elastic modulus, and Poisson's ratio, of intact and degenerated porcine discs. The results showed that the in vitro disc experimental deformations were well fitted with limited finite element simulations and a quadratic response surface regression. The comparison of material properties of intact and degenerated discs showed that the hydraulic permeability significantly decreased but Poisson's ratio significantly increased for the degenerated discs. This study shows that the developed protocol is efficient and effective in defining material properties of a complex structure such as the intervertebral disc.

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

NASA Astrophysics Data System (ADS)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

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

Zhao Yunbin, E-mail: zhaoyy@maths.bham.ac.u

2010-12-15

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the conditionmore » number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.« less

Design of Semiconducting Tetrahedral Mn 1-xZn xO Alloys and Their Application to Solar Water Splitting

DOE PAGES

Peng, Haowei; Ndione, Paul F.; Ginley, David S.; ...

2015-03-18

Transition metal oxides play important roles as contact and electrode materials, but their use as active layers in solar energy conversion requires achieving semiconducting properties akin to those of conventional semiconductors like Si or GaAs. In particular, efficient bipolar carrier transport is a challenge in these materials. Based on the prediction that a tetrahedral polymorph of MnO should have such desirable semiconducting properties, and the possibility to overcome thermodynamic solubility limits by nonequilibrium thin-film growth, we exploit both structure-property and composition-structure relationships to design and realize novel wurtzite-structure Mn 1₋xZn xO alloys. At Zn compositions above x≈0.3, thin films ofmore » these alloys assume the tetrahedral wurtzite structure instead of the octahedral rocksalt structure of MnO, thereby enabling semiconductor properties that are unique among transition metal oxides, i.e., a band gap within the visible spectrum, a band-transport mechanism for both electron and hole carriers, electron doping, and a band lineup suitable for solar hydrogen generation. In conclusion, a proof of principle is provided by initial photo-electrocatalytic device measurements, corroborating, in particular, the predicted favorable hole-transport properties of these alloys.« less

Quadratic Electro-optic Effect in a Novel Nonconjugated Conductive Polymer, iodine-doped Polynorbornene

NASA Astrophysics Data System (ADS)

Narayanan, Ananthakrishnan; Thakur, Mrinal

2009-03-01

Quadratic electro-optic effect in a novel nonconjugated conductive polymer, iodine-doped polynorbornene has been measured using field-induced birefringence at 633 nm. The electrical conductivity^1 of polynorbornene increases by twelve orders of magnitude to about 0.01 S/cm upon doping with iodine. The electro-optic measurement has been made in a film doped at the medium doping-level. The electro-optic modulation signal was recorded using a lock-in amplifier for various applied ac voltages (4 kHz) and the quadratic dependence of the modulation on the applied voltage was observed. A modulation of about 0.01% was observed for an applied electric field of 3 V/micron for a 100 nm thick film The Kerr coefficient as determined is about 1.77x10-11m/V^2. This exceptionally large quadratic electro-optic effect has been attributed to the confinement of this charge-transfer system within a sub-nanometer dimension. 1. A. Narayanan, A. Palthi and M. Thakur, J. Macromol. Sci. -- PAC, accepted.

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.

2002-01-01

Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

Design of reinforced areas of concrete column using quadratic polynomials

NASA Astrophysics Data System (ADS)

Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.

2017-11-01

Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.

Revealing Ozgur's Thoughts of a Quadratic Function with a Clinical Interview: Concepts and Their Underlying Reasons

ERIC Educational Resources Information Center

Ozaltun Celik, Aytug; Bukova Guzel, Esra

2017-01-01

The quadratic function is an important concept for calculus but the students at high school have many difficulties related to this concept. It is important that the teaching of the quadratic function is realized considering the students' thinking. In this context, the aim of this study conducted through a qualitative case study is to reveal the…

Symmetry-breaking instability of quadratic soliton bound states

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

Delque, Michaeel; Departement d'Optique P.M. Duffieux, Institut FEMTO-ST, Universite de Franche-Comte, CNRS UMR 6174, F-25030 Besancon; Fanjoux, Gil

We study both numerically and experimentally two-dimensional soliton bound states in quadratic media and demonstrate their symmetry-breaking instability. The experiment is performed in a potassium titanyl phosphate crystal in a type-II configuration. The bound state is generated by the copropagation of the antisymmetric fundamental beam locked in phase with the symmetrical second harmonic one. Experimental results are in good agreement with numerical simulations of the nonlinear wave equations.

Linear quadratic regulators with eigenvalue placement in a horizontal strip

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar

1987-01-01

A method for optimally shifting the imaginary parts of the open-loop poles of a multivariable control system to the desirable closed-loop locations is presented. The optimal solution with respect to a quadratic performance index is obtained by solving a linear matrix Liapunov equation.

Stochastic resonance in a fractional oscillator driven by multiplicative quadratic noise

NASA Astrophysics Data System (ADS)

Ren, Ruibin; Luo, Maokang; Deng, Ke

2017-02-01

Stochastic resonance of a fractional oscillator subject to an external periodic field as well as to multiplicative and additive noise is investigated. The fluctuations of the eigenfrequency are modeled as the quadratic function of the trichotomous noise. Applying the moment equation method and Shapiro-Loginov formula, we obtain the exact expression of the complex susceptibility and related stability criteria. Theoretical analysis and numerical simulations indicate that the spectral amplification (SPA) depends non-monotonicly both on the external driving frequency and the parameters of the quadratic noise. In addition, the investigations into fractional stochastic systems have suggested that both the noise parameters and the memory effect can induce the phenomenon of stochastic multi-resonance (SMR), which is previously reported and believed to be absent in the case of the multiplicative noise with only a linear term.

Interdependence of different symmetry energy elements

NASA Astrophysics Data System (ADS)

Mondal, C.; Agrawal, B. K.; De, J. N.; Samaddar, S. K.; Centelles, M.; Viñas, X.

2017-08-01

Relations between the nuclear symmetry energy coefficient and its density derivatives are derived. The relations hold for a class of interactions with quadratic momentum dependence and a power-law density dependence. The structural connection between the different symmetry energy elements as obtained seems to be followed by almost all reasonable nuclear energy density functionals, both relativistic and nonrelativistic, suggesting a universality in the correlation structure. This, coupled with known values of some well-accepted constants related to nuclear matter, helps in constraining values of different density derivatives of the nuclear symmetry energy, shedding light on the isovector part of the nuclear interaction.

An amplitude and phase hybrid modulation Fresnel diffractive optical element

NASA Astrophysics Data System (ADS)

Li, Fei; Cheng, Jiangao; Wang, Mengyu; Jin, Xueying; Wang, Keyi

2018-04-01

An Amplitude and Phase Hybrid Modulation Fresnel Diffractive Optical Element (APHMFDOE) is proposed here. We have studied the theory of APHMFDOE and simulated the focusing properties of it along the optical axis, which show that the focus can be blazed to other positions with changing the quadratic phase factor. Moreover, we design a Composite Fresnel Diffraction Optical Element (CFDOE) based on the characteristics of APHMFDOE. It greatly increases the outermost zone width without changing the F-number, which brings a lot of benefits to the design and processing of diffraction device. More importantly, the diffraction efficiency of the CFDOE is almost unchanged compared with AFZP at the same focus.

Thermal response test data of five quadratic cross section precast pile heat exchangers.

PubMed

Alberdi-Pagola, Maria

2018-06-01

This data article comprises records from five Thermal Response Tests (TRT) of quadratic cross section pile heat exchangers. Pile heat exchangers, typically referred to as energy piles, consist of traditional foundation piles with embedded heat exchanger pipes. The data presented in this article are related to the research article entitled "Comparing heat flow models for interpretation of precast quadratic pile heat exchanger thermal response tests" (Alberdi-Pagola et al., 2018) [1]. The TRT data consists of measured inlet and outlet temperatures, fluid flow and injected heat rate recorded every 10 min. The field dataset is made available to enable model verification studies.

Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

NASA Astrophysics Data System (ADS)

Zou, Defeng; Li, Xiaohui; Chai, Tong; Zheng, Hairong

2018-05-01

In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

ERIC Educational Resources Information Center

Brilleslyper, Michael A.

2004-01-01

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Entanglement in a model for Hawking radiation: An application of quadratic algebras

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

Bambah, Bindu A., E-mail: bbsp@uohyd.ernet.in; Mukku, C., E-mail: mukku@iiit.ac.in; Shreecharan, T., E-mail: shreecharan@gmail.com

2013-03-15

Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, wemore » study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.« less

Quadratic semiparametric Von Mises calculus

PubMed Central

Robins, James; Li, Lingling; Tchetgen, Eric

2009-01-01

We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter. For parameters for which the matching cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n–1/2-rate. In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n–1/2-rate. PMID:23087487

A decentralized linear quadratic control design method for flexible structures

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1990-01-01

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

PubMed Central

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. PMID:26381742

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

PubMed

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

Learning quadratic receptive fields from neural responses to natural stimuli.

PubMed

Rajan, Kanaka; Marre, Olivier; Tkačik, Gašper

2013-07-01

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high-dimensional input. In this review, we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g., naturalistic) stimulus distribution, we review several inference methods, focusing in particular on two information theory-based approaches (maximization of stimulus energy and of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered covariance and extensions of generalized linear models). We analyze the formal relationship between the likelihood-based and information-based approaches to demonstrate how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

Multi-Criterion Preliminary Design of a Tetrahedral Truss Platform

NASA Technical Reports Server (NTRS)

Wu, K. Chauncey

1995-01-01

An efficient method is presented for multi-criterion preliminary design and demonstrated for a tetrahedral truss platform. The present method requires minimal analysis effort and permits rapid estimation of optimized truss behavior for preliminary design. A 14-m-diameter, 3-ring truss platform represents a candidate reflector support structure for space-based science spacecraft. The truss members are divided into 9 groups by truss ring and position. Design variables are the cross-sectional area of all members in a group, and are either 1, 3 or 5 times the minimum member area. Non-structural mass represents the node and joint hardware used to assemble the truss structure. Taguchi methods are used to efficiently identify key points in the set of Pareto-optimal truss designs. Key points identified using Taguchi methods are the maximum frequency, minimum mass, and maximum frequency-to-mass ratio truss designs. Low-order polynomial curve fits through these points are used to approximate the behavior of the full set of Pareto-optimal designs. The resulting Pareto-optimal design curve is used to predict frequency and mass for optimized trusses. Performance improvements are plotted in frequency-mass (criterion) space and compared to results for uniform trusses. Application of constraints to frequency and mass and sensitivity to constraint variation are demonstrated.

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

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2014-10-01

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

Free Energy Defect Model for the Cu-In-Ga-Se Tetrahedral Lattice

NASA Astrophysics Data System (ADS)

Stanbery, B. J.

2003-03-01

The most efficient thin-film photovoltaic converters of solar insolation to electrical power have recently achieved conversion efficiencies exceeding 19%, and are based on light absorbing layers containing the binary alloy (CuInSe_2)_1-X(CuGaSe_2)X of the α phases of these ternary chalcopyrite compounds. A statistical quantum mechanical model of the thermodynamic equilibrium defect structure of the tetrahedral lattice of copper, indium, and selenium with composition in the domain between that of the stoichiometric CuIn_1-XGa_XSe2 alloy and the β phase Cu(In_1-XGa_X)_3Se5 composition is presented. Compositions more copper-deficient than the latter have been reported experimentally to result in a breakdown of the tetrahedral coordination characteristic of the chalcopyrite lattice. These computations are based on a cluster expansion algorithm that minimizes the total free energy of the system using the Gibbs-Duhem equation to compute quasichemical reaction equilibria between the neutral clusters, and explicitly incorporates Fermi-Dirac statistics to determine their ionization equilibria and consequent carrier concentrations in the conduction and valence bands. The results are consistent with recent experimental evidence that the stoichiometric CuIn_1-XGa_XSe2 composition segregates in equilibrium into a two-phase mixture of a copper-deficient quaternary Cu_1-γIn_1-XGa_XSe2 composition and the binary Cu_2-δSe compound. The model predicts that the hole majority carrier (p-type) can only be achieved in the equilibrium single-phase chalcopyrite lattice with compositions that correspond to Cu_1-γIn_1-XGa_XSe_2+ɛ with γ and ɛ >0. This predicted requirement for selenium enrichment compared to the stoichiometric CuIn_1-XGa_XSe2 alloy composition for the dominance of holes over electrons as the majority carrier type is consistent with experimental evidence, and is explained in terms of a transition of the dominant lattice defect from the selenium vacancy in the

Soft Chemistry, Coloring and Polytypism in Filled Tetrahedral Semiconductors: Toward Enhanced Thermoelectric and Battery Materials.

PubMed

White, Miles A; Medina-Gonzalez, Alan M; Vela, Javier

2018-03-12

Filled tetrahedral semiconductors are a rich family of compounds with tunable electronic structure, making them ideal for applications in thermoelectrics, photovoltaics, and battery anodes. Furthermore, these materials crystallize in a plethora of related structures that are very close in energy, giving rise to polytypism through the manipulation of synthetic parameters. This Minireview highlights recent advances in the solution-phase synthesis and nanostructuring of these materials. These methods enable the synthesis of metastable phases and polytypes that were previously unobtainable. Additionally, samples synthesized in solution phase have enhanced thermoelectric performance due to their decreased grain size. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

NASA Astrophysics Data System (ADS)

Du, Liang; Zhou, Xiaoting; Fiete, Gregory A.

2017-01-01

In this paper we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three-band model, while leaving the flat band dispersionless. We find a small gap is also opened at the quadratic band touching point by two-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this three-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems.

A linear quadratic regulator approach to the stabilization of uncertain linear systems

NASA Technical Reports Server (NTRS)

Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.

1990-01-01

This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.

Linear-Quadratic Control of a MEMS Micromirror using Kalman Filtering

DTIC Science & Technology

2011-12-01

LINEAR-QUADRATIC CONTROL OF A MEMS MICROMIRROR USING KALMAN FILTERING THESIS Jamie P...A MEMS MICROMIRROR USING KALMAN FILTERING THESIS Presented to the Faculty Department of Electrical Engineering Graduate School of...actuated micromirrors fabricated by PolyMUMPs. Successful application of these techniques enables demonstration of smooth, stable deflections of 50% and

A simple and efficient shear-flexible plate bending element

NASA Technical Reports Server (NTRS)

Chaudhuri, Reaz A.

1987-01-01

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

Tetrahedral Arrangements of Perylene Bisimide Columns via Supramolecular Orientational Memory.

PubMed

Sahoo, Dipankar; Peterca, Mihai; Aqad, Emad; Partridge, Benjamin E; Heiney, Paul A; Graf, Robert; Spiess, Hans W; Zeng, Xiangbing; Percec, Virgil

2017-01-24

Chiral, shape, and liquid crystalline memory effects are well-known to produce commercial macroscopic materials with important applications as springs, sensors, displays, and memory devices. A supramolecular orientational memory effect that provides complex nanoscale arrangements was only recently reported. This supramolecular orientational memory was demonstrated to preserve the molecular orientation and packing within supramolecular units of a self-assembling cyclotriveratrylene crown at the nanoscale upon transition between its columnar hexagonal and Pm3̅n cubic periodic arrays. Here we report the discovery of supramolecular orientational memory in a dendronized perylene bisimide (G2-PBI) that self-assembles into tetrameric crowns and subsequently self-organizes into supramolecular columns and spheres. This supramolecular orientation memory upon transition between columnar hexagonal and body-centered cubic (BCC) mesophases preserves the 3-fold cubic [111] orientations rather than the 4-fold [100] axes, generating an unusual tetrahedral arrangement of supramolecular columns. These results indicate that the supramolecular orientational memory concept may be general for periodic arrays of self-assembling dendrons and dendrimers as well as for other periodic and quasiperiodic nanoscale organizations comprising supramolecular spheres, generated from other organized complex soft matter including block copolymers and surfactants.

Elegant Ince-Gaussian beams in a quadratic-index medium

NASA Astrophysics Data System (ADS)

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2011-09-01

Elegant Ince—Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince—Gaussian beams and they display better symmetry between the Ince-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince—Gaussian beams are discussed.

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

A quadratic regression modelling on paddy production in the area of Perlis

NASA Astrophysics Data System (ADS)

Goh, Aizat Hanis Annas; Ali, Zalila; Nor, Norlida Mohd; Baharum, Adam; Ahmad, Wan Muhamad Amir W.

2017-08-01

Polynomial regression models are useful in situations in which the relationship between a response variable and predictor variables is curvilinear. Polynomial regression fits the nonlinear relationship into a least squares linear regression model by decomposing the predictor variables into a kth order polynomial. The polynomial order determines the number of inflexions on the curvilinear fitted line. A second order polynomial forms a quadratic expression (parabolic curve) with either a single maximum or minimum, a third order polynomial forms a cubic expression with both a relative maximum and a minimum. This study used paddy data in the area of Perlis to model paddy production based on paddy cultivation characteristics and environmental characteristics. The results indicated that a quadratic regression model best fits the data and paddy production is affected by urea fertilizer application and the interaction between amount of average rainfall and percentage of area defected by pest and disease. Urea fertilizer application has a quadratic effect in the model which indicated that if the number of days of urea fertilizer application increased, paddy production is expected to decrease until it achieved a minimum value and paddy production is expected to increase at higher number of days of urea application. The decrease in paddy production with an increased in rainfall is greater, the higher the percentage of area defected by pest and disease.

Constraints on both the quadratic and quartic symmetry energy coefficients by 2β --decay energies

NASA Astrophysics Data System (ADS)

Wan, Niu; Xu, Chang; Ren, Zhongzhou; Liu, Jie

2018-05-01

In this Rapid Communication, the 2 β- -decay energies Q (2 β-) given in the atomic mass evaluation are used to extract not only the quadratic volume symmetry energy coefficient csymv, but also the quartic one csym,4 v. Based on the modified Bethe-Weizsäcker nuclear mass formula of the liquid-drop model, the decay energy Q (2 β-) is found to be closely related to both the quadratic and quartic symmetry energy coefficients csymv and csym,4 v. There are totally 449 data of decay energies Q (2 β-) used in the present analysis where the candidate nuclei are carefully chosen by fulfilling the following criteria: (1) large neutron-proton number difference N -Z , (2) large isospin asymmetry I , and (3) limited shell effect. The values of csymv and csym,4 v are extracted to be 29.345 and 3.634 MeV, respectively. Moreover, the quadratic surface-volume symmetry energy coefficient ratio is determined to be κ =csyms/csymv=1.356 .

SERS assay of telomerase activity at single-cell level and colon cancer tissues via quadratic signal amplification.

PubMed

Shi, Muling; Zheng, Jing; Liu, Changhui; Tan, Guixiang; Qing, Zhihe; Yang, Sheng; Yang, Jinfeng; Tan, Yongjun; Yang, Ronghua

2016-03-15

As an important biomarker and therapeutic target, telomerase has attracted extensive attention concerning its detection and monitoring. Recently, enzyme-assisted amplification approaches have provided useful platforms for the telomerase activity detection, however, further improvement in sensitivity is still hindered by the single-step signal amplification. Herein, we develop a quadratic signal amplification strategy for ultrasensitive surface-enhanced Raman scattering (SERS) detection of telomerase activity. The central idea of our design is using telomerase-induced silver nanoparticles (AgNPs) assembly and silver ions (Ag(+))-mediated cascade amplification. In our approach, each telomerase-aided DNA sequence extension could trigger the formation of a long double-stranded DNA (dsDNA), making numerous AgNPs assembling along with this long strand through specific Ag-S bond, to form a primary amplification element. For secondary amplification, each conjugated AgNP was dissolved into Ag(+), which can effectively induce the 4-aminobenzenethiol (4-ABT) modified gold nanoparticles (AuNPs@4-ABT) to undergo aggregation to form numerous "hot-spots". Through quadratic amplifications, a limit of detection down to single HeLa cell was achieved. More importantly, this method demonstrated good performance when applied to tissues from colon cancer patients, which exhibits great potential in the practical application of telomerase-based cancer diagnosis in early stages. To demonstrate the potential in screening the telomerase inhibitors and telomerase-targeted drugs, the proposed design is successfully employed to measure the inhibition of telomerase activity by 3'-azido-3'-deoxythymidine. Copyright © 2015 Elsevier B.V. All rights reserved.

An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.

PubMed

Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P

2012-01-01

The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example

QUADrATiC: scalable gene expression connectivity mapping for repurposing FDA-approved therapeutics.

PubMed

O'Reilly, Paul G; Wen, Qing; Bankhead, Peter; Dunne, Philip D; McArt, Darragh G; McPherson, Suzanne; Hamilton, Peter W; Mills, Ken I; Zhang, Shu-Dong

2016-05-04

Gene expression connectivity mapping has proven to be a powerful and flexible tool for research. Its application has been shown in a broad range of research topics, most commonly as a means of identifying potential small molecule compounds, which may be further investigated as candidates for repurposing to treat diseases. The public release of voluminous data from the Library of Integrated Cellular Signatures (LINCS) programme further enhanced the utilities and potentials of gene expression connectivity mapping in biomedicine. We describe QUADrATiC ( http://go.qub.ac.uk/QUADrATiC ), a user-friendly tool for the exploration of gene expression connectivity on the subset of the LINCS data set corresponding to FDA-approved small molecule compounds. It enables the identification of compounds for repurposing therapeutic potentials. The software is designed to cope with the increased volume of data over existing tools, by taking advantage of multicore computing architectures to provide a scalable solution, which may be installed and operated on a range of computers, from laptops to servers. This scalability is provided by the use of the modern concurrent programming paradigm provided by the Akka framework. The QUADrATiC Graphical User Interface (GUI) has been developed using advanced Javascript frameworks, providing novel visualization capabilities for further analysis of connections. There is also a web services interface, allowing integration with other programs or scripts. QUADrATiC has been shown to provide an improvement over existing connectivity map software, in terms of scope (based on the LINCS data set), applicability (using FDA-approved compounds), usability and speed. It offers potential to biological researchers to analyze transcriptional data and generate potential therapeutics for focussed study in the lab. QUADrATiC represents a step change in the process of investigating gene expression connectivity and provides more biologically-relevant results than

Detailed intermolecular structure of molecular liquids containing slightly distorted tetrahedral molecules with C(3v) symmetry: chloroform, bromoform, and methyl-iodide.

PubMed

Pothoczki, Szilvia; Temleitner, László; Pusztai, László

2011-01-28

Analyses of the intermolecular structure of molecular liquids containing slightly distorted tetrahedral molecules of the CXY(3)-type are described. The process is composed of the determination of several different distance-dependent orientational correlation functions, including ones that are introduced here. As a result, a complete structure classification could be provided for CXY(3) molecular liquids, namely for liquid chloroform, bromoform, and methyl-iodide. In the present work, the calculations have been conducted on particle configurations resulting from reverse Monte Carlo computer modeling: these particle arrangements have the advantage that they are fully consistent with structure factors from neutron and x-ray diffraction measurements. It has been established that as the separation between neighboring molecules increases, the dominant mutual orientations change from face-to-face to edge-to-edge, via the edge-to-face arrangements. Depending on the actual liquid, these geometrical elements (edges and faces of the distorted tetrahedra) were found to contain different atoms. From the set of liquids studied here, the structure of methyl-iodide was found to be easiest to describe on the basis of pure steric effects (molecular shape, size, and density) and the structure of liquid chloroform seems to be the furthest away from the corresponding "flexible fused hard spheres" like reference system.

Design of Linear Quadratic Regulators and Kalman Filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L.

1986-01-01

AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

Influence of total soluble salt concentration on growth and elemental concentration of winged bean seedlings, Psophocarpus tetragonolobus (L. ) DC

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

Csizinszky, A.A.

Winged bean (Psophocarpus tetragonolobus) (L.) DC) seedlings of the accession TPT-1, were grown in a greenhouse with graded, balanced total soluble salt (TSS) concentrations. After 45 days, plant height increased quadratically, with a maximum (149 cm) at 3000 ppm TSS. Seedlings were shortest at 1000 and 10,000 ppm TSS, 44.0 and 79.0 cm, respectively. Fresh weight of shoots increased quadratically with greatest weight, 29.03 g, at 5000 ppm TSS. Percent dry matter increased linearly with increasing TSS. Concentration of N, K and P increased quadratically with an increase in the TSS concentration in the growth medium. Concentration of Ca decreasedmore » quadratically with increasing TSS. Among the micronutrients, Fe and Mo concentration was quadratic, both elements were highest in the seedlings at 1000 and 10,000 ppm TSS rates. Concentrations of Mn and Zn increased linearly with increasing TSS. Winged bean seedlings at the 1000 to 3000 ppm TSS rates had spindly stems and a sparse, yellow foliage, typical for winged bean seedlings observed in the field during the first 4 to 5 weeks of growth. Seedlings at the 4000 and 5000 ppm TSS rates had sturdy stems and an abundant green foliage. At higher TSS concentrations, 5000 to 10,000 ppm TSS, seedlings had short intermodes and dark green foliage.« less

Field-antifield and BFV formalisms for quadratic systems with open gauge algebras

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

Nirov, K.S.; Razumov, A.V.

1992-09-20

In this paper the Lagrangian field-antifield (BV) and Hamiltonian (BFV) BRST formalisms for the general quadratic systems with open gauge algebra are considered. The equivalence between the Lagrangian and Hamiltonian formalisms is proven.

Quasi-automatic 3D finite element model generation for individual single-rooted teeth and periodontal ligament.

PubMed

Clement, R; Schneider, J; Brambs, H-J; Wunderlich, A; Geiger, M; Sander, F G

2004-02-01

The paper demonstrates how to generate an individual 3D volume model of a human single-rooted tooth using an automatic workflow. It can be implemented into finite element simulation. In several computational steps, computed tomography data of patients are used to obtain the global coordinates of the tooth's surface. First, the large number of geometric data is processed with several self-developed algorithms for a significant reduction. The most important task is to keep geometrical information of the real tooth. The second main part includes the creation of the volume model for tooth and periodontal ligament (PDL). This is realized with a continuous free form surface of the tooth based on the remaining points. Generating such irregular objects for numerical use in biomechanical research normally requires enormous manual effort and time. The finite element mesh of the tooth, consisting of hexahedral elements, is composed of different materials: dentin, PDL and surrounding alveolar bone. It is capable of simulating tooth movement in a finite element analysis and may give valuable information for a clinical approach without the restrictions of tetrahedral elements. The mesh generator of FE software ANSYS executed the mesh process for hexahedral elements successfully.

First report of soybean pest, Euschistus quadrator (Hempitera: pentatomidae) in Mississippi

USDA-ARS?s Scientific Manuscript database

Here we report on the first state and county record of Euschistus quadrator Ralston (Hemiptera: Pentatomidae) in Washington County, Mississippi. The species has been documented from Honduras to Virginia primarily on soybeans, cotton, various row crops, fruit, and non-crop hosts. The local impact...

Importance of the cutoff value in the quadratic adaptive integrate-and-fire model.

PubMed

Touboul, Jonathan

2009-08-01

The quadratic adaptive integrate-and-fire model (Izhikevich, 2003 , 2007 ) is able to reproduce various firing patterns of cortical neurons and is widely used in large-scale simulations of neural networks. This model describes the dynamics of the membrane potential by a differential equation that is quadratic in the voltage, coupled to a second equation for adaptation. Integration is stopped during the rise phase of a spike at a voltage cutoff value V(c) or when it blows up. Subsequently the membrane potential is reset, and the adaptation variable is increased by a fixed amount. We show in this note that in the absence of a cutoff value, not only the voltage but also the adaptation variable diverges in finite time during spike generation in the quadratic model. The divergence of the adaptation variable makes the system very sensitive to the cutoff: changing V(c) can dramatically alter the spike patterns. Furthermore, from a computational viewpoint, the divergence of the adaptation variable implies that the time steps for numerical simulation need to be small and adaptive. However, divergence of the adaptation variable does not occur for the quartic model (Touboul, 2008 ) and the adaptive exponential integrate-and-fire model (Brette & Gerstner, 2005 ). Hence, these models are robust to changes in the cutoff value.

Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

NASA Astrophysics Data System (ADS)

Du, Liang; Zhou, Xiaoting; Fiete, Gregory; The CenterComplex Quantum Systems Team

In this work we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three band model, while leaving the flat-band dispersionless. We find a small gap is also opened at the quadratic band touching point by 2-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this 3-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems. We gratefully acknowledge funding from ARO Grant W911NF-14-1-0579 and NSF DMR-1507621.

Confidence set interference with a prior quadratic bound. [in geophysics

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

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.

Highly parallel demagnetization field calculation using the fast multipole method on tetrahedral meshes with continuous sources

NASA Astrophysics Data System (ADS)

Palmesi, P.; Exl, L.; Bruckner, F.; Abert, C.; Suess, D.

2017-11-01

The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Computational improvements can relieve problems related to this bottleneck. This work presents an efficient implementation of the Fast Multipole Method [FMM] for the magnetic scalar potential as used in micromagnetics. The novelty lies in extending FMM to linearly magnetized tetrahedral sources making it interesting also for other areas of computational physics. We treat the near field directly and in use (exact) numerical integration on the multipole expansion in the far field. This approach tackles important issues like the vectorial and continuous nature of the magnetic field. By using FMM the calculations scale linearly in time and memory.

Design of Linear-Quadratic-Regulator for a CSTR process

NASA Astrophysics Data System (ADS)

Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.

2017-11-01

This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory

NASA Technical Reports Server (NTRS)

Koppang, Paul; Leland, Robert

1996-01-01

Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.

Theoretical Studies of Routes to Synthesis of Tetrahedral N4

NASA Technical Reports Server (NTRS)

Lee, Timothy J.; Dateo, Christopher E.

2007-01-01

A paper [Chem. Phys. Lett. 345, 295 (2001)] describes theoretical studies of excited electronic states of nitrogen molecules, with a view toward utilizing those states in synthesizing tetrahedral N4, or Td N4 a metastable substance under consideration as a high-energy-density rocket fuel. Several ab initio theoretical approaches were followed in these studies, including complete active space self-consistent field (CASSCF), state-averaged CASSCF (SA-CASSCF), singles configuration interaction (CIS), CIS with second-order and third-order correlation corrections [CIS(D) and CIS(3)], and linear response singles and doubles coupled-cluster (LRCCSD). Standard double zeta polarized and triple zeta double polarized one-particle basis sets were used. The CASSCF calculations overestimated the excitation energies, while SACASSCF calculations partly corrected these overestimates. The accuracy of the CIS calculations varied, depending on the particular state, while the CIS(D), CIS(3), and LRCCSD results were in generally good agreement. The energies of the lowest six excited singlet states of Td N4 as calculated by the LRCCSD were compared with the energies of possible excited states of N2 + N2 fragments, leading to the conclusion that the most likely route for synthesis of Td N4 would involve a combination of two bound quintet states of N2.

Visualising the Complex Roots of Quadratic Equations with Real Coefficients

ERIC Educational Resources Information Center

Bardell, Nicholas S.

2012-01-01

The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

Vagal activity is quadratically related to prosocial traits, prosocial emotions, and observer perceptions of prosociality.

PubMed

Kogan, Aleksandr; Oveis, Christopher; Carr, Evan W; Gruber, June; Mauss, Iris B; Shallcross, Amanda; Impett, Emily A; van der Lowe, Ilmo; Hui, Bryant; Cheng, Cecilia; Keltner, Dacher

2014-12-01

In the present article, we introduce the quadratic vagal activity-prosociality hypothesis, a theoretical framework for understanding the vagus nerve's involvement in prosociality. We argue that vagus nerve activity supports prosocial behavior by regulating physiological systems that enable emotional expression, empathy for others' mental and emotional states, the regulation of one's own distress, and the experience of positive emotions. However, we contend that extremely high levels of vagal activity can be detrimental to prosociality. We present 3 studies providing support for our model, finding consistent evidence of a quadratic relationship between respiratory sinus arrhythmia--the degree to which the vagus nerve modulates the heart rate--and prosociality. Individual differences in vagal activity were quadratically related to prosocial traits (Study 1), prosocial emotions (Study 2), and outside ratings of prosociality by complete strangers (Study 3). Thus, too much or too little vagal activity appears to be detrimental to prosociality. The present article provides the 1st theoretical and empirical account of the nonlinear relationship between vagal activity and prosociality.

Quadratic integrand double-hybrid made spin-component-scaled

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

Brémond, Éric, E-mail: eric.bremond@iit.it; Savarese, Marika; Sancho-García, Juan C.

2016-03-28

We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.

Modeling hemodynamics in intracranial aneurysms: Comparing accuracy of CFD solvers based on finite element and finite volume schemes.

PubMed

Botti, Lorenzo; Paliwal, Nikhil; Conti, Pierangelo; Antiga, Luca; Meng, Hui

2018-06-01

Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms (IAs) but its adoption in the clinical practice has been missing, partially due to lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations CFD solvers generally rely on two spatial discretization schemes: Finite Volume (FV) and Finite Element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study we benchmark two representative CFD solvers in simulating flow in a patient-specific IA model: (1) ANSYS Fluent, a commercial FV-based solver and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provide better accuracy per degree of freedom but worse accuracy per Jacobian non-zero entry as compared to FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between under-resolved velocity fields suggests that mesh independence is reached following different paths. This article is protected by copyright. All rights reserved.

Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Martin, Corless

2004-01-01

We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

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

Lee, T.-W, E-mail: attwl@asu.edu; An, Keju

2016-06-15

We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

An application of nonlinear programming to the design of regulators of a linear-quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

Fast and Exact Fiber Surfaces for Tetrahedral Meshes.

PubMed

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

2017-07-01

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

Mapping the absolute magnetic field and evaluating the quadratic Zeeman-effect-induced systematic error in an atom interferometer gravimeter

NASA Astrophysics Data System (ADS)

Hu, Qing-Qing; Freier, Christian; Leykauf, Bastian; Schkolnik, Vladimir; Yang, Jun; Krutzik, Markus; Peters, Achim

2017-09-01

Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the μ Gal regime (1 μ Gal =10-8m /s2 ≈10-9g ). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the gravimetric atom interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step-size-dependent magnetic field measurement uncertainty, present vector light shift and tensor light shift induced magnetic field measurement offset, and map the absolute magnetic field inside the interferometer chamber of GAIN with an uncertainty of 0.72 nT and a spatial resolution of 12.8 mm. We evaluate the quadratic Zeeman-effect-induced gravity measurement error in GAIN as 2.04 μ Gal . The methods shown in this paper are important for precisely mapping the absolute magnetic field in vacuum and reducing the quadratic Zeeman-effect-induced systematic error in Raman transition-based precision measurements, such as atomic interferometer gravimeters.

Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state

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

Sharov, G.S., E-mail: german.sharov@mail.ru

Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H ( z ) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale r {sub s} ( z {sub d} ). Among the considered models the best value of χ{sup 2} is achieved formore » the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.« less

On the classification of elliptic foliations induced by real quadratic fields with center

NASA Astrophysics Data System (ADS)

Puchuri, Liliana; Bueno, Orestes

2016-12-01

Related to the study of Hilbert's infinitesimal problem, is the problem of determining the existence and estimating the number of limit cycles of the linear perturbation of Hamiltonian fields. A classification of the elliptic foliations in the projective plane induced by the fields obtained by quadratic fields with center was already studied by several authors. In this work, we devise a unified proof of the classification of elliptic foliations induced by quadratic fields with center. This technique involves using a formula due to Cerveau & Lins Neto to calculate the genus of the generic fiber of a first integral of foliations of these kinds. Furthermore, we show that these foliations induce several examples of linear families of foliations which are not bimeromorphically equivalent to certain remarkable examples given by Lins Neto.

Robustness in linear quadratic feedback design with application to an aircraft control problem

NASA Technical Reports Server (NTRS)

Patel, R. V.; Sridhar, B.; Toda, M.

1977-01-01

Some new results concerning robustness and asymptotic properties of error bounds of a linear quadratic feedback design are applied to an aircraft control problem. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed based on Linear Quadratic (LQ) theory and the results developed in this paper. The variation of the error bounds to changes in the weighting matrices in the LQ design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable error bound for variations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.

Calculus students' understanding of the vertex of the quadratic function in relation to the concept of derivative

NASA Astrophysics Data System (ADS)

Burns-Childers, Annie; Vidakovic, Draga

2018-07-01

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up group interviews. Students' personal meanings of the vertex, including misconceptions, were explored, along with students' understanding to solve problems pertaining to the derivative of a quadratic function. Results give evidence of students' weak schema of the vertex, lack of connection between different problem types and the importance of linguistics in relation to levels of APOS theory. A preliminary genetic decomposition was developed based on the results. Future research is suggested as a continuation to improve student understanding of the relationship between the vertex of quadratic functions and the derivative.

Rigorous Numerical Study of Low-Period Windows for the Quadratic Map

NASA Astrophysics Data System (ADS)

Galias, Zbigniew

An efficient method to find all low-period windows for the quadratic map is proposed. The method is used to obtain very accurate rigorous bounds of positions of all periodic windows with periods p ≤ 32. The contribution of period-doubling windows on the total width of periodic windows is discussed. Properties of periodic windows are studied numerically.

Differentiated Learning Environment--A Classroom for Quadratic Equation, Function and Graphs

ERIC Educational Resources Information Center

Dinç, Emre

2017-01-01

This paper will cover the design of a learning environment as a classroom regarding the Quadratic Equations, Functions and Graphs. The goal of the learning environment offered in the paper is to design a classroom where students will enjoy the process, use their skills they already have during the learning process, control and plan their learning…

Differentiation of Students' Reasoning on Linear and Quadratic Geometric Number Patterns

ERIC Educational Resources Information Center

Lin, Fou-Lai; Yang, Kai-Lin

2004-01-01

There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing,…

Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities.

PubMed

Zeng, Xianglong; Guo, Hairun; Zhou, Binbin; Bache, Morten

2012-11-19

We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency. Numerical results show that compressed pulses with less than three-cycle duration can be achieved even when the compression factor is very large, and in contrast to standard soliton compression, these compressed pulses have minimal pedestal and high quality factor.

Trace element levels in drinking water and cognitive function among elderly Chinese.

PubMed

Emsley, C L; Gao, S; Li, Y; Liang, C; Ji, R; Hall, K S; Cao, J; Ma, F; Wu, Y; Ying, P; Zhang, Y; Sun, S; Unverzagt, F W; Slemenda, C W; Hendrie, H C

2000-05-01

The relation between trace element levels in drinking water and cognitive function was investigated in a population-based study of elderly residents (n = 1,016) in rural China in 1996-1997. Cognitive function was measured using a Chinese translation of the Community Screening Interview for Dementia. A mixed effects model was used to evaluate the effect of each of the elements on cognitive function while adjusting for age, sex, and educational level. Several of the elements examined had a significant effect on cognitive function when they were assessed in a univariate context. However, after adjustment for other elements, many of these results were not significant. There was a significant quadratic effect for calcium and a significant zinc-cadmium interaction. Cognitive function increased with calcium level up to a certain point and then decreased as calcium continued to increase. Zinc showed a positive relation with cognitive function at low cadmium levels but a negative relation at high levels.

The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

NASA Technical Reports Server (NTRS)

Townsend, Barbara K.

1987-01-01

A control-system design method, quadratic optimal cooperative control synthesis (CCS), is applied to the design of a stability and control augmentation system (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design method, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and linear quadratic regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

NASA Technical Reports Server (NTRS)

Townsend, Barbara K.

1986-01-01

A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

Quadratic genetic modifications: a streamlined route to cosmological simulations with controlled merger history

NASA Astrophysics Data System (ADS)

Rey, Martin P.; Pontzen, Andrew

2018-02-01

Recent work has studied the interplay between a galaxy's history and its observable properties using `genetically modified' cosmological zoom simulations. The approach systematically generates alternative histories for a halo, while keeping its cosmological environment fixed. Applications to date altered linear properties of the initial conditions, such as the mean overdensity of specified regions; we extend the formulation to include quadratic features, such as local variance, that determines the overall importance of smooth accretion relative to mergers in a galaxy's history. We introduce an efficient algorithm for this new class of modification and demonstrate its ability to control the variance of a region in a one-dimensional toy model. Outcomes of this work are twofold: (i) a clarification of the formulation of genetic modifications and (ii) a proof of concept for quadratic modifications leading the way to a forthcoming implementation in cosmological simulations.

A tutorial on the LQG/LTR method. [Linear Quadratic Gaussian/Loop Transfer Recovery

NASA Technical Reports Server (NTRS)

Athans, M.

1986-01-01

In this paper the so-called Linear-Quadratic-Gaussian method with Loop-Transfer-Recovery is surveyed. The objective is to provide a pragmatic exposition, with special emphasis on the step-by-step characteristics for designing multivariable feedback control systems.

A comparison between block and smooth modeling in finite element simulations of tDCS*

PubMed Central

Indahlastari, Aprinda; Sadleir, Rosalind J.

2018-01-01

Current density distributions in five selected structures, namely, anterior superior temporal gyrus (ASTG), hippocampus (HIP), inferior frontal gyrus (IFG), occipital lobe (OCC) and pre-central gyrus (PRC) were investigated as part of a comparison between electrostatic finite element models constructed directly from MRI-resolution data (block models), and smoothed tetrahedral finite element models (smooth models). Three electrode configurations were applied, mimicking different tDCS therapies. Smooth model simulations were found to require three times longer to complete. The percentage differences between mean and median current densities of each model type in arbitrarily chosen brain structures ranged from −33.33–48.08%. No clear relationship was found between structure volumes and current density differences between the two model types. Tissue regions nearby the electrodes demonstrated the least percentage differences between block and smooth models. Therefore, block models may be adequate to predict current density values in cortical regions presumed targeted by tDCS. PMID:26737023

Adaptive finite element modelling of three-dimensional magnetotelluric fields in general anisotropic media

NASA Astrophysics Data System (ADS)

Liu, Ying; Xu, Zhenhuan; Li, Yuguo

2018-04-01

We present a goal-oriented adaptive finite element (FE) modelling algorithm for 3-D magnetotelluric fields in generally anisotropic conductivity media. The model consists of a background layered structure, containing anisotropic blocks. Each block and layer might be anisotropic by assigning to them 3 × 3 conductivity tensors. The second-order partial differential equations are solved using the adaptive finite element method (FEM). The computational domain is subdivided into unstructured tetrahedral elements, which allow for complex geometries including bathymetry and dipping interfaces. The grid refinement process is guided by a global posteriori error estimator and is performed iteratively. The system of linear FE equations for electric field E is solved with a direct solver MUMPS. Then the magnetic field H can be found, in which the required derivatives are computed numerically using cubic spline interpolation. The 3-D FE algorithm has been validated by comparisons with both the 3-D finite-difference solution and 2-D FE results. Two model types are used to demonstrate the effects of anisotropy upon 3-D magnetotelluric responses: horizontal and dipping anisotropy. Finally, a 3D sea hill model is modelled to study the effect of oblique interfaces and the dipping anisotropy.

Soliton creation, propagation, and annihilation in aeromechanical arrays of one-way coupled bistable elements

NASA Astrophysics Data System (ADS)

Rosenberger, Tessa; Lindner, John F.

We study the dynamics of mechanical arrays of bistable elements coupled one-way by wind. Unlike earlier hydromechanical unidirectional arrays, our aeromechanical one-way arrays are simpler, easier to study, and exhibit a broader range of phenomena. Soliton-like waves propagate in one direction at speeds proportional to wind speeds. Periodic boundaries enable solitons to annihilate in pairs in even arrays where adjacent elements are attracted to opposite stable states. Solitons propagate indefinitely in odd arrays where pairing is frustrated. Large noise spontaneously creates soliton- antisoliton pairs, as predicted by prior computer simulations. Soliton annihilation times increase quadratically with initial separations, as expected for random walk models of soliton collisions.

A bivariate rational interpolation with a bi-quadratic denominator

NASA Astrophysics Data System (ADS)

Duan, Qi; Zhang, Huanling; Liu, Aikui; Li, Huaigu

2006-10-01

In this paper a new rational interpolation with a bi-quadratic denominator is developed to create a space surface using only values of the function being interpolated. The interpolation function has a simple and explicit rational mathematical representation. When the knots are equally spaced, the interpolating function can be expressed in matrix form, and this form has a symmetric property. The concept of integral weights coefficients of the interpolation is given, which describes the "weight" of the interpolation points in the local interpolating region.

A 4-node assumed-stress hybrid shell element with rotational degrees of freedom

NASA Technical Reports Server (NTRS)

Aminpour, Mohammad A.

1990-01-01

An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or drilling degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8-node isoparametric element. This process is accomplished by assuming quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields along the edges of the element. In addition, the degrees of freedom at midside nodes are approximated in terms of the degrees of freedom at corner nodes. During this process the rotational degrees of freedom at the corner nodes enter into the formulation of the element. The stress field are expressed in the element natural-coordinate system such that the element remains invariant with respect to node numbering.

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1985-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

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.

Frequency-independent approach to calculate physical optics radiations with the quadratic concave phase variations

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

Wu, Yu Mao, E-mail: yumaowu@fudan.edu.cn; Teng, Si Jia, E-mail: sjteng12@fudan.edu.cn

In this work, we develop the numerical steepest descent path (NSDP) method to calculate the physical optics (PO) radiations with the quadratic concave phase variations. With the surface integral equation method, the physical optics (PO) scattered fields are formulated and further reduced to the surface integrals. The high frequency physical critical points contributions, including the stationary phase points, the boundary resonance points and the vertex points are comprehensively studied via the proposed NSDP method. The key contributions of this work are twofold. One is that together with the PO integrals taking the quadratic parabolic and hyperbolic phase terms, this workmore » makes the NSDP theory be complete for treating the PO integrals with quadratic phase variations. Another is that, in order to illustrate the transition effect of the high frequency physical critical points, in this work, we consider and further extend the NSDP method to calculate the PO integrals with the coalescence of the high frequency critical points. Numerical results for the highly oscillatory PO integral with the coalescence of the critical points are given to verify the efficiency of the proposed NSDP method. The NSDP method could achieve the frequency independent computational workload and error controllable accuracy in all the numerical experiments, especially for the case of the coalescence of the high frequency critical points.« less

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

Graphical Description of Johnson-Neyman Outcomes for Linear and Quadratic Regression Surfaces.

ERIC Educational Resources Information Center

Schafer, William D.; Wang, Yuh-Yin

A modification of the usual graphical representation of heterogeneous regressions is described that can aid in interpreting significant regions for linear or quadratic surfaces. The standard Johnson-Neyman graph is a bivariate plot with the criterion variable on the ordinate and the predictor variable on the abscissa. Regression surfaces are drawn…

Thermo-Elastic Triangular Sandwich Element for the Complete Stress Field Based on a Single-Layer Theory

NASA Technical Reports Server (NTRS)

Das, M.; Barut, A.; Madenci, E.; Ambur, D. R.

2004-01-01

This study presents a new triangular finite element for modeling thick sandwich panels, subjected to thermo-mechanical loading, based on a {3,2}-order single-layer plate theory. A hybrid energy functional is employed in the derivation of the element because of a C interelement continuity requirement. The single-layer theory is based on five weighted-average field variables arising from the cubic and quadratic representations of the in-plane and transverse displacement fields, respectively. The variations of temperature and distributed loading acting on the top and bottom surfaces are non-uniform. The temperature varies linearly through the thickness.

Tetrahedral silsesquioxane-C2H2Ti complex for hydrogen storage

NASA Astrophysics Data System (ADS)

Konda, Ravinder; Tavhare, Priyanka; Ingale, Nilesh; Chaudhari, Ajay

2018-04-01

The interaction of molecular hydrogen with tetrahedral silsesquioxane (T4)-C2H2Ti complex has been studied using Density Functional Theory with M06-2X functional and MP2 method with 6-311++G** basis set. T4-C2H2Ti complex can absorb maximum five hydrogen molecules with the gravimetric hydrogen storage capacity of 3.4 wt %. Adsorption energy calculations show that H2 adsorption on T4-C2H2Ti complex is favorable at room temperature by both the methods. We have studied the effect of temperature and pressure on Gibbs free energy corrected adsorption energies. Molecular dynamics simulations for H2 adsorbed T4-C2H2Ti complex have also been performed at 300K and show that loosely bonded H2 molecule flies away within 1fs. Various interaction energies within the complex are studied. Stability of a complex is predicted by means of a gap between Highest Occupied Molecular Orbital (HUMO) and Lowest Unoccupied Molecular Orbital (LUMO). The H2 desorption temperature for T4-C2H2Ti complex is calculated with Van't Hoff equation and it is found to be 229K.

Towards a unifying approach to diversity measures: bridging the gap between the Shannon entropy and Rao's quadratic index.

PubMed

Ricotta, Carlo; Szeidl, Laszlo

2006-11-01

The diversity of a species assemblage has been studied extensively for many decades in relation to its possible connection with ecosystem functioning and organization. In this view most diversity measures, such as Shannon's entropy, rely upon information theory as a basis for the quantification of diversity. Also, traditional diversity measures are computed using species relative abundances and cannot account for the ecological differences between species. Rao first proposed a diversity index, termed quadratic diversity (Q) that incorporates both species relative abundances and pairwise distances between species. Quadratic diversity is traditionally defined as the expected distance between two randomly selected individuals. In this paper, we show that quadratic diversity can be interpreted as the expected conflict among the species of a given assemblage. From this unusual interpretation, it naturally follows that Rao's Q can be related to the Shannon entropy through a generalized version of the Tsallis parametric entropy.

Some insights on hard quadratic assignment problem instances

NASA Astrophysics Data System (ADS)

Hussin, Mohamed Saifullah

2017-11-01

Since the formal introduction of metaheuristics, a huge number Quadratic Assignment Problem (QAP) instances have been introduced. Those instances however are loosely-structured, and therefore made it difficult to perform any systematic analysis. The QAPLIB for example, is a library that contains a huge number of QAP benchmark instances that consists of instances with different size and structure, but with a very limited availability for every instance type. This prevents researchers from performing organized study on those instances, such as parameter tuning and testing. In this paper, we will discuss several hard instances that have been introduced over the years, and algorithms that have been used for solving them.

Frontogenesis driven by horizontally quadratic distributions of density

NASA Technical Reports Server (NTRS)

Jacqmin, David

1991-01-01

Attention is given to the quadratic density distribution in a channel, which has been established by Simpson and Linden to be the simplest case of the horizontally nonlinear distribution of fluid density required for the production of frontogenesis. The porous-media and Boussinesq flow models are examined, and their evolution equations are reduced to one-dimensional systems. While both the porous-media and the inviscid/nondiffusive Boussinesq systems exhibit classic frontogenesis behavior, the viscous Boussinesq system exhibits a more complex behavior: boundary-layer effects force frontogenesis away from the lower boundary, and at late times the steepest density gradients are close to mid-channel.

Uniform sparse bounds for discrete quadratic phase Hilbert transforms

NASA Astrophysics Data System (ADS)

Kesler, Robert; Arias, Darío Mena

2017-09-01

For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form < H^{α } f , g > for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.

s-Ordered Exponential of Quadratic Forms Gained via IWSOP Technique

NASA Astrophysics Data System (ADS)

Bazrafkan, M. R.; Shähandeh, F.; Nahvifard, E.

2012-11-01

Using the generalized bar{s}-ordered Wigner operator, in which bar{s} is a vector over the field of complex numbers, the technique of integration within an s-ordered product of operators (IWSOP) has been extended to multimode case. We derive the bar{s}-ordered form of the widely applicable multimode exponential of quadratic form exp\\{sum_{i,j = 1}n ai^{dag}\\varLambda_{ij}{aj}\\} , each mode being in some particular order s i , applying this method.

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

NASA Astrophysics Data System (ADS)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

Prediction of sound fields in acoustical cavities using the boundary element method. M.S. Thesis

NASA Technical Reports Server (NTRS)

Kipp, C. R.; Bernhard, R. J.

1985-01-01

A method was developed to predict sound fields in acoustical cavities. The method is based on the indirect boundary element method. An isoparametric quadratic boundary element is incorporated. Pressure, velocity and/or impedance boundary conditions may be applied to a cavity by using this method. The capability to include acoustic point sources within the cavity is implemented. The method is applied to the prediction of sound fields in spherical and rectangular cavities. All three boundary condition types are verified. Cases with a point source within the cavity domain are also studied. Numerically determined cavity pressure distributions and responses are presented. The numerical results correlate well with available analytical results.

Insights into Substrate Specificity and Metal Activation of Mammalian Tetrahedral Aspartyl Aminopeptidase*

PubMed Central

Chen, Yuanyuan; Farquhar, Erik R.; Chance, Mark R.; Palczewski, Krzysztof; Kiser, Philip D.

2012-01-01

Aminopeptidases are key enzymes involved in the regulation of signaling peptide activity. Here, we present a detailed biochemical and structural analysis of an evolutionary highly conserved aspartyl aminopeptidase called DNPEP. We show that this peptidase can cleave multiple physiologically relevant substrates, including angiotensins, and thus may play a key role in regulating neuron function. Using a combination of x-ray crystallography, x-ray absorption spectroscopy, and single particle electron microscopy analysis, we provide the first detailed structural analysis of DNPEP. We show that this enzyme possesses a binuclear zinc-active site in which one of the zinc ions is readily exchangeable with other divalent cations such as manganese, which strongly stimulates the enzymatic activity of the protein. The plasticity of this metal-binding site suggests a mechanism for regulation of DNPEP activity. We also demonstrate that DNPEP assembles into a functionally relevant tetrahedral complex that restricts access of peptide substrates to the active site. These structural data allow rationalization of the enzyme's preference for short peptide substrates with N-terminal acidic residues. This study provides a structural basis for understanding the physiology and bioinorganic chemistry of DNPEP and other M18 family aminopeptidases. PMID:22356908

Failures and Inabilities of High School Students about Quadratic Equations and Functions

ERIC Educational Resources Information Center

Memnun, Dilek Sezgin; Aydin, Bünyamin; Dinç, Emre; Çoban, Merve; Sevindik, Fatma

2015-01-01

In this research study, it was aimed to examine failures and inabilities of eleventh grade students about quadratic equations and functions. For this purpose, these students were asked ten open-ended questions. The analysis of the answers given by the students to these questions indicated that a significant part of these students had failures and…

Accuracy of quadrat sampling in studying forest reproduction on cut-over areas

Treesearch

I. T. Haig

1929-01-01

The quadrat method, first introduced into ecological studies by Pound and Clements in i898, has been adopted by both foresters and ecologists as one of the most accurate means of studying the occurrence, distribution, and development of vegetation (Clements, '05; Weaver, '18). This method is unquestionably more precise than the descriptive method which it...

Brief note on Ashtekar-Magnon-Das conserved quantities in quadratic curvature theories

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

Pang Yi

2011-04-15

In this note, we correct a mistake in the mass formula in [N. Okuyama and J. i. Koga, Phys. Rev. D 71, 084009 (2005).] which generalizes the Ashtekar-Magnon-Das method to incorporate extended gravities with quadratic curvature terms. The corrected mass formula confirms that the black hole masses for recently discovered critical gravities vanish.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields.

PubMed

Yang, R; Zelyak, O; Fallone, B G; St-Aubin, J

2018-01-30

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields

NASA Astrophysics Data System (ADS)

Yang, R.; Zelyak, O.; Fallone, B. G.; St-Aubin, J.

2018-02-01

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.

The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems

PubMed Central

Jiang, Yanan; Han, Maoan; Xiao, Dongmei

2014-01-01

We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ3. PMID:24982980

Slow magnetic relaxation at zero field in the tetrahedral complex [Co(SPh)4]2-.

PubMed

Zadrozny, Joseph M; Long, Jeffrey R

2011-12-28

The Ph(4)P(+) salt of the tetrahedral complex [Co(SPh)(4)](2-), possessing an S = (3)/(2) ground state with an axial zero-field splitting of D = -70 cm(-1), displays single-molecule magnet behavior in the absence of an applied magnetic field. At very low temperatures, ac magnetic susceptibility data show the magnetic relaxation time, τ, to be temperature-independent, while above 2.5 K thermally activated Arrhenius behavior is apparent with U(eff) = 21(1) cm(-1) and τ(0) = 1.0(3) × 10(-7) s. Under an applied field of 1 kOe, τ more closely approximates Arrhenius behavior over the entire temperature range. Upon dilution of the complex within a matrix of the isomorphous compound (Ph(4)P)(2)[Zn(SPh)(4)], ac susceptibility data reveal the molecular nature of the slow magnetic relaxation and indicate that the quantum tunneling pathway observed at low temperatures is likely mediated by intermolecular dipolar interactions. © 2011 American Chemical Society

A note on the relationship between the quadratic mean stand diameter and harmonic mean basal area under size-biased distribution theory

Treesearch

Jeffrey H. Gove

2003-01-01

This note seeks to extend the utility of size-biased distribution theory as applied to forestry through two relationships regarding the quadratic mean stand diameter. First, the quadratic mean stand diameter's relationship to the harmonic mean basal area for horizontal point sampling, which has been known algebraically from early on, is proved under size-biased...

TU-AB-202-05: GPU-Based 4D Deformable Image Registration Using Adaptive Tetrahedral Mesh Modeling

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

Zhong, Z; Zhuang, L; Gu, X

Purpose: Deformable image registration (DIR) has been employed today as an automated and effective segmentation method to transfer tumor or organ contours from the planning image to daily images, instead of manual segmentation. However, the computational time and accuracy of current DIR approaches are still insufficient for online adaptive radiation therapy (ART), which requires real-time and high-quality image segmentation, especially in a large datasets of 4D-CT images. The objective of this work is to propose a new DIR algorithm, with fast computational speed and high accuracy, by using adaptive feature-based tetrahedral meshing and GPU-based parallelization. Methods: The first step ismore » to generate the adaptive tetrahedral mesh based on the image features of a reference phase of 4D-CT, so that the deformation can be well captured and accurately diffused from the mesh vertices to voxels of the image volume. Subsequently, the deformation vector fields (DVF) and other phases of 4D-CT can be obtained by matching each phase of the target 4D-CT images with the corresponding deformed reference phase. The proposed 4D DIR method is implemented on GPU, resulting in significantly increasing the computational efficiency due to its parallel computing ability. Results: A 4D NCAT digital phantom was used to test the efficiency and accuracy of our method. Both the image and DVF results show that the fine structures and shapes of lung are well preserved, and the tumor position is well captured, i.e., 3D distance error is 1.14 mm. Compared to the previous voxel-based CPU implementation of DIR, such as demons, the proposed method is about 160x faster for registering a 10-phase 4D-CT with a phase dimension of 256×256×150. Conclusion: The proposed 4D DIR method uses feature-based mesh and GPU-based parallelism, which demonstrates the capability to compute both high-quality image and motion results, with significant improvement on the computational speed.« less

Quadratic String Method for Locating Instantons in Tunneling Splitting Calculations.

PubMed

Cvitaš, Marko T

2018-03-13

The ring-polymer instanton (RPI) method is an efficient technique for calculating approximate tunneling splittings in high-dimensional molecular systems. In the RPI method, tunneling splitting is evaluated from the properties of the minimum action path (MAP) connecting the symmetric wells, whereby the extensive sampling of the full potential energy surface of the exact quantum-dynamics methods is avoided. Nevertheless, the search for the MAP is usually the most time-consuming step in the standard numerical procedures. Recently, nudged elastic band (NEB) and string methods, originaly developed for locating minimum energy paths (MEPs), were adapted for the purpose of MAP finding with great efficiency gains [ J. Chem. Theory Comput. 2016 , 12 , 787 ]. In this work, we develop a new quadratic string method for locating instantons. The Euclidean action is minimized by propagating the initial guess (a path connecting two wells) over the quadratic potential energy surface approximated by means of updated Hessians. This allows the algorithm to take many minimization steps between the potential/gradient calls with further reductions in the computational effort, exploiting the smoothness of potential energy surface. The approach is general, as it uses Cartesian coordinates, and widely applicable, with computational effort of finding the instanton usually lower than that of determining the MEP. It can be combined with expensive potential energy surfaces or on-the-fly electronic-structure methods to explore a wide variety of molecular systems.

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.

A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong

2013-02-01

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.

An Improved Correction for Range Restricted Correlations Under Extreme, Monotonic Quadratic Nonlinearity and Heteroscedasticity.

PubMed

Culpepper, Steven Andrew

2016-06-01

Standardized tests are frequently used for selection decisions, and the validation of test scores remains an important area of research. This paper builds upon prior literature about the effect of nonlinearity and heteroscedasticity on the accuracy of standard formulas for correcting correlations in restricted samples. Existing formulas for direct range restriction require three assumptions: (1) the criterion variable is missing at random; (2) a linear relationship between independent and dependent variables; and (3) constant error variance or homoscedasticity. The results in this paper demonstrate that the standard approach for correcting restricted correlations is severely biased in cases of extreme monotone quadratic nonlinearity and heteroscedasticity. This paper offers at least three significant contributions to the existing literature. First, a method from the econometrics literature is adapted to provide more accurate estimates of unrestricted correlations. Second, derivations establish bounds on the degree of bias attributed to quadratic functions under the assumption of a monotonic relationship between test scores and criterion measurements. New results are presented on the bias associated with using the standard range restriction correction formula, and the results show that the standard correction formula yields estimates of unrestricted correlations that deviate by as much as 0.2 for high to moderate selectivity. Third, Monte Carlo simulation results demonstrate that the new procedure for correcting restricted correlations provides more accurate estimates in the presence of quadratic and heteroscedastic test score and criterion relationships.

Quadratic Electro-optic Effect in a Novel Nano-optical Polymer (iodine-doped polyisoprene)

NASA Astrophysics Data System (ADS)

Swamy, Rajendra; Titus, Jitto; Thakur, Mrinal

2004-03-01

In this report, exceptionally large quadratic electro-optic effect in a novel nano-optical polymer will be discussed. The material involved is cis-1,4-polyisoprene or natural rubber which is a nonconjugated conductive polymer[1,2].Upon doping with an acceptor such as iodine, an electron is transferred from its isolated double bond to the dopant leading to a charge-transfer complex. The positive charge (hole) thus created is localized around the double-bond site, within a nanometer dimension - thus, forming a nano-optical material. The quadratic electro-optic measurement on the doped polyisoprene film was made using field-induced birefringence method. The measured Kerr coefficient is about sixty six times that of nitrobenzene at 632 nm. Significant electroabsorption was also observed in this material at 632 nm. 1. M. Thakur, J. Macromol. Sci. - PAC, 2001, A38(12), 1337. 2. M. Thakur, S. Khatavkar and E.J. Parish, J. Macromol. Sci. - PAC, 2003, A40 (12), 1397.

Building Students' Understanding of Quadratic Equation Concept Using Naïve Geometry

ERIC Educational Resources Information Center

Fachrudin, Achmad Dhany; Putri, Ratu Ilma Indra; Darmawijoyo

2014-01-01

The purpose of this research is to know how Naïve Geometry method can support students' understanding about the concept of solving quadratic equations. In this article we will discuss one activities of the four activities we developed. This activity focused on how students linking the Naïve Geometry method with the solving of the quadratic…

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

Estimation of stature from sternum - Exploring the quadratic models.

PubMed

Saraf, Ashish; Kanchan, Tanuj; Krishan, Kewal; Ateriya, Navneet; Setia, Puneet

2018-04-14

Identification of the dead is significant in examination of unknown, decomposed and mutilated human remains. Establishing the biological profile is the central issue in such a scenario, and stature estimation remains one of the important criteria in this regard. The present study was undertaken to estimate stature from different parts of the sternum. A sample of 100 sterna was obtained from individuals during the medicolegal autopsies. Length of the deceased and various measurements of the sternum were measured. Student's t-test was performed to find the sex differences in stature and sternal measurements included in the study. Correlation between stature and sternal measurements were analysed using Karl Pearson's correlation, and linear and quadratic regression models were derived. All the measurements were found to be significantly larger in males than females. Stature correlated best with the combined length of sternum, among males (R = 0.894), females (R = 0.859), and for the total sample (R = 0.891). The study showed that the models derived for stature estimation from combined length of sternum are likely to give the most accurate estimates of stature in forensic case work when compared to manubrium and mesosternum. Accuracy of stature estimation further increased with quadratic models derived for the mesosternum among males and combined length of sternum among males and females when compared to linear regression models. Future studies in different geographical locations and a larger sample size are proposed to confirm the study observations. Copyright © 2018 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

Definition of large components assembled on-orbit and robot compatible mechanical joints

NASA Technical Reports Server (NTRS)

Williamsen, J.; Thomas, F.; Finckenor, J.; Spiegel, B.

1990-01-01

One of four major areas of project Pathfinder is in-space assembly and construction. The task of in-space assembly and construction is to develop the requirements and the technology needed to build elements in space. A 120-ft diameter tetrahedral aerobrake truss is identified as the focus element. A heavily loaded mechanical joint is designed to robotically assemble the defined aerobrake element. Also, typical large components such as habitation modules, storage tanks, etc., are defined, and attachment concepts of these components to the tetrahedral truss are developed.

Constrained multiple indicator kriging using sequential quadratic programming

NASA Astrophysics Data System (ADS)

Soltani-Mohammadi, Saeed; Erhan Tercan, A.

2012-11-01

Multiple indicator kriging (MIK) is a nonparametric method used to estimate conditional cumulative distribution functions (CCDF). Indicator estimates produced by MIK may not satisfy the order relations of a valid CCDF which is ordered and bounded between 0 and 1. In this paper a new method has been presented that guarantees the order relations of the cumulative distribution functions estimated by multiple indicator kriging. The method is based on minimizing the sum of kriging variances for each cutoff under unbiasedness and order relations constraints and solving constrained indicator kriging system by sequential quadratic programming. A computer code is written in the Matlab environment to implement the developed algorithm and the method is applied to the thickness data.

Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori

NASA Astrophysics Data System (ADS)

T. Sardari, Naser

2018-03-01

Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.

Half-quadratic variational regularization methods for speckle-suppression and edge-enhancement in SAR complex image

NASA Astrophysics Data System (ADS)

Zhao, Xia; Wang, Guang-xin

2008-12-01

Synthetic aperture radar (SAR) is an active remote sensing sensor. It is a coherent imaging system, the speckle is its inherent default, which affects badly the interpretation and recognition of the SAR targets. Conventional methods of removing the speckle is studied usually in real SAR image, which reduce the edges of the images at the same time as depressing the speckle. Morever, Conventional methods lost the information about images phase. Removing the speckle and enhancing the target and edge simultaneously are still a puzzle. To suppress the spckle and enhance the targets and the edges simultaneously, a half-quadratic variational regularization method in complex SAR image is presented, which is based on the prior knowledge of the targets and the edge. Due to the non-quadratic and non- convex quality and the complexity of the cost function, a half-quadratic variational regularization variation is used to construct a new cost function,which is solved by alternate optimization. In the proposed scheme, the construction of the model, the solution of the model and the selection of the model peremeters are studied carefully. In the end, we validate the method using the real SAR data.Theoretic analysis and the experimental results illustrate the the feasibility of the proposed method. Further more, the proposed method can preserve the information about images phase.

The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (C)

NASA Astrophysics Data System (ADS)

Artés, Joan C.; Rezende, Alex C.; Oliveira, Regilene D. S.

Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. Our goal is to make a global study of the family QsnSN of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the collision of two infinite singular points. This family can be divided into three different subfamilies, all of them with the finite saddle-node in the origin of the plane with the eigenvectors on the axes and with the eigenvector associated with the zero eigenvalue on the horizontal axis and (A) with the infinite saddle-node in the horizontal axis, (B) with the infinite saddle-node in the vertical axis and (C) with the infinite saddle-node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and time homotheties are three-dimensional and we give the bifurcation diagram of their closure with respect to specific normal forms, in the three-dimensional real projective space. The subfamilies (A) and (B) have already been studied [Artés et al., 2013b] and in this paper we provide the complete study of the geometry of the last family (C). The bifurcation diagram for the subfamily (C) yields 371 topologically distinct phase portraits with and without limit cycles for systems in the closure /line{QsnSN(C)} within the representatives of QsnSN(C) given by a chosen normal form. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincaré disk. The bifurcation set of /line{QsnSN(C)} is not only algebraic due to the presence of some surfaces found numerically. All points in these surfaces correspond to either connections of separatrices, or the

Quadratic Blind Linear Unmixing: A Graphical User Interface for Tissue Characterization

PubMed Central

Gutierrez-Navarro, O.; Campos-Delgado, D.U.; Arce-Santana, E. R.; Jo, Javier A.

2016-01-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. PMID:26589467

''Did Something Happen to You over the Summer?'': Tensions in Intentions for Chemistry Education

ERIC Educational Resources Information Center

Lewthwaite, Brian; Doyle, Tanya; Owen, Thomas

2014-01-01

This paper examines teachers' experiences in responding to a new Chemistry curriculum in the province of Manitoba in Canada informed by a "tetrahedral" orientation (Mahaffy, 2005) as a pedagogical framework for the teaching of Chemistry. This tetrahedral orientation endorses macroscopic, microscopic, symbolic and human element teaching…

A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

2012-01-01

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…

Application’s Method of Quadratic Programming for Optimization of Portfolio Selection

NASA Astrophysics Data System (ADS)

Kawamoto, Shigeru; Takamoto, Masanori; Kobayashi, Yasuhiro

Investors or fund-managers face with optimization of portfolio selection, which means that determine the kind and the quantity of investment among several brands. We have developed a method to obtain optimal stock’s portfolio more rapidly from twice to three times than conventional method with efficient universal optimization. The method is characterized by quadratic matrix of utility function and constrained matrices divided into several sub-matrices by focusing on structure of these matrices.

Classification of constraints and degrees of freedom for quadratic discrete actions

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

Höhn, Philipp A., E-mail: phoehn@perimeterinstitute.ca

2014-11-15

We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form and employs the canonical formalism developed in Dittrich and Höhn [“Constraint analysis for variational discrete systems,” J. Math. Phys. 54, 093505 (2013); e-print http://arxiv.org/abs/arXiv:1303.4294 [math-ph

A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application.

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem. Copyright © 2012 Elsevier Ltd. All rights reserved.

Solution to Projectile Motion with Quadratic Drag and Graphing the Trajectory in Spreadsheets

ERIC Educational Resources Information Center

Benacka, Jan

2010-01-01

This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and…

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

Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART

NASA Astrophysics Data System (ADS)

Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.

2017-12-01

Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.

Application of quadratic optimization to supersonic inlet control

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Zeller, J. R.

1971-01-01

The application of linear stochastic optimal control theory to the design of the control system for the air intake (inlet) of a supersonic air-breathing propulsion system is discussed. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant control systems are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain the best linear controller that minimizes the nonquadratic performance index. The two systems are compared on the basis of unstart prevention, control effort requirements, and sensitivity to parameter variations.

Two-photon Anderson localization in a disordered quadratic waveguide array

NASA Astrophysics Data System (ADS)

Bai, Y. F.; Xu, P.; Lu, L. L.; Zhong, M. L.; Zhu, S. N.

2016-05-01

We theoretically investigate two-photon Anderson localization in a χ (2) waveguide array with off-diagonal disorder. The nonlinear parametric down-conversion process would enhance both the single-photon and the two-photon Anderson localization. In the strong disorder regime, the two-photon position correlation exhibits a bunching distribution around the pumped waveguides, which is independent of pumping conditions and geometrical structures of waveguide arrays. Quadratic nonlinearity can be supplied as a new ingredient for Anderson localization. Also, our results pave the way for engineering quantum states through nonlinear quantum walks.

Graphical Representation of Complex Solutions of the Quadratic Equation in the "xy" Plane

ERIC Educational Resources Information Center

McDonald, Todd

2006-01-01

This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.

Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch.

PubMed

Bache, Morten; Nielsen, Hanne; Laegsgaard, Jesper; Bang, Ole

2006-06-01

We consider an index-guiding silica photonic crystal fiber with a triangular hole pattern and a periodically poled quadratic nonlinearity. By tuning the pitch and the relative hole size, second-harmonic generation with zero group-velocity mismatch is found for any fundamental wavelength above 780 nm. The nonlinear strength is optimized when the fundamental has maximum confinement in the core. The conversion bandwidth allows for femtosecond-pulse conversion, and 4%-180%W(-1)cm(-2) relative efficiencies were found.

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases.

PubMed

D'Amico, María Belén; Calandrini, Guillermo L

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

NASA Astrophysics Data System (ADS)

D'Amico, María Belén; Calandrini, Guillermo L.

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

Bi-quadratic interlayer exchange coupling in Co{sub 2}MnSi/Ag/Co{sub 2}MnSi pseudo spin-valve

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

Goripati, Hari S.; Hono, K.; Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-0047

2011-12-15

Bi-quadratic interlayer exchange coupling is found below 100 K in a Co{sub 2}MnSi/Ag/Co{sub 2}MnSi current-perpendicular-to-plane pseudo spin valves. The bi-quadratic coupling constant J{sub 2} was estimated to be {approx}-0.30 erg/cm{sup 2} at 5 K and the strong temperature dependence of the coupling strength points its likely origin to the ''loose spin'' model. Application of current of {approx}2 x 10{sup 7} A/cm{sup 2} below 100 K leads to an increase in the magnetoresistance (MR), indicating current induced antiparallel alignment of the two magnetic layers. These results strongly suggest that the presence of the bi-quadratic interlayer exchange coupling causes the reduction ofmore » the magnetoresistance at low temperature and illustrates the importance of understanding the influence of interlayer exchange coupling on magnetization configuration in magnetic nanostructures.« less

Gain scheduled linear quadratic control for quadcopter

NASA Astrophysics Data System (ADS)

Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.

2017-12-01

This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.

Security analysis of quadratic phase based cryptography

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.

2016-09-01

The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.

Identify Secretory Protein of Malaria Parasite with Modified Quadratic Discriminant Algorithm and Amino Acid Composition.

PubMed

Feng, Yong-E

2016-06-01

Malaria parasite secretes various proteins in infected red blood cell for its growth and survival. Thus identification of these secretory proteins is important for developing vaccine or drug against malaria. In this study, the modified method of quadratic discriminant analysis is presented for predicting the secretory proteins. Firstly, 20 amino acids are divided into five types according to the physical and chemical characteristics of amino acids. Then, we used five types of amino acids compositions as inputs of the modified quadratic discriminant algorithm. Finally, the best prediction performance is obtained by using 20 amino acid compositions, the sensitivity of 96 %, the specificity of 92 % with 0.88 of Mathew's correlation coefficient in fivefold cross-validation test. The results are also compared with those of existing prediction methods. The compared results shown our method are prominent in the prediction of secretory proteins.

An empirical analysis of the quantitative effect of data when fitting quadratic and cubic polynomials

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1974-01-01

A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.

Kernels, Degrees of Freedom, and Power Properties of Quadratic Distance Goodness-of-Fit Tests

PubMed Central

Lindsay, Bruce G.; Markatou, Marianthi; Ray, Surajit

2014-01-01

In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests. First, we introduce the concept of a root kernel and discuss the considerations that enter the selection of this kernel. We derive an easy to use normal approximation to the power of quadratic distance goodness-of-fit tests and base the construction of a noncentrality index, an analogue of the traditional noncentrality parameter, on it. This leads to a method akin to the Neyman-Pearson lemma for constructing optimal kernels for specific alternatives. We then introduce a midpower analysis as a device for choosing optimal degrees of freedom for a family of alternatives of interest. Finally, we introduce a new diffusion kernel, called the Pearson-normal kernel, and study the extent to which the normal approximation to the power of tests based on this kernel is valid. Supplementary materials for this article are available online. PMID:24764609

Finite element modeling of mass transport in high-Péclet cardiovascular flows

NASA Astrophysics Data System (ADS)

Hansen, Kirk; Arzani, Amirhossein; Shadden, Shawn

2016-11-01

Mass transport plays an important role in many important cardiovascular processes, including thrombus formation and atherosclerosis. These mass transport problems are characterized by Péclet numbers of up to 108, leading to several numerical difficulties. The presence of thin near-wall concentration boundary layers requires very fine mesh resolution in these regions, while large concentration gradients within the flow cause numerical stabilization issues. In this work, we will discuss some guidelines for solving mass transport problems in cardiovascular flows using a stabilized Galerkin finite element method. First, we perform mesh convergence studies in a series of idealized and patient-specific geometries to determine the required near-wall mesh resolution for these types of problems, using both first- and second-order tetrahedral finite elements. Second, we investigate the use of several boundary condition types at outflow boundaries where backflow during some parts of the cardiac cycle can lead to convergence issues. Finally, we evaluate the effect of reducing Péclet number by increasing mass diffusivity as has been proposed by some researchers. This work was supported by the NSF GRFP and NSF Career Award #1354541.

On a Microscopic Representation of Space-Time V

NASA Astrophysics Data System (ADS)

Dahm, R.

2017-01-01

In previous parts of this publication series, starting from the Dirac algebra and SU*(4), the ’dual’ compact rank-3 group SU(4) and Lie theory, we have developed some arguments and the reasoning to use (real) projective and (line) Complex geometry directly. Here, we want to extend this approach further in terms of line and Complex geometry and give some analytical examples. As such, we start from quadratic Complexe which we’ve identified in parts III and IV already as yielding naturally the ’light cone’ x_12 + x_22 + x_32 - x_02 = 0 when being related to (homogeneous) point coordinates x_α ^2 and infinitesimal dynamics by tetrahedral Complexe (or line elements). This introduces naturally projective transformations by preserving anharmonic ratios. We summarize some old work of Plücker relating quadratic Complexe to optics and discuss briefly their relation to spherical (and Schrödinger-type) equations as well as an obvious interpretation based on homogeneous coordinates and relations to conics and second order surfaces. Discussing (linear) symplectic symmetry and line coordinates, the main purpose and thread within this paper, however, is the identification and discussion of special relativity as direct invariance properties of line/Complex coordinates as well as their relation to ’quantum field theory’ by complexification of point coordinates or Complexe. This can be established by the Lie mapping1 which relates lines/Complexe to sphere geometry so that SU(2), SU(2)×U(1), SU(2)×SU(2) and the Dirac spinor description emerge without additional assumptions. We give a short outlook in that quadratic Complexe are related to dynamics e.g. power expressions in terms of six-vector products of Complexe, and action principles may be applied. (Quadratic) products like {Fμ ν }{Fμ ν }{{ or }}{Fα {{ }μ ν }}Fμ ν ^α ,1 ≤ α ≤ 3 are natural quadratic Complex expressions which may be extended by line constraints λk · ɛ = 0 with respect to an �

Growth Mechanism and Origin of High s p3 Content in Tetrahedral Amorphous Carbon

NASA Astrophysics Data System (ADS)

Caro, Miguel A.; Deringer, Volker L.; Koskinen, Jari; Laurila, Tomi; Csányi, Gábor

2018-04-01

We study the deposition of tetrahedral amorphous carbon (ta-C) films from molecular dynamics simulations based on a machine-learned interatomic potential trained from density-functional theory data. For the first time, the high s p3 fractions in excess of 85% observed experimentally are reproduced by means of computational simulation, and the deposition energy dependence of the film's characteristics is also accurately described. High confidence in the potential and direct access to the atomic interactions allow us to infer the microscopic growth mechanism in this material. While the widespread view is that ta-C grows by "subplantation," we show that the so-called "peening" model is actually the dominant mechanism responsible for the high s p3 content. We show that pressure waves lead to bond rearrangement away from the impact site of the incident ion, and high s p3 fractions arise from a delicate balance of transitions between three- and fourfold coordinated carbon atoms. These results open the door for a microscopic understanding of carbon nanostructure formation with an unprecedented level of predictive power.

Linear quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements

NASA Astrophysics Data System (ADS)

Paschall, Randall N.; Anderson, David J.

1993-11-01

A linear quadratic Gaussian method is proposed for a deformable mirror adaptive optics system control. Estimates of system states describing the distortion are generated by a Kalman filter based on Hartmann wave front measurements of the wave front gradient.

Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

PubMed

Kiselev, Aleksei P; Plachenov, Alexandr B

2016-04-01

The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.

Formalism for the solution of quadratic Hamiltonians with large cosine terms

NASA Astrophysics Data System (ADS)

Ganeshan, Sriram; Levin, Michael

2016-02-01

We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

Quadratic blind linear unmixing: A graphical user interface for tissue characterization.

PubMed

Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A

2016-02-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

ERIC Educational Resources Information Center

Didis, Makbule Gozde; Erbas, Ayhan Kursat

2015-01-01

This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight…

A methodology for quadrilateral finite element mesh coarsening

DOE PAGES

Staten, Matthew L.; Benzley, Steven; Scott, Michael

2008-03-27

High fidelity finite element modeling of continuum mechanics problems often requires using all quadrilateral or all hexahedral meshes. The efficiency of such models is often dependent upon the ability to adapt a mesh to the physics of the phenomena. Adapting a mesh requires the ability to both refine and/or coarsen the mesh. The algorithms available to refine and coarsen triangular and tetrahedral meshes are very robust and efficient. However, the ability to locally and conformally refine or coarsen all quadrilateral and all hexahedral meshes presents many difficulties. Some research has been done on localized conformal refinement of quadrilateral and hexahedralmore » meshes. However, little work has been done on localized conformal coarsening of quadrilateral and hexahedral meshes. A general method which provides both localized conformal coarsening and refinement for quadrilateral meshes is presented in this paper. This method is based on restructuring the mesh with simplex manipulations to the dual of the mesh. Finally, this method appears to be extensible to hexahedral meshes in three dimensions.« less

A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

NASA Astrophysics Data System (ADS)

Mestel, B. D.; Osbaldestin, A. H.

2004-10-01

We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.

Direct formulation of a 4-node hybrid shell element with rotational degrees of freedom

NASA Technical Reports Server (NTRS)

Aminpour, Mohammad A.

1990-01-01

A simple 4-node assumed-stress hybrid quadrilateral shell element with rotational or drilling degrees of freedom is formulated. The element formulation is based directly on a 4-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 8-node isoparametric element in which the midside degrees of freedom are eliminated in favor of rotational degree of freedom at the corner nodes. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom including rotational degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields are assumed along the edges of the element. The element Cartesian-coordinate system is chosen such as to make the stress field invariant with respect to node numbering. The membrane part of the stress field is based on a 9-parameter equilibrating stress field, while the bending part is based on a 13-parameter equilibrating stress field. The element passes the patch test, is nearly insensitive to mesh distortion, does not lock, possesses the desirable invariance properties, has no spurious modes, and produces accurate and reliable results.

Elastic Model Transitions: a Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

NASA Technical Reports Server (NTRS)

Jurenko, Robert J.; Bush, T. Jason; Ottander, John A.

2014-01-01

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.

A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

NASA Astrophysics Data System (ADS)

Xu, Jiuping; Li, Jun

2002-09-01

In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with a Quadratic Trap

NASA Astrophysics Data System (ADS)

Chen, Xuwen

2013-11-01

We consider the dynamics of the three-dimensional N-body Schrödinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N 3 β-1 V( N β x). We justify the mean-field approximation and offer a rigorous derivation of the three-dimensional cubic nonlinear Schrödinger equation (NLS) with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon (Commun Math Phys 279:169-185, 2008) for by adapting and simplifying an argument in Chen and Pavlović (Annales Henri Poincaré, 2013) which solves the problem for in the absence of a trap.

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

1994-01-01

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

Repopulation Kinetics and the Linear-Quadratic Model

NASA Astrophysics Data System (ADS)

O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

2009-08-01

The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Neural network for solving convex quadratic bilevel programming problems.

PubMed

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

2014-03-01

In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

NASA Technical Reports Server (NTRS)

Maliassov, Serguei

1996-01-01

In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.

Tetrahedral node for Transmission-Line Modeling (TLM) applied to Bio-heat Transfer.

PubMed

Milan, Hugo F M; Gebremedhin, Kifle G

2016-12-01

Transmission-Line Modeling (TLM) is a numerical method used to solve complex and time-domain bio-heat transfer problems. In TLM, parallelepipeds are used to discretize three-dimensional problems. The drawback in using parallelepiped shapes is that instead of refining only the domain of interest, a large additional domain would also have to be refined, which results in increased computational time and memory space. In this paper, we developed a tetrahedral node for TLM applied to bio-heat transfer that does not have the drawback associated with the parallelepiped node. The model includes heat source, blood perfusion, boundary conditions and initial conditions. The boundary conditions could be adiabatic, temperature, heat flux, or convection. The predicted temperature and heat flux were compared against results from an analytical solution and the results agreed within 2% for a mesh size of 69,941 nodes and a time step of 5ms. The method was further validated against published results of maximum skin-surface temperature difference in a breast with and without tumor and the results agreed within 6%. The published results were obtained from a model that used parallelepiped TLM node. An open source software, TLMBHT, was written using the theory developed herein and is available for download free-of-charge. Copyright © 2016 Elsevier Ltd. All rights reserved.

Structural instability of the CoO 4 tetrahedral chain in SrCoO 3-δ thin films

DOE PAGES

Glamazda, A.; Choi, Kwang-yong; Lemmens, P.; ...

2015-08-31

Raman scattering experiments together with detailed lattice dynamic calculations are performed to elucidate crystallographic and electronic peculiarities of SrCoO 3-δ films. We observe that the 85 cm -1 phonon mode involving the rotation of a CoO 4 tetrahedron undergoes a hardening by 21 cm -1 when the temperature is decreased. In addition, new phonon modes appear at 651.5 and 697.6 cm -1 . The latter modes are attributed to the Jahn-Teller activated modes. Upon cooling from room temperature, all phonons exhibit an exponential-like increase of intensity with a characteristic energy of about 103–107 K. We attribute this phenomenon to anmore » instability of the CoO 4 tetrahedral chain structure, which constitutes a key ingredient to understand the electronic and structural properties of the brownmillerite SrCoO 2.5.« less

Characterization of the excited states of a squaraine molecule with quadratic electroabsorption spectroscopy

NASA Astrophysics Data System (ADS)

Poga, C.; Brown, T. M.; Kuzyk, M. G.; Dirk, Carl W.

1995-04-01

We apply quadratic electroabsorption spectroscopy (QES) to thin-film solid solutions of squarylium dye molecules in poly(methyl methacrylate) polymer to study the dye's electronic excited states and to investigate the importance of these states with regard to their contribution to the third-order nonlinear-optical susceptibility. We first show that the room-temperature tensor ratio a= chi (3)3333/ chi (3)1133 \\approximately 3 throughout most of the visible region to establish that the electronic mechanism dominates. Because QES is a third-order nonlinear-optical susceptibility measurement, it can be used to identify two photon states. By obtaining good agreement between the quadratic electroabsorption spectrum and a three level model, we conclude that there are two dominant states that contribute to the near-resonant and a two-photon state that are separated by less than 0.2 eV in energy. QES is thus shown to be a versatile tool for measuring the nature of excited states in a molecule. Furthermore, by applying a Kramers-Kronig transformation to determine the real part of the response, we are able to assess the two-photon all-optical device figure of merit of these materials. Such an

Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

NASA Astrophysics Data System (ADS)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2015-10-01

In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

Development of C++ Application Program for Solving Quadratic Equation in Elementary School in Nigeria

ERIC Educational Resources Information Center

Bandele, Samuel Oye; Adekunle, Adeyemi Suraju

2015-01-01

The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…

A reduced successive quadratic programming strategy for errors-in-variables estimation.

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

Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.

Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases atmore » least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.« less

The design of dual-mode complex signal processors based on quadratic modular number codes

NASA Astrophysics Data System (ADS)

Jenkins, W. K.; Krogmeier, J. V.

1987-04-01

It has been known for a long time that quadratic modular number codes admit an unusual representation of complex numbers which leads to complete decoupling of the real and imaginary channels, thereby simplifying complex multiplication and providing error isolation between the real and imaginary channels. This paper first presents a tutorial review of the theory behind the different types of complex modular rings (fields) that result from particular parameter selections, and then presents a theory for a 'dual-mode' complex signal processor based on the choice of augmented power-of-2 moduli. It is shown how a diminished-1 binary code, used by previous designers for the realization of Fermat number transforms, also leads to efficient realizations for dual-mode complex arithmetic for certain augmented power-of-2 moduli. Then a design is presented for a recursive complex filter based on a ROM/ACCUMULATOR architecture and realized in an augmented power-of-2 quadratic code, and a computer-generated example of a complex recursive filter is shown to illustrate the principles of the theory.

Evaluating the efficiency of a one-square-meter quadrat sampler for riffle-dwelling fish

USGS Publications Warehouse

Peterson, J.T.; Rabeni, C.F.

2001-01-01

We evaluated the efficacy of a 1-m2 quadrat sampler for collecting riffle-dwelling fishes in an Ozark stream. We used a dual-gear approach to evaluate sampler efficiency in relation to species, fish size, and habitat variables. Quasi-likelihood regression showed sampling efficiency to differ significantly (P 0.05). Sampling efficiency was significantly influenced by physical habitat characteristics. Mean current velocity negatively influenced sampling efficiencies for Cyprinidae (P = 0.009), Cottidae (P = 0.006), and Percidae (P < 0.001), and the amount of cobble substrate negatively influenced sampling efficiencies for Cyprinidae (P = 0.025), Ictaluridae (P < 0.001), and Percidae (P < 0.001). Water temperature negatively influenced sampling efficiency for Cyprinidae (P = 0.009) and Ictaluridae (P = 0.006). Species-richness efficiency was positively influenced (P = 0.002) by percentage of riffle sampled. Under average habitat conditions encountered in stream riffles, the 1-m2 quadrat sampler was most efficient at estimating the densities of Cyprinidae (84%) and Cottidae (80%) and least efficient for Percidae (57%) and Ictaluridae (31%).

Analysis of warping deformation modes using higher order ANCF beam element

NASA Astrophysics Data System (ADS)

Orzechowski, Grzegorz; Shabana, Ahmed A.

2016-02-01

Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.

Random vibrations of quadratic damping systems. [optimum damping analysis for automobile suspension system

NASA Technical Reports Server (NTRS)

Sireteanu, T.

1974-01-01

An oscillating system with quadratic damping subjected to white noise excitation is replaced by a nonlinear, statistically equivalent system for which the associated Fokker-Planck equation can be exactly solved. The mean square responses are calculated and the optimum damping coefficient is determined with respect to the minimum mean square acceleration criteria. An application of these results to the optimization of automobile suspension damping is given.

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

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

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Reconstruction of quadratic curves in 3D using two or more perspective views: simulation studies

NASA Astrophysics Data System (ADS)

Kumar, Sanjeev; Sukavanam, N.; Balasubramanian, R.

2006-01-01

The shapes of many natural and man-made objects have planar and curvilinear surfaces. The images of such curves usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we describe a method of reconstruction of a quadratic curve in 3-D space as an intersection of two cones containing the respective projected curve images. The correspondence between this pair of projections of the curve is assumed to be established in this work. Using least-square curve fitting, the parameters of a curve in 2-D space are found. From this we are reconstructing the 3-D quadratic curve. Relevant mathematical formulations and analytical solutions for obtaining the equation of reconstructed curve are given. The result of the described reconstruction methodology are studied by simulation studies. This reconstruction methodology is applicable to LBW decision in cricket, path of the missile, Robotic Vision, path lanning etc.

Multi-phase arrival tracking using tetrahedral cells within a 3D layered titled transversely isotropic anisotropic model involving undulating topography and irregular interfaces

NASA Astrophysics Data System (ADS)

Li, Xing-Wang; Bai, Chao-Ying; Yue, Xiao-Peng; Greenhalgh, Stewart

2018-02-01

To overcome a major problem in current ray tracing methods, which are only capable of tracing first arrivals, and occasionally primary reflections (or mode conversions) in regular cell models, we extend in this paper the multistage triangular shortest-path method (SPM) into 3D titled transversely isotropic (TTI) anisotropic media. The proposed method is capable of tracking multi-phase arrivals composed of any kind of combinations of transmissions, mode conversions and reflections. In model parameterization, five elastic parameters, plus two angles defining the titled axis of symmetry of TTI media are sampled at the primary nodes of the tetrahedral cell, and velocity value at secondary node positions are linked by a tri-linear velocity interpolation function to the primary node velocity value of that of a tetrahedral cell, from which the group velocities of the three wave modes (qP, qSV and qSH) are computed. The multistage triangular SPM is used to track multi-phase arrivals. The uniform anisotropic test indicates that the numerical solution agrees well with the analytic solution, thus verifying the accuracy of the methodology. Several simulations and comparison results for heterogeneous models show that the proposed algorithm is able to efficiently and accurately approximate undulating surface topography and irregular subsurface velocity discontinuities. It is suitable for any combination of multi-phase arrival tracking in arbitrary tilt angle TTI media and can accommodate any magnitude of anisotropy.

Finite Element Analysis of a Copper Single Crystal Shape Memory Alloy-Based Endodontic Instruments

NASA Astrophysics Data System (ADS)

Vincent, Marin; Thiebaud, Frédéric; Bel Haj Khalifa, Saifeddine; Engels-Deutsch, Marc; Ben Zineb, Tarak

2015-10-01

The aim of the present paper is the development of endodontic Cu-based single crystal Shape Memory Alloy (SMA) instruments in order to eliminate the antimicrobial and mechanical deficiencies observed with the conventional Nickel-Titane (NiTi) SMA files. A thermomechanical constitutive law, already developed and implemented in a finite element code by our research group, is adopted for the simulation of the single crystal SMA behavior. The corresponding material parameters were identified starting from experimental results for a tensile test at room temperature. A computer-aided design geometry has been achieved and considered for a finite element structural analysis of the endodontic Cu-based single crystal SMA files. They are meshed with tetrahedral continuum elements to improve the computation time and the accuracy of results. The geometric parameters tested in this study are the length of the active blade, the rod length, the pitch, the taper, the tip diameter, and the rod diameter. For each set of adopted parameters, a finite element model is built and tested in a combined bending-torsion loading in accordance with ISO 3630-1 norm. The numerical analysis based on finite element procedure allowed purposing an optimal geometry suitable for Cu-based single crystal SMA endodontic files. The same analysis was carried out for the classical NiTi SMA files and a comparison was made between the two kinds of files. It showed that Cu-based single crystal SMA files are less stiff than the NiTi files. The Cu-based endodontic files could be used to improve the root canal treatments. However, the finite element analysis brought out the need for further investigation based on experiments.

A Space-Time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes

NASA Technical Reports Server (NTRS)

Zhang, Zeng-Chan; Yu, S. T. John; Chang, Sin-Chung; Jorgenson, Philip (Technical Monitor)

2001-01-01

In this paper, we report a version of the Space-Time Conservation Element and Solution Element (CE/SE) Method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing ease of implementing non-reflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without using a dimensional-splitting approach. In particular, because Riemann solvers, the cornerstones of the Godunov-type upwind schemes, are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.

Structural characterization of rondorfite, calcium silica chlorine mineral containing magnesium in tetrahedral position [MgO4]6-, with the aid of the vibrational spectroscopies and fluorescence.

PubMed

Dulski, M; Bulou, A; Marzec, K M; Galuskin, E V; Wrzalik, R

2013-01-15

Raman and infrared spectra of rondorfite Ca8Mg(SiO4)4Cl2, a calcium chlorosilica mineral containing magnesium in tetrahedral position, has been studied in terms of spectra-structure relations. Raman spectra have been measured at different excited laser lines: 780 nm, 532 nm, 488 nm and 457 nm. This mineral is characterized by a single sharp intense Raman band at 863 cm(-1) assigned to the ν1 [SiO4]4- (Ag) symmetric stretching mode in the magnesiosilicate pentamer. Due to symmetry restriction the other Raman bands have a small intensity. Two Raman bands observed at 564 cm(-1) and 526 cm(-1) are associated simultaneously with ν4 [MgO4]6- and ν4 [SiO4]4- symmetric and antisymmetric modes where magnesium occurs in the tetrahedral configuration. The weak bands at 422 cm(-1) and 386 cm(-1) are associated with the ν2 bending mode of CaO6 in octahedral configuration, respectively. Moreover the infrared spectrum shows very weak bands associated with the hydroxyl group and/or water molecule. Additionally, the strong fluorescence phenomenon was observed and related to the presence of chlorine atoms, magnesium Mg2+ ions in atypical configuration or point defects. Copyright © 2012 Elsevier B.V. All rights reserved.

Constraint analysis of two-dimensional quadratic gravity from { BF} theory

NASA Astrophysics Data System (ADS)

Valcárcel, C. E.

2017-01-01

Quadratic gravity in two dimensions can be formulated as a background field ( BF) theory plus an interaction term which is polynomial in both, the gauge and background fields. This formulation is similar to the one given by Freidel and Starodubtsev to obtain MacDowell-Mansouri gravity in four dimensions. In this article we use the Dirac's Hamiltonian formalism to analyze the constraint structure of the two-dimensional Polynomial BF action. After we obtain the constraints of the theory, we proceed with the Batalin-Fradkin-Vilkovisky procedure to obtain the transition amplitude. We also compare our results with the ones obtained from generalized dilaton gravity.

Multi-threading performance of Geant4, MCNP6, and PHITS Monte Carlo codes for tetrahedral-mesh geometry.

PubMed

Han, Min Cheol; Yeom, Yeon Soo; Lee, Hyun Su; Shin, Bangho; Kim, Chan Hyeong; Furuta, Takuya

2018-05-04

In this study, the multi-threading performance of the Geant4, MCNP6, and PHITS codes was evaluated as a function of the number of threads (N) and the complexity of the tetrahedral-mesh phantom. For this, three tetrahedral-mesh phantoms of varying complexity (simple, moderately complex, and highly complex) were prepared and implemented in the three different Monte Carlo codes, in photon and neutron transport simulations. Subsequently, for each case, the initialization time, calculation time, and memory usage were measured as a function of the number of threads used in the simulation. It was found that for all codes, the initialization time significantly increased with the complexity of the phantom, but not with the number of threads. Geant4 exhibited much longer initialization time than the other codes, especially for the complex phantom (MRCP). The improvement of computation speed due to the use of a multi-threaded code was calculated as the speed-up factor, the ratio of the computation speed on a multi-threaded code to the computation speed on a single-threaded code. Geant4 showed the best multi-threading performance among the codes considered in this study, with the speed-up factor almost linearly increasing with the number of threads, reaching ~30 when N  =  40. PHITS and MCNP6 showed a much smaller increase of the speed-up factor with the number of threads. For PHITS, the speed-up factors were low when N  =  40. For MCNP6, the increase of the speed-up factors was better, but they were still less than ~10 when N  =  40. As for memory usage, Geant4 was found to use more memory than the other codes. In addition, compared to that of the other codes, the memory usage of Geant4 more rapidly increased with the number of threads, reaching as high as ~74 GB when N  =  40 for the complex phantom (MRCP). It is notable that compared to that of the other codes, the memory usage of PHITS was much lower, regardless of both the complexity of the

Deviations from idealised geometries part 3: approximately tetrahedral molecules of form MX 2Y 2 studied by SCF and MP2 calculations

NASA Astrophysics Data System (ADS)

Palmer, Michael H.

1997-03-01

The relatively minor deviations from true tetrahedral geometry for molecules of type MX 2Y 2 where M is tetravalent, and X, Y are either H, Me or halogen are discussed, in the light of ab initio calculations of equilibrium geometry with a large (triple zeta valence + polarisation) basis, at both the SCF and MP2 levels. The results are compared with known experimental structural and dipole moment data; in most cases a very close correlation with experiment is found, with slight improvements in the MP2 data. The study is coupled with a localised orbital study of relevance to Bent's Rule.

Investigation of quadratic electro-optic effects and electro-absorption process in GaN/AlGaN spherical quantum dot

PubMed Central

2014-01-01

Quadratic electro-optic effects (QEOEs) and electro-absorption (EA) process in a GaN/AlGaN spherical quantum dot are theoretically investigated. It is found that the magnitude and resonant position of third-order nonlinear optical susceptibility depend on the nanostructure size and aluminum mole fraction. With increase of the well width and barrier potential, quadratic electro-optic effect and electro-absorption process nonlinear susceptibilities are decreased and blueshifted. The results show that the DC Kerr effect in this case is much larger than that in the bulk case. Finally, it is observed that QEOEs and EA susceptibilities decrease and broaden with the decrease of relaxation time. PMID:24646318

Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

NASA Technical Reports Server (NTRS)

Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

2009-01-01

The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

Sensitive SERS detection of lead ions via DNAzyme based quadratic signal amplification.

PubMed

Tian, Aihua; Liu, Yu; Gao, Jian

2017-08-15

Highly sensitive detection of Pb 2+ is very necessary for water quality control, clinical toxicology, and industrial monitoring. In this work, a simple and novel DNAzyme-based SERS quadratic amplification method is developed for the detection of Pb 2+ . This strategy possesses some remarkable features compared to the conventional DNAzyme-based SERS methods, which are as follows: (i) Coupled DNAzyme-activated hybridization chain reaction (HCR) with bio barcodes; a quadratic amplification method is designed using the unique catalytic selectivity of DNAzyme. The SERS signal is significantly amplified. This method is rapid with a detection time of 2h. (ii) The problem of high background induced by excess bio barcodes is circumvented by using magnetic beads (MBs) as the carrier of signal-output products, and this sensing system is simple in design and can easily be carried out by simple mixing and incubation. Given the unique and attractive characteristics, a simple and universal strategy is designed to accomplish sensitive detection of Pb 2+ . The detection limit of Pb 2+ via SERS detection is 70 fM, with the linear range from 1.0×10 -13 M to 1.0×10 -7 M. The method can be further extended to the quantitative detection of a variety of targets by replacing the lead-responsive DNAzyme with other functional DNA. Copyright © 2017 Elsevier B.V. All rights reserved.

Large radius of curvature measurement based on virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer.

PubMed

Yang, Zhongming; Wang, Kailiang; Cheng, Jinlong; Gao, Zhishan; Yuan, Qun

2016-06-10

We have proposed a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer to measure the large radius of curvature for a spherical surface. In a quadratic polar coordinate system, linear carrier testing Newton rings interferogram and virtual Newton rings interferogram form the moiré fringes. It is possible to retrieve the wavefront difference data between the testing and standard spherical surface from the moiré fringes after low-pass filtering. Based on the wavefront difference data, we deduced a precise formula to calculate the radius of curvature in the quadratic polar coordinate system. We calculated the retrace error in the nonnull interferometer using the multi-configuration model of the nonnull interferometric system in ZEMAX. Our experimental results indicate that the measurement accuracy is better than 0.18% for a spherical mirror with a radius of curvature of 41,400 mm.

Solid-state reversible quadratic nonlinear optical molecular switch with an exceptionally large contrast.

PubMed

Sun, Zhihua; Luo, Junhua; Zhang, Shuquan; Ji, Chengmin; Zhou, Lei; Li, Shenhui; Deng, Feng; Hong, Maochun

2013-08-14

Exceptional nonlinear optical (NLO) switching behavior, including an extremely large contrast (on/off) of ∼35 and high NLO coefficients, is displayed by a solid-state reversible quadratic NLO switch. The favorable results, induced by very fast molecular motion and anionic ordering, provides impetus for the design of a novel second-harmonic-generation switch involving molecular motion. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Item Pool Construction Using Mixed Integer Quadratic Programming (MIQP). GMAC® Research Report RR-14-01

ERIC Educational Resources Information Center

Han, Kyung T.; Rudner, Lawrence M.

2014-01-01

This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…

Elasticity, strength, and toughness of single crystal silicon carbide, ultrananocrystalline diamond, and hydrogen-free tetrahedral amorphous carbon

NASA Astrophysics Data System (ADS)

Espinosa, H. D.; Peng, B.; Moldovan, N.; Friedmann, T. A.; Xiao, X.; Mancini, D. C.; Auciello, O.; Carlisle, J.; Zorman, C. A.; Merhegany, M.

2006-08-01

In this work, the authors report the mechanical properties of three emerging materials in thin film form: single crystal silicon carbide (3C-SiC), ultrananocrystalline diamond, and hydrogen-free tetrahedral amorphous carbon. The materials are being employed in micro- and nanoelectromechanical systems. Several reports addressed some of the mechanical properties of these materials but they are based in different experimental approaches. Here, they use a single testing method, the membrane deflection experiment, to compare these materials' Young's moduli, characteristic strengths, fracture toughnesses, and theoretical strengths. Furthermore, they analyze the applicability of Weibull theory [Proc. Royal Swedish Inst. Eng. Res. 153, 1 (1939); ASME J. Appl. Mech. 18, 293 (1951)] in the prediction of these materials' failure and document the volume- or surface-initiated failure modes by fractographic analysis. The findings are of particular relevance to the selection of micro- and nanoelectromechanical systems materials for various applications of interest.

Direct Observation of Very Large Zero-Field Splitting in a Tetrahedral Ni(II)Se4 Coordination Complex.

PubMed

Jiang, Shang-Da; Maganas, Dimitrios; Levesanos, Nikolaos; Ferentinos, Eleftherios; Haas, Sabrina; Thirunavukkuarasu, Komalavalli; Krzystek, J; Dressel, Martin; Bogani, Lapo; Neese, Frank; Kyritsis, Panayotis

2015-10-14

The high-spin (S = 1) tetrahedral Ni(II) complex [Ni{(i)Pr2P(Se)NP(Se)(i)Pr2}2] was investigated by magnetometry, spectroscopic, and quantum chemical methods. Angle-resolved magnetometry studies revealed the orientation of the magnetization principal axes. The very large zero-field splitting (zfs), D = 45.40(2) cm(-1), E = 1.91(2) cm(-1), of the complex was accurately determined by far-infrared magnetic spectroscopy, directly observing transitions between the spin sublevels of the triplet ground state. These are the largest zfs values ever determined--directly--for a high-spin Ni(II) complex. Ab initio calculations further probed the electronic structure of the system, elucidating the factors controlling the sign and magnitude of D. The latter is dominated by spin-orbit coupling contributions of the Ni ions, whereas the corresponding effects of the Se atoms are remarkably smaller.

Finite-element time-domain modeling of electromagnetic data in general dispersive medium using adaptive Padé series

NASA Astrophysics Data System (ADS)

Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin; Zhdanov, Michael S.

2017-12-01

The induced polarization (IP) method has been widely used in geophysical exploration to identify the chargeable targets such as mineral deposits. The inversion of the IP data requires modeling the IP response of 3D dispersive conductive structures. We have developed an edge-based finite-element time-domain (FETD) modeling method to simulate the electromagnetic (EM) fields in 3D dispersive medium. We solve the vector Helmholtz equation for total electric field using the edge-based finite-element method with an unstructured tetrahedral mesh. We adopt the backward propagation Euler method, which is unconditionally stable, with semi-adaptive time stepping for the time domain discretization. We use the direct solver based on a sparse LU decomposition to solve the system of equations. We consider the Cole-Cole model in order to take into account the frequency-dependent conductivity dispersion. The Cole-Cole conductivity model in frequency domain is expanded using a truncated Padé series with adaptive selection of the center frequency of the series for early and late time. This approach can significantly increase the accuracy of FETD modeling.

Cosmology for quadratic gravity in generalized Weyl geometry

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

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Koivisto, Tomi S.

A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excludingmore » pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.« less

Quadratic dissipation effect on the moonpool resonance

NASA Astrophysics Data System (ADS)

Liu, Heng-xu; Chen, Hai-long; Zhang, Liang; Zhang, Wan-chao; Liu, Ming

2017-12-01

This paper adopted a semi-analytical method based on eigenfunction matching to solve the problem of sharp resonance of cylindrical structures with a moonpool that has a restricted entrance. To eliminate the sharp resonance and to measure the viscous effect, a quadratic dissipation is introduced by assuming an additional dissipative disk at the moonpool entrance. The fluid domain is divided into five cylindrical subdomains, and the velocity potential in each subdomain is obtained by meeting the Laplace equation as well as the boundary conditions. The free-surface elevation at the center of the moonpool, along with the pressure and velocity at the restricted entrance for first-order wave are evaluated. By choosing appropriate dissipation coefficients, the free-surface elevation calculated at the center of the moonpool is in coincidence with the measurements in model tests both at the peak period and amplitude at resonance. It is shown that the sharp resonance in the potential flow theory can be eliminated and the viscous effect can be estimated with a simple method in some provided hydrodynamic models.

Extremal Optimization for Quadratic Unconstrained Binary Problems

NASA Astrophysics Data System (ADS)

Boettcher, S.

We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.

A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S.; Klang, Eric C.

2001-01-01

The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.

Excited-state absorption in tetrapyridyl porphyrins: comparing real-time and quadratic-response time-dependent density functional theory

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

Bowman, David N.; Asher, Jason C.; Fischer, Sean A.

2017-01-01

Threemeso-substituted tetrapyridyl porphyrins (free base, Ni(ii), and Cu(ii)) were investigated for their optical limiting (OL) capabilities using real-time (RT-), linear-response (LR-), and quadratic-response (QR-) time-dependent density functional theory (TDDFT) methods.

73Ge, 119Sn and 207Pb: general cooperative effects of single atom ligands on the NMR signals observed in tetrahedral [MXnY4-n] (M = Ge, Sn, Pb; 1 ≤ n ≤ 4; X, Y = Cl, Br, I) coordination compounds of heavier XIV group elements.

PubMed

Benedetti, M; De Castro, F; Fanizzi, F P

2017-02-28

An inverse linear relationship between 73 Ge, 119 Sn and 207 Pb NMR chemical shifts and the overall sum of ionic radii of coordinated halido ligands has been discovered in tetrahedral [MX n Y 4-n ] (M = Ge, Sn, Pb; 1 ≤ n ≤ 4; X, Y = Cl, Br, I) coordination compounds. This finding is consistent with a previously reported correlation found in octahedral, pentacoordinate and square planar platinum complexes. The effect of the coordinated halido ligands acting on the metal as shielding conducting rings is therefore confirmed also by 73 Ge, 119 Sn and 207 Pb NMR spectroscopy.

A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.

2018-01-01

We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.

Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers

NASA Astrophysics Data System (ADS)

Chen, Baoqin; Hong, Lihong; Hu, Chenyang; Zhang, Chao; Liu, Rongjuan; Li, Zhiyuan

2018-03-01

Nonlinear frequency conversion offers an effective way to extend the laser wavelength range. Quadratic nonlinear photonic crystals (NPCs) are artificial materials composed of domain-inversion structures whose sign of nonlinear coefficients are modulated with desire to implement quasi-phase matching (QPM) required for nonlinear frequency conversion. These structures can offer various reciprocal lattice vectors (RLVs) to compensate the phase-mismatching during the quadratic nonlinear optical processes, including second-harmonic generation (SHG), sum-frequency generation and the cascaded third-harmonic generation (THG). The modulation pattern of the nonlinear coefficients is flexible, which can be one-dimensional or two-dimensional (2D), be periodic, quasi-periodic, aperiodic, chirped, or super-periodic. As a result, these NPCs offer very flexible QPM scheme to satisfy various nonlinear optics and laser frequency conversion problems via design of the modulation patterns and RLV spectra. In particular, we introduce the electric poling technique for fabricating QPM structures, a simple effective nonlinear coefficient model for efficiently and precisely evaluating the performance of QPM structures, the concept of super-QPM and super-periodically poled lithium niobate for finely tuning nonlinear optical interactions, the design of 2D ellipse QPM NPC structures enabling continuous tunability of SHG in a broad bandwidth by simply changing the transport direction of pump light, and chirped QPM structures that exhibit broadband RLVs and allow for simultaneous radiation of broadband SHG, THG, HHG and thus coherent white laser from a single crystal. All these technical, theoretical, and physical studies on QPM NPCs can help to gain a deeper insight on the mechanisms, approaches, and routes for flexibly controlling the interaction of lasers with various QPM NPCs for high-efficiency frequency conversion and creation of novel lasers.

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

NASA Astrophysics Data System (ADS)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2015-11-01

We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

Single-photon frequency conversion via cascaded quadratic nonlinear processes

NASA Astrophysics Data System (ADS)

Xiang, Tong; Sun, Qi-Chao; Li, Yuanhua; Zheng, Yuanlin; Chen, Xianfeng

2018-06-01

Frequency conversion of single photons is an important technology for quantum interface and quantum communication networks. Here, single-photon frequency conversion in the telecommunication band is experimentally demonstrated via cascaded quadratic nonlinear processes. Using cascaded quasi-phase-matched sum and difference frequency generation in a periodically poled lithium niobate waveguide, the signal photon of a photon pair from spontaneous down-conversion is precisely shifted to identically match its counterpart, i.e., the idler photon, in frequency to manifest a clear nonclassical dip in the Hong-Ou-Mandel interference. Moreover, quantum entanglement between the photon pair is maintained after the frequency conversion, as is proved in time-energy entanglement measurement. The scheme is used to switch single photons between dense wavelength-division multiplexing channels, which holds great promise in applications in realistic quantum networks.

Thermodynamics of charged Lifshitz black holes with quadratic corrections

NASA Astrophysics Data System (ADS)

Bravo-Gaete, Moisés; Hassaïne, Mokhtar

2015-03-01

In arbitrary dimension, we consider the Einstein-Maxwell Lagrangian supplemented by the more general quadratic-curvature corrections. For this model, we derive four classes of charged Lifshitz black hole solutions for which the metric function is shown to depend on a unique integration constant. The masses of these solutions are computed using the quasilocal formalism based on the relation established between the off-shell Abbott-Deser-Tekin and Noether potentials. Among these four solutions, three of them are interpreted as extremal in the sense that their masses vanish identically. For the last family of solutions, both the quasilocal mass and the electric charge are shown to depend on the integration constant. Finally, we verify that the first law of thermodynamics holds for each solution and a Smarr formula is also established for the four solutions.

Two healing lengths in a two-band GL-model with quadratic terms: Numerical results

NASA Astrophysics Data System (ADS)

Macias-Medri, A. E.; Rodríguez-Núñez, J. J.

2018-05-01

A two-band and quartic interaction order Ginzburg-Landau model in the presence of a single vortex is studied in this work. Interactions of second (quadratic, with coupling parameter γ) and fourth (quartic, with coupling parameter γ˜) order between the two superconducting order parameters (fi with i = 1,2) are incorporated in a functional. Terms beyond quadratic gradient contributions are neglected in the corresponding minimized free energy. The solution of the system of coupled equations is solved by numerical methods to obtain the fi-profiles, where our starting point was the calculation of the superconducting critical temperature Tc. With this at hand, we evaluate fi and the magnetic field along the z-axis, B0, as function of γ, γ˜, the radial distance r/λ1(0) and the temperature T, for T ≈ Tc. The self-consistent equations allow us to compute λ (penetration depth) and the healing lengths of fi (Lhi with i = 1,2) as functions of T, γ and γ˜. At the end, relevant discussions about type-1.5 superconductivity in the compounds we have studied are presented.

IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach

NASA Astrophysics Data System (ADS)

Kunze, Herb; La Torre, Davide; Lin, Jianyi

2017-01-01

We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.

Low photon count based digital holography for quadratic phase cryptography.

PubMed

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Ryle, James P; Healy, John J; Lee, Byung-Geun; Sheridan, John T

2017-07-15

Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.

A finite element head and neck model as a supportive tool for deformable image registration.

PubMed

Kim, Jihun; Saitou, Kazuhiro; Matuszak, Martha M; Balter, James M

2016-07-01

A finite element (FE) head and neck model was developed as a tool to aid investigations and development of deformable image registration and patient modeling in radiation oncology. Useful aspects of a FE model for these purposes include ability to produce realistic deformations (similar to those seen in patients over the course of treatment) and a rational means of generating new configurations, e.g., via the application of force and/or displacement boundary conditions. The model was constructed based on a cone-beam computed tomography image of a head and neck cancer patient. The three-node triangular surface meshes created for the bony elements (skull, mandible, and cervical spine) and joint elements were integrated into a skeletal system and combined with the exterior surface. Nodes were additionally created inside the surface structures which were composed of the three-node triangular surface meshes, so that four-node tetrahedral FE elements were created over the whole region of the model. The bony elements were modeled as a homogeneous linear elastic material connected by intervertebral disks. The surrounding tissues were modeled as a homogeneous linear elastic material. Under force or displacement boundary conditions, FE analysis on the model calculates approximate solutions of the displacement vector field. A FE head and neck model was constructed that skull, mandible, and cervical vertebrae were mechanically connected by disks. The developed FE model is capable of generating realistic deformations that are strain-free for the bony elements and of creating new configurations of the skeletal system with the surrounding tissues reasonably deformed. The FE model can generate realistic deformations for skeletal elements. In addition, the model provides a way of evaluating the accuracy of image alignment methods by producing a ground truth deformation and correspondingly simulated images. The ability to combine force and displacement conditions provides

On the prediction of free turbulent jets with swirl using a quadratic pressure-strain model

NASA Technical Reports Server (NTRS)

Younis, Bassam A.; Gatski, Thomas B.; Speziale, Charles G.

1994-01-01

Data from free turbulent jets both with and without swirl are used to assess the performance of the pressure-strain model of Speziale, Sarkar and Gatski which is quadratic in the Reynolds stresses. Comparative predictions are also obtained with the two versions of the Launder, Reece and Rodi model which are linear in the same terms. All models are used as part of a complete second-order closure based on the solution of differential transport equations for each non-zero component of the Reynolds stress tensor together with an equation for the scalar energy dissipation rate. For non-swirling jets, the quadratic model underestimates the measured spreading rate of the plane jet but yields a better prediction for the axisymmetric case without resolving the plane jet/round jet anomaly. For the swirling axisymmetric jet, the same model accurately reproduces the effects of swirl on both the mean flow and the turbulence structure in sharp contrast with the linear models which yield results that are in serious error. The reasons for these differences are discussed.

Quadratic time dependent Hamiltonians and separation of variables

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2017-06-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

Effects of Process Parameters on Copper Powder Compaction Process Using Multi-Particle Finite Element Method

NASA Astrophysics Data System (ADS)

Güner, F.; Sofuoğlu, H.

2018-01-01

Powder metallurgy (PM) has been widely used in several industries; especially automotive and aerospace industries and powder metallurgy products grow up every year. The mechanical properties of the final product that is obtained by cold compaction and sintering in powder metallurgy are closely related to the final relative density of the process. The distribution of the relative density in the die is affected by parameters such as compaction velocity, friction coefficient and temperature. Moreover, most of the numerical studies utilizing finite element approaches treat the examined environment as a continuous media with uniformly homogeneous porosity whereas Multi-Particle Finite Element Method (MPFEM) treats every particles as an individual body. In MPFEM, each of the particles can be defined as an elastic- plastic deformable body, so the interactions of the particles with each other and the die wall can be investigated. In this study, each particle was modelled and analyzed as individual deformable body with 3D tetrahedral elements by using MPFEM approach. This study, therefore, was performed to investigate the effects of different temperatures and compaction velocities on stress distribution and deformations of copper powders of 200 µm-diameter in compaction process. Furthermore, 3-D MPFEM model utilized von Mises material model and constant coefficient of friction of μ=0.05. In addition to MPFEM approach, continuum modelling approach was also performed for comparison purposes.

Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.

PubMed

Ginzburg, D; Mann, A

2014-03-10

A Lie algebraic method for propagation of the Wigner quasi-distribution function (QDF) under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of QDFs, which we call the "Gaussian class." This class contains as special cases the well-known Wigner, Husimi, Glauber, and Kirkwood-Rihaczek QDFs. We present some examples of the calculation of the time evolution of those functions.

Erasing no-man's land by thermodynamically stabilizing the liquid-liquid transition in tetrahedral particles.

PubMed

Smallenburg, Frank; Filion, Laura; Sciortino, Francesco

2014-09-01

One of the most controversial hypotheses for explaining the origin of the thermodynamic anomalies characterizing liquid water postulates the presence of a metastable second-order liquid-liquid critical point [1] located in the "no-man's land" [2]. In this scenario, two liquids with distinct local structure emerge near the critical temperature. Unfortunately, since spontaneous crystallization is rapid in this region, experimental support for this hypothesis relies on significant extrapolations, either from the metastable liquid or from amorphous solid water [3, 4]. Although the liquid-liquid transition is expected to feature in many tetrahedrally coordinated liquids, including silicon [5], carbon [6] and silica, even numerical studies of atomic and molecular models have been unable to conclusively prove the existence of this transition. Here we provide such evidence for a model in which it is possible to continuously tune the softness of the interparticle interaction and the flexibility of the bonds, the key ingredients controlling the existence of the critical point. We show that conditions exist where the full coexistence is thermodynamically stable with respect to crystallization. Our work offers a basis for designing colloidal analogues of water exhibiting liquid-liquid transitions in equilibrium, opening the way for experimental confirmation of the original hypothesis.

Conductive tracks of 30-MeV C60 clusters in doped and undoped tetrahedral amorphous carbon

NASA Astrophysics Data System (ADS)

Krauser, J.; Gehrke, H.-G.; Hofsäss, H.; Trautmann, C.; Weidinger, A.

2013-07-01

In insulating tetrahedral amorphous carbon (ta-C), the irradiation with 30-MeV C60 cluster ions leads to the formation of well conducting tracks. While electrical currents through individual tracks produced with monoatomic projectiles (e.g. Au or U) often exhibit rather large track to track fluctuations, C60 clusters are shown to generate highly conducting tracks with very narrow current distributions. Additionally, all recorded current-voltage curves show linear characteristics. These findings are attributed to the large specific energy loss dE/dx of the 30-MeV C60 clusters. We also investigated C60 tracks in ta-C films which were slightly doped with B, N or Fe during film growth. Doping apparently increases the ion track conductivity. However, at the same time the insulating characteristics of the pristine ta-C film can be reduced. The present C60 results are compared with data from earlier experiments with monoatomic heavy ion beams. The investigations were performed by means of atomic force microscopy including temperature dependent conductivity measurements of single ion tracks.

Erasing no-man’s land by thermodynamically stabilizing the liquid-liquid transition in tetrahedral particles

NASA Astrophysics Data System (ADS)

Smallenburg, Frank; Filion, Laura; Sciortino, Francesco

2014-09-01

One of the most controversial hypotheses for explaining the origin of the thermodynamic anomalies characterizing liquid water postulates the presence of a metastable second-order liquid-liquid critical point located in the `no-man’s land’. In this scenario, two liquids with distinct local structure emerge near the critical temperature. Unfortunately, as spontaneous crystallization is rapid in this region, experimental support for this hypothesis relies on significant extrapolations, either from the metastable liquid or from amorphous solid water. Although the liquid-liquid transition is expected to feature in many tetrahedrally coordinated liquids, including silicon, carbon and silica, even numerical studies of atomic and molecular models have been unable to conclusively prove the existence of this transition. Here we provide such evidence for a model in which it is possible to continuously tune the softness of the interparticle interaction and the flexibility of the bonds, the key ingredients controlling the existence of the critical point. We show that conditions exist where the full coexistence is thermodynamically stable with respect to crystallization. Our work offers a basis for designing colloidal analogues of water exhibiting liquid-liquid transitions in equilibrium, opening the way for experimental confirmation of the original hypothesis.