Tetrahedral spectral elements for CFD
NASA Astrophysics Data System (ADS)
Sherwin, S. J.; Karniadakis, G. E.
In this paper we describe the foundation of a new hierarchical basis suitable for spectral and h - p type finite elements in complex, three-dimensional domains. It is based on Jacobi polynomials of mixed weights and allows for a variable order in each element, which is a crucial property for efficient adaptive discretizations on unstructured meshes. In addition, it has the desirable property of an O(N 2) spectrum scaling for the convective operator as in tensorial spectral methods; this is important in explicit time-integration of the Navier-Stokes equations. The general Galerkin formulation for elliptic equations and a high-order splitting scheme used to solve the two-dimensional Navier-Stokes equations has been documented in [2]. Here we elaborate on the three-dimensional basis and demonstrate its properties through different numerical examples. The new algorithms have been implemented in the general code N, ?kT ?r, which represents the new generation of spectral element methods for unstructured meshes.
Steven E. Benzley; Ernest Perry; Karl Merkley; Brett Clark; Greg Sjaardama
1995-01-01
This paper compares the accuracy of elastic and elastio-plastic solid continuum finite element analyses modeled with either all hexagonal or all tetrahedral meshes. Eigenvalues of element stiffness matrices, linear static displacements and stresses, dynamic modal frequencies, and plastic flow values in are computed and compared. Elements with both linear and quadratic displacement functions are evaluated. Linear incompressibility conditions are also
Finite element LES and VMS methods on tetrahedral meshes
NASA Astrophysics Data System (ADS)
John, Volker; Kindl, Adela; Suciu, Carina
2010-04-01
Finite element methods for problems given in complex domains are often based on tetrahedral meshes. This paper demonstrates that the so-called rational Large Eddy Simulation model and a projection-based Variational Multiscale method can be extended in a straightforward way to tetrahedral meshes. Numerical studies are performed with an inf-sup stable second order pair of finite elements with discontinuous pressure approximation.
Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur.
Ramos, A; Simões, J A
2006-11-01
The objective of this study was to evaluate and compare tetrahedral and hexahedral finite element meshes of simplified and realistic proximal intact femur geometries. Theoretical expressions of stresses and strains were derived for the simplified model of the femur. For the analysis of the realistic geometry of the proximal femur, a CAD model of the third generation composite femur (Pacific Research Labs, Vashion Island, WA) was used and simulations were performed with Hyperworks (Altair Engineering, Inc., Troy, MI) finite element analysis software. Convergence tests with hexahedral (8- and 20-node brick-elements) and tetrahedral (4- and 10-node tetrahedrons) elements were analysed by comparing the periosteal von Mises stresses and principal strains at a selected point of the femur. The numerical periosteal strains were also compared with experimental ones to determine the accuracy of the finite elements. Overall, we concluded, for the simplified femur, that tetrahedral linear element allowed results more closely to theoretical ones, but hexahedral quadratic elements seem to be more stable and less influenced to the degree of refinement (NDOF) of the mesh. It was not possible to correlate these findings with those observed for the realistic proximal femur simulations where no significant differences were seen using refined meshes, with more than NDOF=20,000 for hexahedral elements. PMID:16464628
Non-locking Tetrahedral Finite Element for Surgical Simulation
Joldes, Grand Roman; Wittek, Adam; Miller, Karol
2009-01-01
To obtain a very fast solution for finite element models used in surgical simulations low order elements such as the linear tetrahedron or the linear under-integrated hexahedron must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper we extend the average nodal pressure tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way, with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing TLED (Total Lagrangian Explicit Dynamics) algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared to the average nodal pressure element in case of models consisting of multiple materials.
A computational study of nodal-based tetrahedral element behavior.
Gullerud, Arne S.
2010-09-01
This report explores the behavior of nodal-based tetrahedral elements on six sample problems, and compares their solution to that of a corresponding hexahedral mesh. The problems demonstrate that while certain aspects of the solution field for the nodal-based tetrahedrons provide good quality results, the pressure field tends to be of poor quality. Results appear to be strongly affected by the connectivity of the tetrahedral elements. Simulations that rely on the pressure field, such as those which use material models that are dependent on the pressure (e.g. equation-of-state models), can generate erroneous results. Remeshing can also be strongly affected by these issues. The nodal-based test elements as they currently stand need to be used with caution to ensure that their numerical deficiencies do not adversely affect critical values of interest.
A suitable low-order, eight-node tetrahedral finite element for solids
S. W. Key; M. S. Heinstein; C. M. Stone; F. J. Mello; M. L. Blanford; K. G. Budge
1998-01-01
To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the
Ho, Philip Wai-Sun
1977-01-01
COMPARISON OF LINEAR STRAIN TRIANGULAR AND TETRAHEDRAL ELEMENTS WITH ISOPARAMETRIC ELEMENTS IN TWO- AND THREE-DIMENSIONAL FINITE ELEMENT ANALYSES A Thesis by Philip Wai-Sun Ho Submitted to the Graduate College of Texas A&M University...-DIMENSIONAL FINITE ELEMENT ANALYSES A Thesis by Philip Wai-Sun Ho Approved as to style and content by: (Chairman of Committee) (Head of Department (Mes r) (Member) December 1977 ABSTRACT Comparison of Linear Strain Triangular and Tetrahedral Elements...
A suitable low-order, eight-node tetrahedral finite element for solids
Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.
1998-03-01
To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the eight-node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties.
Implementation and Verification of a Nodally-Integrated Tetrahedral Element in FEBio
Utah, University of
geometric information for segmentation and mesh generation. However, mesh generation can be very difficult techniques [6]. Triangular and tetrahedral elements can be very effective for FE analyses of field variables solid mechanics, linear tetrahedral elements are overly stiff and can "lock" in problems where nearly
Calculation of non-linear vibration of rotating beams by using tetrahedral and solid finite elements
J. J. Jiang; C. L. Hsiao; A. A. Shabana
1991-01-01
A development is presented of the non-linear dynamic equations that govern the motion of the tetrahedral and solid finite elements that undergo large displacements. The development presented is exemplified by using the four-node, 12-degree-of-freedom tetrahedral element and the eight-node, 24-degree-of-freedom solid element. It is shown that the element shape functions used in this investigation can be used to describe large
A simple algorithm for adaptive refinement of tetrahedral meshes combined with edge elements
P. Olszewski; T. Nakata; N. Takahashi; K. Fujiwara
1993-01-01
A simple algorithm yielding unique face subdivision patterns of locally refined tetrahedral elements by the Delaunay tessellation process is presented. Due to the numerous advantages of edge elements, the algorithm is combined with the magnetostatic edge element computer code. A comparative analysis of four different error estimates used to locate elements for refinement, including a new one suitable for edge
C. C. Pain; A. P. Umpleby; C. R. E. de Oliveira; A. J. H. Goddard
2001-01-01
A method for optimising a pre-existing mesh of tetrahedral finite elements is described. It is based on a series of mesh connectivity and node position searches of the landscape defining mesh quality. A Riemannian metric, reflecting the a posteriori error measure, is used to calculate element size and shape. A functional is defined which embodies both shape and size quality
E. Cojocaru
2009-10-20
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic triangular elements may lead to an improved accuracy. Here we present a collection of elemental matrices evaluated analytically for quadratic triangular elements. They could be useful for the finite element method in advanced electromagnetics.
Tetrahedral element shape optimization via the Jacobian determinant and condition number.
Freitag, L. A.; Knupp, P. M.
1999-07-30
We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. We use this shape measure to formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the tetrahedral mesh; the second aims to improve the worst-quality element in the mesh. Because the element condition number is not defined for tetrahedral with negative volume, these objective functions can be used only when the initial mesh is valid. Therefore, we formulate a third objective function using the determinant of the element Jacobian that is suitable for mesh untangling. We review the optimization techniques used with each objective function and present experimental results that demonstrate the effectiveness of the mesh improvement and untangling methods. We show that a combined optimization approach that uses both condition number objective functions obtains the best-quality meshes.
Adaptive Surface Modeling Using a Quadtree of Quadratic Finite Elements
G. P. Nikishkov
2005-01-01
\\u000a This article presents special quadrilateral quadratic refinement elements, which provide geometry and field continuity across\\u000a T-junctions where two elements are connected to one side of a larger quadrilateral. The main idea in element refinement is\\u000a to place one or more nodes outside the element area and to modify element shape functions in order to maintain continuity\\u000a at refinement edges. Special
NASA Astrophysics Data System (ADS)
Zehner, Björn; Börner, Jana H.; Görz, Ines; Spitzer, Klaus
2015-06-01
Subsurface processing numerical simulations require accurate discretization of the modeling domain such that the geological units are represented correctly. Unstructured tetrahedral grids are particularly flexible in adapting to the shape of geo-bodies and are used in many finite element codes. In order to generate a tetrahedral mesh on a 3D geological model, the tetrahedrons have to belong completely to one geological unit and have to describe geological boundaries by connected facets of tetrahedrons. This is especially complicated at the contact points between several units and for irregular sharp-shaped bodies, especially in case of faulted zones. This study develops, tests and validates three workflows to generate a good tetrahedral mesh from a geological basis model. The tessellation of the model needs (i) to be of good quality to guarantee a stable calculation, (ii) to include certain nodes to apply boundary conditions for the numerical solution, and (iii) support local mesh refinement. As a test case we use the simulation of a transient electromagnetic measurement above a salt diapir. We can show that the suggested workflows lead to a tessellation of the structure on which the simulation can be run robustly. All workflows show advantages and disadvantages with respect to the workload, the control the user has over the resulting mesh and the skills in software handling that are required.
A discontinuity capturing SUPG formulation using quadratic element
Tony W. H. Sheu; Philip G. Y. Husang; Morten M. T. Wang
1992-01-01
The purpose of the present study is to add the discontinuity capturing term into the quadratic streamline upwind Petrov-Galerkin (SUPG) finite element formulation for predicting high resolution solution in a flowfield containing possible discontinuities. Both good stability and high-order accuracy can be achieved in solving the linear one-dimensional Burgers' equation containing three profiles of different characters and nonlinear Burgers' equation.
A three-dimensional FE analysis of large deformations for impact loadings using tetrahedral elements
NASA Astrophysics Data System (ADS)
Yoo, Y. H.; Lee, M.
A three-dimensional dynamic program for the anaysis of large deformations in contact-penetration problems is developed using the finite element Lagrangian method with explicit time integration. By incorporating a tetrahedral element, which allows a single-point integration without a special hourglass control scheme, this program can be more effective to the present problem. The position code algorithm is used to search contact surface. Eroding surfaces are also considered. The defense node algorithm was slightly modified for the calculation of contact forces. A study of obliquity effects on metallic plate perforation and ricochet processes in thin plates impacted by a sphere was conducted. It is well simulated that on separation of two parts of the sphere, the portion still within the crater tends to perforate, while the portion in contact with the plate surface ricochets. This deformation pattern is observed in experiments, especially at high obliquities. A long rod that impacts an oblique steel plate at high impact velocity was also simulated in order to study the dynamics of the rod caused by the three dimensional asymmetric contact. The agreement between simulated and experimental results is quite good. Fracture phenomena occuring at high obliquity deserves further investigations.
Quadratic Finite Element Method for 1D Deterministic Neutron Transport
Tolar, Jr., D R; Ferguson, J M
2004-11-24
We focus on improving the angular discretization of the angular flux for the one-dimensional (1D) spherical geometry neutron transport equation. Unlike the conventional SN method, we model the angular dependence of the flux with a Petrov-Galerkin finite element approximation for the differencing of the angular variable in developing the 1D spherical geometry S{sub N} equations. That is, we use both a piecewise bi-linear and a quadratic function in each angular bin to approximate the angular dependence of the flux. This new algorithm that we have developed shows faster convergence with angular resolution than conventional SN algorithms. (U)
Wave Propagation in QuadraticFiniteElement Approximations to Hyperbolic Equations #
Wave Propagation in QuadraticFiniteElement Approximations to Hyperbolic Equations # Dale R. Durran # University of Washington, USA October 8, 1999 SUMMARY Eigenmodes for the quadraticfiniteelement arise as part of the conventional analysis. KEYWORDS: 65P25 Finite Elements 76M10 Finite Element Methods
The quarter-point quadratic isoparametric element as a singular element for crack problems
NASA Technical Reports Server (NTRS)
Hussain, M. A.; Lorensen, W. E.; Pflegel, G.
1976-01-01
The quadratic isoparametric elements which embody the inverse square root singularity are used for calculating the stress intensity factors at tips of cracks. The strain singularity at a point or an edge is obtained in a simple manner by placing the mid-side nodes at quarter points in the vicinity of the crack tip or an edge. These elements are implemented in NASTRAN as dummy elements. The method eliminates the use of special crack tip elements and in addition, these elements satisfy the constant strain and rigid body modes required for convergence.
Ho, Philip Wai-Sun
1977-01-01
COMPOSITE LINEAR STRAIN ELEMENTS 19 Ouadrilateral Element Stiffness Condensation Mass Condensation Three-Dimensional Brick Element 19 22 23 26 IV COMPARISON OF NUMERICAL RESULTS 31 Two-Dimensional Elements Eigenvalues Comparison Structural... Idealizations Dynamic Response Three-Dimensional Elements Structural Idealizations 31 31 34 42 42 47 V DISCUSSION AND CONCLUSIONS 52 Discussion Conclusions 52 53 REFERENCES 54 PAGE APPENDIX A ELASTICITY NATRICES APPENDIX B ISOPARAMETRIC SHAPE...
NSDL National Science Digital Library
Shows how the roots of a quadratic change as the b term in the equation changes. The equation was chosen to illustrate the fact that only real roots are seen as points where the curve crosses the x-axis. This can lead to a useful discussion of what is meant by a physically meaningful solution.
Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics
Duran, Ricardo
Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics A. Berm the level of noise in aircraft or cars. Let us mention for instance [18], where a pressure/potential formulation of the uid is given and numerically solved by #12;nite element and modal reduction methods. #3
Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics
Rodríguez, Rodolfo
Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics A. Berm or cars. Let us mention for instance [18], where a pressure/potential formulation of the fluid is given and numerically solved by finite element and modal reduction methods. Departamento de Matem´atica Aplicada
Progressive tetrahedralizations
Oliver G. Staadt; Markus H. Gross
1998-01-01
This paper describes some fundamental issues for robust implementations of progressively refined tetrahedralizations generated through sequences of edge collapses. We address the definition of appropriate cost functions and explain on various tests which are necessary to preserve the consis- tency of the mesh when collapsing edges. Although being considered a special case of progressive simplicial com- plexes (10), the results
Haptic Rendering of Data on Unstructured Tetrahedral Grids
Roman Y. Novoselov; Dale A. Lawrence; Lucy Y. Pao
2002-01-01
An algorithm is developed to interpolate data in unstructured tetrahedral meshes for improved real-time haptic rendering. Given a Cartesian location in the data set, the containing tetrahedral element in the unstructured mesh must be located. Then the data at the nodes of this tetrahedral element are interpolated to yield the proper data value(s) to render. Comparisons are made with a
A study of adaptively remeshed finite element problems using higher order tetrahedra
K. T. Schuetze; P. S. Shiakolas; S. N. Muthukrishnan; R. V. Nambiar; K. L. Lawrence
1995-01-01
A study has been performed for various three-dimensional elasticity problems to evaluate the performance of a three-dimensional FEM preprocessor, processor and companion remeshing modules. Both straight-sided and curve-sided tetrahedral finite elements were employed. All the problems analyzed started with initial meshes varying from 5 to 20 linear strain or quadratic strain tetrahedral elements. Remeshing was based on Zienkiewicz-Zhu error indicators
NSDL National Science Digital Library
Center for Engineering Educational Outreach,
Working in teams of four, students build tetrahedral kites following specific instructions and using specific materials. They use the basic processes of manufacturing systems – cutting, shaping, forming, conditioning, assembling, joining, finishing, and quality control – to manufacture complete tetrahedral kites within a given time frame. Project evaluation takes into account team efficiency and the quality of the finished product.
NSDL National Science Digital Library
Working in teams of four, you and your team will build a tetrahedral kite following a specific set of directions and using specific provided materials. You will use basic processes of manufacturing systems - cutting, shaping, forming, conditioning, assembling, joining, finishing, and quality control - to manufacture a complete tetrahedral kite within a given time frame. Evaluation of your project will involve the efficiency of your team as well as your finished product.
J. William Helton; Reza Rashidi Far; Roland Speicher
2007-01-01
We show that the quadratic matrix equation $VW + \\\\eta (W)W = I$, for given\\u000a$V$ with positive real part and given analytic mapping $\\\\eta$ with some\\u000apositivity preserving properties, has exactly one solution $W$ with positive\\u000areal part. We point out the relevance of this result in the context of\\u000aoperator-valued free probability theory and for the determination of
ROTATION-VIBRATION TETRAHEDRAL
Sadovskií, Dmitrií
ANALYSIS OF ROTATION-VIBRATION RELATIVE EQUILIBRIA ON THE EXAMPLE OF A TETRAHEDRAL FOUR ATOM (RE) of a nonrigid molecule which vibrates about a well de#12;ned equilibrium con#12;guration and rotates as a whole. Our analysis uni#12;es the theory of rotational and vibrational RE. We rely
ON 'SOLID-SHELL' ELEMENTS WITH LINEAR AND QUADRATIC SHAPE FUNCTIONS FOR SMALL AND LARGE DEFORMATIONS
M. Harnau; K. Schweizerhof; R. Hauptmann
The well known Solid-Shell concept was originally developed as 'four-node type' elements with trilinear shape functions (20), (24) and (15). Every 'nodal point' consists of one node on the upper surface and one node on the lower surface with three displace- ment degrees of freedom each. In this contribution these four-node respectively eight-node elements are extended to nine-node respectively eighteen-node
Tetrahedral and Hexahedral Mesh Adaptation for CFD Problems
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger C.; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically without mesh quality problems. Furthermore, hexahedral meshes yield more accurate solutions than their tetrahedral counterparts for the same number of edges. Both the tetrahedral and hexahedral mesh adaptation procedures use edge-based data structures that facilitate efficient subdivision by allowing individual edges to be marked for refinement or coarsening. However, for hexahedral adaptation, pyramids, prisms, and tetrahedra are used as buffer elements between refined and unrefined regions to eliminate hanging vertices. Computational results indicate that the hexahedral adaptation procedure is a viable alternative to adaptive tetrahedral schemes.
Parallel tetrahedral mesh refinement with MOAB.
Thompson, David C.; Pebay, Philippe Pierre
2008-12-01
In this report, we present the novel functionality of parallel tetrahedral mesh refinement which we have implemented in MOAB. This report details work done to implement parallel, edge-based, tetrahedral refinement into MOAB. The theoretical basis for this work is contained in [PT04, PT05, TP06] while information on design, performance, and operation specific to MOAB are contained herein. As MOAB is intended mainly for use in pre-processing and simulation (as opposed to the post-processing bent of previous papers), the primary use case is different: rather than refining elements with non-linear basis functions, the goal is to increase the number of degrees of freedom in some region in order to more accurately represent the solution to some system of equations that cannot be solved analytically. Also, MOAB has a unique mesh representation which impacts the algorithm. This introduction contains a brief review of streaming edge-based tetrahedral refinement. The remainder of the report is broken into three sections: design and implementation, performance, and conclusions. Appendix A contains instructions for end users (simulation authors) on how to employ the refiner.
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.
1971-01-01
Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.
Quadratic Elongation: A Quantitative Measure of Distortion in Coordination Polyhedra
Keith Robinson; G. V. Gibbs; P. H. Ribbe
1971-01-01
Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elongation is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.
NSDL National Science Digital Library
2013-06-21
The quadratic formula is easy to solve, yet sufficiently sophisticated that it provides insight into oscillations of masses connected by springs, as well as insight into chemical bonds between atoms. The purpose of this video is to illustrate what it means to find the "zeros" or "roots" of the quadratic equation, both using a graphical description, as well as by analytically completing the square to obtain the famous quadratic formula.
Tetrahedral and hexahedral mesh adaptation for CFD problems
Rupak Biswas; Roger C. Strawn
1998-01-01
This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically
Transmission-line modeling (TLM) based upon unstructured tetrahedral meshes
Phillip Sewell; Trevor M. Benson; Christos Christopoulos; David W. P. Thomas; Ana Vukovic; James G. Wykes
2005-01-01
This paper presents a transmission-line modeling (TLM) algorithm, which is based upon unstructured tetrahedral meshes. In comparison with the conventional, usually Cartesian, scheme, the use of such meshes provides a significant enhancement in the flexibility and accuracy of the TLM simulations, permitting both smooth boundary approximations and the use of diversely sized elements in multiscale problems. A full theoretical development
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…
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, together with low friction coefficients.
Nuclear tetrahedral configurations at spin zero
Krzysztof Zberecki; Paul-Henri Heenen; Piotr Magierski
2009-02-04
The possibility of the existence of stable tetrahedral deformations at spin zero is investigated using the Skyrme-HFBCS approach and the generator coordinate method (GCM). The study is limited to nuclei in which the tetrahedral mode has been predicted to be favored on the basis of non self-consistent models. Our results indicate that a clear identification of tetrahedral deformations is unlikely as they are strongly mixed with the axial octupole mode. However, the excitation energies related to the tetrahedral mode are systematically lower than those of the axial octupole mode in all the nuclei included in this study.
Interactive Isosurface Ray Tracing of Time-Varying Tetrahedral Volumes
Ingo Wald; Heiko Friedrich; Aaron Knoll; Charles D. Hansen
2007-01-01
We describe a system for interactively rendering isosurfaces of tetrahedral finite-element scalar fields using coherent ray tracing tech- niques on the CPU. By employing state-of-the art methods in polygonal ray tracing, namely aggressive packet\\/frustum traversal of a bounding volume hierarchy, we can accomodate large and time-varying unstructured data. In conjunction with this efficiency structure, we introduce a novel technique for
NASA Technical Reports Server (NTRS)
Kim, Sang-Wook
1988-01-01
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.
Parallel tetrahedral mesh refinement with MOAB
David C. Thompson; Philippe Pierre Pebay
2008-01-01
In this report, we present the novel functionality of parallel tetrahedral mesh refinement which we have implemented in MOAB. This report details work done to implement parallel, edge-based, tetrahedral refinement into MOAB. The theoretical basis for this work is contained in [PT04, PT05, TP06] while information on design, performance, and operation specific to MOAB are contained herein. As MOAB is
A finite element computational method for high Reynolds number laminar flows
NASA Technical Reports Server (NTRS)
Kim, Sang-Wook
1987-01-01
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.
Solving quadratic Introduction
Vickers, James
Solving quadratic equations 3.2 Introduction A quadratic equation is one which can be written. In this section we describe several ways in which quadratic equations can be solved. ' & $ % Prerequisites Before completing this Section you should be able to . . . recognise a quadratic equation solve a quadratic
Burton, Geoffrey R.
Quadratic Forms Hyperbolic surfaces Closed Geodesics Spectral Theory Pell's Equation Algorithm for solving x Geodesics Y. Petridis Quadratic Forms Hyperbolic surfaces Closed Geodesics Spectral Theory Pell's EquationQuadratic Forms and Closed Geodesics Y. Petridis Outline Quadratic Forms and Closed Geodesics
3D Harmonic Mapping and Tetrahedral Meshing of Brain Imaging Data
Thompson, Paul
a surface-based de- formation to the whole brain volume. Christensen et al. [7] presented diffeo- morphic, Hansen et al. [11] demonstrated the importance of finite element based brain models in a surgery3D Harmonic Mapping and Tetrahedral Meshing of Brain Imaging Data Yalin Wang1 , Xianfeng Gu2 , Paul
Adaptive Tetrahedral Meshing for Personalized Cardiac Simulations
Andrzejak, Artur
Adaptive Tetrahedral Meshing for Personalized Cardiac Simulations Hans Lamecker, Tommaso Mansi accuracy and speed. This can be achieved by adapting the mesh resolution, and by providing well-quality, adaptive meshes, and show how the framework can be applied to specific cardiac simulations. Our aim
Tetrahedral boron in naturally occurring tourmaline
Tagg, S.L.; Cho, H. [Pacific Northwest National Lab., Richland, WA (United States). Environmental Molecular Sciences Lab.; Dyar, M.D. [Mount Holyoke Coll., South Hadley, MA (United States). Dept. of Geology and Geography; Grew, E.S. [Univ. of Maine, Orono, ME (United States). Dept. of Geological Sciences
1999-09-01
Evidence for boron in both trigonal and tetrahedral coordination has been found in {sup 11}B magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectra of natural, inclusion-free specimens of aluminum-rich lithian tourmaline from granitic pregmatites.
Tetrahedral boron in naturally occurring tourmaline
S. L. Tagg; HERMAN CHO; M. D ARBY DYAR; EDWARD S. GREW
1999-01-01
Evidence for boron in both trigonal and tetrahedral coordination has been found in Â¹Â¹B magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectra of natural, inclusion-free specimens of aluminum-rich lithian tourmaline from granitic pregmatites.
Tetrahedral Grid Refinement Jurgen Bey, Tubingen
: Tetrahedral grid refinement, stable refinements, consistent triangulations, green closure, grid coarsening]), which no longer require the underlying meshes to be quasiÂuniform, in contrast to the early theory, e the following assumptions. Let\\Omega ae IR 3 be a polyhedral domain, and assume that an initial triangula
Circuit analog of quadratic optomechanics
Eun-jong Kim; J. R. Johansson; Franco Nori
2014-12-22
We propose a superconducting electrical circuit that simulates a quadratic optomechanical system. A capacitor placed between two transmission-line (TL) resonators acts like a semi-transparent membrane, and a superconducting quantum interference device (SQUID) that terminates a TL resonator behaves like a movable mirror. Combining these circuit elements, it is possible to simulate a quadratic optomechanical coupling whose coupling strength is determined by the coupling capacitance and the tunable bias flux through the SQUIDs. Estimates using realistic parameters suggest that an improvement in the coupling strength could be realized, to five orders of magnitude from what has been observed in membrane-in-the-middle cavity optomechanical systems. This leads to the possibility of achieving the strong-coupling regime of quadratic optomechanics.
Circuit analog of quadratic optomechanics
NASA Astrophysics Data System (ADS)
Kim, Eun-jong; Johansson, J. R.; Nori, Franco
2015-03-01
We propose a superconducting electrical circuit that simulates a quadratic optomechanical system. A capacitor placed between two transmission-line (TL) resonators acts like a semitransparent membrane, and a superconducting quantum interference device (SQUID) that terminates a TL resonator behaves like a movable mirror. Combining these circuit elements, it is possible to simulate a quadratic optomechanical coupling whose coupling strength is determined by the coupling capacitance and the tunable bias flux through the SQUIDs. Estimates using realistic parameters suggest that an improvement in the coupling strength could be realized, to five orders of magnitude from what has been observed in membrane-in-the-middle cavity optomechanical systems. This leads to the possibility of achieving the strong-coupling regime of quadratic optomechanics.
On a combined adaptive tetrahedral tracing and edge diffraction model
NASA Astrophysics Data System (ADS)
Hart, Carl R.
A major challenge in architectural acoustics is the unification of diffraction models and geometric acoustics. For example, geometric acoustics is insufficient to quantify the scattering characteristics of acoustic diffusors. Typically the time-independent boundary element method (BEM) is the method of choice. In contrast, time-domain computations are of interest for characterizing both the spatial and temporal scattering characteristics of acoustic diffusors. Hence, a method is sought that predicts acoustic scattering in the time-domain. A prediction method, which combines an advanced image source method and an edge diffraction model, is investigated for the prediction of time-domain scattering. Adaptive tetrahedral tracing is an advanced image source method that generates image sources through an adaptive process. Propagating tetrahedral beams adapt to ensonified geometry mapping the geometric sound field in space and along boundaries. The edge diffraction model interfaces with the adaptive tetrahedral tracing process by the transfer of edge geometry and visibility information. Scattering is quantified as the contribution of secondary sources along a single or multiple interacting edges. Accounting for a finite number of diffraction permutations approximates the scattered sound field. Superposition of the geometric and scattered sound fields results in a synthesized impulse response between a source and a receiver. Evaluation of the prediction technique involves numerical verification and numerical validation. Numerical verification is based upon a comparison with analytic and numerical (BEM) solutions for scattering geometries. Good agreement is shown for the selected scattering geometries. Numerical validation is based upon experimentally determined scattered impulse responses of acoustic diffusors. Experimental data suggests that the predictive model is appropriate for high-frequency predictions. For the experimental determination of the scattered impulse response the merits of a maximum length sequence (MLS) versus a logarithmic swept-sine (LSS) are compared and contrasted. It is shown that a LSS is an appropriate stimuli for testing acoustic diffusors by comparing against scattered relative levels measured by a MLS signal.
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.
Boundary Recovery For Delaunay Tetrahedral Meshes Using Local Topological Transformations
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
Back to Elements - Tetrahedra vs. Hexahedra
Erke Wang; Thomas Nelson; Rainer Rauch
This paper presents some analytical results and some test results for different mechanical problems, which are then simulated using finite element analysis with tetrahedral and hexahedral shaped elements. The comparison is done for linear static problems, modal analyses and nonlinear analyses involving large deflections, contact and plasticity. The advantages and disadvantages are shown using tetrahedral and hexahedral elements. We also
Stacking Fault Energies of Tetrahedrally Coordinated Crystals
S. Takeuchi; K. Suzuki
1999-01-01
The energies of the intrinsic stacking fault in 20 tetrahedrally coordinated crystals, determined by electron microscopy from the widths of extended dislocations, range from a few mJ\\/m2 to 300 mJ\\/m2. The reduced stacking fault energy (RSFE: stacking fault energy per bond perpendicular to the fault plane) has been found to have correlations with the effective charge, the charge redistribution index
NSDL National Science Digital Library
Robert Lengacher
2012-07-05
This is an introductory lesson to graphing quadratic equations. This lesson uses graphing technology to illustrate the differences between quadratic equations and linear equations. In addition, it allows students to identify important parts of the quadratic equation and how each piece changes the look of the graph.
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…
Tetrahedrally coordinated carbonates in Earth's lower mantle.
Boulard, Eglantine; Pan, Ding; Galli, Giulia; Liu, Zhenxian; Mao, Wendy L
2015-01-01
Carbonates are the main species that bring carbon deep into our planet through subduction. They are an important rock-forming mineral group, fundamentally distinct from silicates in the Earth's crust in that carbon binds to three oxygen atoms, while silicon is bonded to four oxygens. Here we present experimental evidence that under the sufficiently high pressures and high temperatures existing in the lower mantle, ferromagnesian carbonates transform to a phase with tetrahedrally coordinated carbons. Above 80?GPa, in situ synchrotron infrared experiments show the unequivocal spectroscopic signature of the high-pressure phase of (Mg,Fe)CO3. Using ab-initio calculations, we assign the new infrared signature to C-O bands associated with tetrahedrally coordinated carbon with asymmetric C-O bonds. Tetrahedrally coordinated carbonates are expected to exhibit substantially different reactivity than low-pressure threefold coordinated carbonates, as well as different chemical properties in the liquid state. Hence, this may have significant implications for carbon reservoirs and fluxes, and the global geodynamic carbon cycle. PMID:25692448
Small Power Technology for Tetrahedral Rovers
NASA Astrophysics Data System (ADS)
Clark, P. E.; Floyd, S. R.; Butler, C. D.; Flom, Y.
2006-01-01
The Small Power Technology (SPOT) being studied at GSFC has the potential to be an efficient and compact radioisotope based electrical power system. Such a system would provide power for innovative tetrahedral robotic arms and walkers to support the lunar exploration initiative within the next decade. Presently, NASA has designated two flight qualified Radioisotope Power Supplies (RPS): the Multi-Mission RTG (MMRTG) which uses thermocouple technology and the more efficient but more massive Stirling RTG (SRTG) which uses a mechanical heat (Stirling) engine technology. With SPOT, thermal output from a radioisotope source is converted to electrical power using a combination of shape memory material and piezoelectric crystals. The SPOT combined energy conversion technologies are potentially more efficient than thermocouples and do not require moving parts, thus keeping efficiency high with an excellent mass to power ratio. Applications of particular interest are highly modular, addressable, reconfigurable arrays of tetrahedral structural components designed to be arms or rovers with high mobility in rough terrain. Such prototypes are currently being built at GSFC. Missions requiring long-lived operation in unilluminated environments preclude the use of solar cells as the main power source and must rely on the use of RPS technology. The design concept calls for a small motor and battery assembly for each strut, and thus a distributed power system. We estimate, based on performance of our current tetrahedral prototypes and power scaling for small motors, that such devices require tens of watts of power output per kilogram of power supply. For these reasons, SPOT is a good candidate for the ART (addressable Reconfigurable Technology) baseline power system.
Design of inorganic compounds with tetrahedral anions
NASA Astrophysics Data System (ADS)
Lazoryak, B. I.
1996-04-01
The review deals with aspects of the modelling of the compositions and properties of inorganic compounds with tetrahedral anions on the basis of crystal-chemical information. One of the possible algorithms employing crystal-chemical data for the modelling of the compositions, structures, and properties of new compounds is proposed on the basis of the structures of six structural types (glaserite, ?-K2SO4, bredigite, palmierite, NASICON, and whitlockite). The likely usefulness of such data for the solution of various problems in materials science is demonstrated. The bibliography includes 208 references.
Direct observation of tetrahedral hydrogen jumps in ice Ih
F. Fujara; S. Wefing; W. F. Kuhs
1988-01-01
Using deuteron NMR, spin alignment tetrahedral jumps of 2H in deuterated polycrystalline hexagonal ice (Ih) have been observed. Both geometry and time scale of the process are determined directly. At T=230 K the correlation time of these jumps is 0.21(3) ms. The tetrahedral hydrogen jumps turn out to scatter—most characteristically for the disorder within the hydrogen subsystem—randomly about the tetrahedral
Theory of prospective tetrahedral perovskite ferroelectrics
Roy, Anindya
2010-01-01
Using first-principles methods, we predict the energy landscape and ferroelectric states of double perovskites of the form AA$'$BB$'$O$_6$ in which the atoms on both the A and B sites are arranged in rock-salt order. While we are not aware of compounds that occur naturally in this structure, we argue that they might be realizable by directed synthesis. The high-symmetry structure formed by this arrangement belongs to the tetrahedral $F\\bar{4}3m$ space group. If a ferroelectric instability occurs, the energy landscape will tend to have minima with the polarization along tetrahedral directions, leading to a rhombohedral phase, or along Cartesian directions, leading to an orthorhombic phase. We find that the latter scenario applies to CaBaTiZrO$_6$ and KCaZrNbO$_6$, which are weakly ferroelectric, and the former one applies to PbSnTiZrO$_6$, which is strongly ferroelectric. The results are modeled with a fourth- or fifth-order Landau-Devonshire expansion, providing good agreement with the first-principles calcul...
ADAPTIVE TETRAHEDRAL GRID REFINEMENT AND COARSENING IN MESSAGE-PASSING ENVIRONMENTS
Hallberg, J.; Stagg, A. [and others
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 solver calculations.
A new characterization of simple elements in a tetrahedral mesh
Frey, Pascal
the importance of topological parameters in analyzing images of biological organs. The analysis of 3D digital used to produce 3D digital images that carry much important information about anatomy and function imaging. A 3D digital image, in general, is a discrete subdivision of the 3D Euclidean space
Quadratic Forms, Geodesics and
Wirosoetisno, Djoko
Forms Hyperbolic surfaces Closed Geodesics Spectral Theory Propaganda Outline Quadratic Forms Hyperbolic surfaces Closed Geodesics Spectral Theory Propaganda #12;Indefinite Quadratic Forms, Closed Geodesics Propaganda Pell's Equation Algorithm for solving x2 - 2y2 = ±1 (Pythagoreans) Start with x1 = 1, y1 = 1 We
Quadratic eigenvalue problems.
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
Simulation of polymer chains on a tetrahedral lattice
Frederick T. Wall; Frederic Mandel; R. Allen White
1975-01-01
A thorough analysis of partially restricted random walks on a tetrahedral lattice has been carried out to demonstrate the validity of Wall's recent theory of polymer chain configurations. Tetrahedral lattice walks of order six (those for which ring closures corresponding to polygons of six of fewer vertices are forbidden) were studied both analytically and numerically. A set of forty-one different
ADAPTIVE PHYSICS BASED TETRAHEDRAL MESH GENERATION USING LEVEL SETS
Fedkiw, Ron
ADAPTIVE PHYSICS BASED TETRAHEDRAL MESH GENERATION USING LEVEL SETS Robert Bridson2 Joseph Teran1, U.S.A. fedkiw@cs.stanford.edu ABSTRACT We present a tetrahedral mesh generation algorithm designed lattice of subdivision-invariant tetrahedra. The level set is then used to guide a red green adaptive
Computational aspects of the refinement of 3D tetrahedral meshes
J. P. Su ´; P. Abad; A. Plaza
The refinement of tetrahedral meshes is a significant task in many numerical and discretizations methods. The computational aspects for implementing refinement of meshes with complex geometry need to be carefully considered in order to have real-time and optimal results. In this paper we study some computational aspects of a class of tetrahedral refinement algorithms. For local adaptive refinement we give
On Convex Relaxations for Quadratically Constrained Quadratic ...
2010-07-28
Jul 28, 2010 ... relaxation of the convex hull of the quadratic form that imposes ... of QCQP problems, corresponding to planar circle-packing (or ..... the algorithm of [18], but still required up to 104 CPU seconds on a 2.7 GHz Linux-based.
Capozziello, Salvatore; Lattanzi, Alessandra
2006-08-01
On the basis of empirical Fischer projections, we develop an algebraic approach to the central molecular chirality of tetrahedral molecules. The elements of such an algebra are obtained from the 24 projections which a single chiral tetrahedron can generate in S and R absolute configurations. They constitute a matrix representation of the O4 orthogonal group. According to this representation, given a molecule with n chiral centres, it is possible to define an "index of chirality chi identical with {n, p}", where n is the number of stereogenic centres of the molecule and p the number of permutations observed under rotations and superimpositions of the tetrahedral molecule to its mirror image. The chirality index not only assigns the global chirality of a given tetrahedral chain, but indicates also a way to predict the same property for new compounds, which can be built up consistently. PMID:16612801
Quadratic Inverse Eigenvalue Problems, Active Vibration Control and Model Updating
Datta, Biswa
important applications of model updating in damage detection and health monitoring in vibrating structuresQuadratic Inverse Eigenvalue Problems, Active Vibration Control and Model Updating Biswa N. Datta,1 to active vibration control and finite element model updating. 1. Introduction The Quadratic Inverse
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION KARIM JOHANNES BECHER AND DAVID B. LEEP Abstract. The radical of a field consists of all nonzero elements that are represented by every binary quadratic form representing 1. Here, the radical is studied in relation to localglobal principles
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION KARIM JOHANNES BECHER AND DAVID B. LEEP Abstract. The radical of a field consists of all nonzero elements that are represented by every binary quadratic form representing 1. Here, the radical is studied in relation to local-global principles
Quadratic Functions: Workshop 4
NSDL National Science Digital Library
Annenberg Media, Insights into Algebra, Teaching for Learning
2009-12-23
Lesson 1 of two lessons requires students to explore quadratic functions by examining the family of functions described by y = a (x - h)squared+ k. In Lesson 2 students explore quadratic functions by using a motion detector known as a Calculator Based Ranger (CBR) to examine the heights of the different bounces of a ball. Students will represent each bounce with a quadratic function of the form y = a (x - h)squared + k. Background information, resources, references and videos of the lessons are included. Students work in teams of four.
Quadratic Liénard Equations with Quadratic Damping
Freddy Dumortier; Chengzhi Li
1997-01-01
In this paper we study the generalized Liénard equations x+f(x)x+g(x)=0 with quadratic polynomialsfandg. We prove that these kind of equations can have at most one limit cycle, and we give the complete bifurcation diagram and classification of the phase portraits. The paper also contains a shorter proof for the result in A. Lins, W. de Melo, and C. C. Pugh,
Patrick Devlin
2014-05-08
This only works for zero; that is why when a quadratic equation is factorable, we ... to solve an equation that involves a perfect square, isolate the perfect ... changed into perfect squares by using a procedure called completing the square.
Main graphs: Quadratic equation
Utrecht, Universiteit
a>0 OR OR OR x x x xxx x x x y y y Quadratic equation: The general solution of a quadratic equation equations: Equation dN dt = kN has the solution: N(t) = N0ekt; N0 is an (arbitrary) initial value of N. Systems of linear differential equations: For system dx dt = ax+by dy dt = cx+dy , the characteristic
Enriching low-order finite elements by interpolation covers
Kim, Jae Hyung, Ph. D. Massachusetts Institute of Technology
2013-01-01
This dissertation presents an enriched finite element procedure based on the use of interpolation cover functions for low-order finite elements, namely, the 3-node triangular and 4- node tetrahedral elements. The standard ...
Constraint propagation on quadratic constraints
Ferenc Domes; Arnold Neumaier
2010-01-01
This paper considers constraint propagation methods for continuous constraint satisfaction problems consisting of linear and quadratic constraints. All methods can be applied after suitable preprocessing to arbitrary algebraic constraints. The basic new techniques consist in eliminating bilinear entries from a quadratic constraint, and solving the resulting separable quadratic constraints by means of a sequence of univariate quadratic problems. Care is
Application of Mimetic Operators to Tetrahedral Mesh MHD Codes
NASA Astrophysics Data System (ADS)
Marklin, George; Jarboe, Tom
2008-11-01
Mimetic operators are numerical approximations to the grad, div and curl operators that 'mimic' the orthogonality properties of their analytic counterparts, div(curl)=0 and curl(grad)=0. They define different components of vector fields at different parts of the mesh and can be viewed as a special type of finite element basis and can be defined to arbitrarily high order. They have been used in electromagnetic simulation codes for many years. This poster will show how they can be defined to lowest order on a tetrahedral mesh and applied to Taylor state computations and to the induction equation in an MHD simulation. They have the advantage of being able to exactly maintain zero divergence in both the magnetic field and current density and to make an exact separation of static and inductive electric fields. Mimetic Operators can also be used in the momentum equation and the results will be compared to other commonly used methods like the finite volume and discontinuous Galerkin methods. The new code will be used to run simulations of the HIT-SI experiment with insulated conductor boundary conditions and different injector configurations and results compared to the experiment and to simulations done with the NIMROD code.
Adaptive hybrid prismatic-tetrahedral grids for viscous flows
NASA Technical Reports Server (NTRS)
Kallinderis, Yannis; Khawaja, Aly; Mcmorris, Harlan
1995-01-01
The paper presents generation of adaptive 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 an Automatic Receding Method (ARM) 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 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 division of tetrahedra, as well as 2-D directional division of prisms.
Streaming Compression of Tetrahedral Volume Meshes
Isenburg, M; Lindstrom, P; Gumhold, S; Shewchuk, J
2005-11-21
Geometry processing algorithms have traditionally assumed that the input data is entirely in main memory and available for random access. This assumption does not scale to large data sets, as exhausting the physical memory typically leads to IO-inefficient thrashing. Recent works advocate processing geometry in a 'streaming' manner, where computation and output begin as soon as possible. Streaming is suitable for tasks that require only local neighbor information and batch process an entire data set. We describe a streaming compression scheme for tetrahedral volume meshes that encodes vertices and tetrahedra in the order they are written. To keep the memory footprint low, the compressor is informed when vertices are referenced for the last time (i.e. are finalized). The compression achieved depends on how coherent the input order is and how many tetrahedra are buffered for local reordering. For reasonably coherent orderings and a buffer of 10,000 tetrahedra, we achieve compression rates that are only 25 to 40 percent above the state-of-the-art, while requiring drastically less memory resources and less than half the processing time.
Utah, University of
Finite Element Refinements for Inverse Electrocardiography: Hybrid Shaped Elements and High of Utah, Salt Lake City, UT, USA Abstract We study how finite element method (FEM) can be selected and prismatic/tetrahedral elements in 3D. Another method uses high-order FEM, ex- tracts from the resulting
Parallel Unstructured Tetrahedral Mesh Adaptation: Algorithms, Implementation and Scalability
Utah, University of
Parallel Unstructured Tetrahedral Mesh Adaptation: Algorithms, Implementation and Scalability P to the irregular and frequently changing nature of the data and its distribution. A parallel mesh adaptation diffraction problem. 1 Introduction Spatial mesh adaptation techniques are increasingly being used
Experimental and computational analysis of random tetrahedral packings with applications
NASA Astrophysics Data System (ADS)
Jaoshvili, Alexander
Random packings are prevalent in chemical engineering applications and they can serve as prototype models of particulate materials. In this research, comprehensive studies on tetrahedral packings were carried out experimentally. Experiment was conducted on regular tetrahedral dice. MRI imaging was used to image the tetrahedral packs, an algorithm was developed which allowed us to retrieve each of the particle center positions as well as the 3D orientation from the digital data. To our best knowledge this is the first time that such an in-depth analysis was performed on non spherical objects. This numerical approach makes it possible to study detailed packing structure, packing density, the onset of ordering, and wall effects. Important applications for tetrahedral packings include multiphase flow in catalytic beds, heat transfer, bulk storage and transportation, and manufacturing of fibrous composites.
Low-energy tetrahedral polymorphs of carbon, silicon, and germanium
NASA Astrophysics Data System (ADS)
Mujica, Andrés; Pickard, Chris J.; Needs, Richard J.
2015-06-01
Searches for low-energy tetrahedral polymorphs of carbon and silicon have been performed using density functional theory computations and the ab initio random structure searching approach. Several of the hypothetical phases obtained in our searches have enthalpies that are lower or comparable to those of other polymorphs of group 14 elements that have either been experimentally synthesized or recently proposed as the structure of unknown phases obtained in experiments, and should thus be considered as particularly interesting candidates. A structure of P b a m symmetry with 24 atoms in the unit cell was found to be a low-energy, low-density metastable polymorph in carbon, silicon, and germanium. In silicon, P b a m is found to have a direct band gap at the zone center with an estimated value of 1.4 eV, which suggests applications as a photovoltaic material. We have also found a low-energy chiral framework structure of P 41212 symmetry with 20 atoms per cell containing fivefold spirals of atoms, whose projected topology is that of the so-called Cairo-type two-dimensional pentagonal tiling. We suggest that P 41212 is a likely candidate for the structure of the unknown phase XIII of silicon. We discuss P b a m and P 41212 in detail, contrasting their energetics and structures with those of other group 14 elements, particularly the recently proposed P 42/n c m structure, for which we also provide a detailed interpretation as a network of tilted diamondlike tetrahedra.
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2015-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
Luis Alvarez-Gaume; Alex Kehagias; Costas Kounnas; Dieter Lust; Antonio Riotto
2015-05-28
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-theory. We demonstrate that string theory on non-compact $CY_3$ manifolds, like a line bundle over $\\mathbb{CP}^2$, may indeed lead to gravity dynamics determined by a higher curvature action.
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]…
Generalized quadratic Liénard equations
S. Lynch
1998-01-01
In this article we give explicit formulae for the Liapunov quantities of generalized Liénard systems with either quadratic damping or restoring coefficients. These quantities provide necessary conditions in order for the origin to be a centre. Recent results are also presented for these systems.
A Quadratic Programming Bibliography
2001-02-27
Feb 27, 2001 ... programming is often used as the basis for ”program trading” where stocks are ..... this defect, the extension of the quadratic programming method is .... for such a behaviour to be accurately predicted and the previously mentioned ..... in the framework of the probabilistic adequacy assessment of large inter-.
Mating Siegel Quadratic Polynomials
Michael Yampolsky; Saeed Zakeri
1998-01-01
Let F be a quadratic rational map of the sphere which has two fixed Siegel disks with bounded type rotation numbers theta and nu. Using a new degree 3 Blaschke product model for the dynamics of F and an adaptation of complex a priori bounds for renormalization of critical circle maps, we prove that F can be realized as the
GPU Accelerated Isosurface Extraction on Tetrahedral Grids
Boyer, Edmond
(CFD), finite element modeling and medical and seismic tomography. These applications often use large by the Marching Cubes [13], so we now review the main steps of this algorithm. The Marching Cubes algorithm
Gesture Recognition Using Quadratic Curves
Qiulei Dong; Yihong Wu; Zhanyi Hu
2006-01-01
This paper presents a novel method for human gesture recog- nition based on quadratic curves. Firstly, face and hands in the images are extracted by skin color and their central points are kept tracked by a modifled Greedy Exchange algorithm. Then in each trajectory, the cen- tral points are fltted into a quadratic curve and 6 invariants from this quadratic
Unidirectional formation of tetrahedral voids in irradiated silicon carbide
Kondo, S.; Katoh, Y.; Snead, L. L. [Materials Science and Technology Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6138 (United States)
2008-10-20
The (111) tetrahedral voids induced by neutron irradiation in 3C-SiC were found to be spatially oriented in only one of two possible directions. The tetrahedral shape was unexpected as the surface-to-volume ratio is larger than the alternative (111) octahedral void common in both metals and ceramics. From a geometric viewpoint, all faces of the observed voids are either Si- or C-terminated surfaces. By comparing the surface area with the octahedral void (composed of the both Si- and C-surfaces) of the same volume, the considerable difference in surface energy between the Si(111) and C(111) was implicated.
Main graphs: Quadratic equation
Utrecht, Universiteit
Main graphs: Quadratic equation: Equation A2 +B+C = 0, has solutions given by the following 'abc equations: Equation dN dt = kN has the solution: N(t) = N0ekt; N0 is an (arbitrary) initial value of N. Characteristic time of change is = 1/k. Systems of linear differential equations: For system dx dt = ax+by dy dt
On the 3-Pfister number of quadratic forms Melanie Raczek
. Brosnan, Reichstein and Vistoli [2010] define the m-Pfister number Pfm(q) of a quadratic form [q] Im (F call m-fold Pfister elements. The m-Pfister number Pfm() of an element Im [V ] is the least number
Hardware-Based Ray Casting for Tetrahedral Meshes
Manfred Weiler; Martin Kraus; Markus Merz; Thomas Ertl
2003-01-01
We present the first implementation of a volume ray casting algorithm for tetrahedral meshes running on off-the-shelf programmable graphics hardware. Our implementation avoids the memory transfer bottleneck of the graphics bus since the complete mesh data is stored in the local memory of the graphics adapter and all computations, in particular ray traversal and ray integration, are performed by the
A tetrahedral entropy for water Pradeep Kumara,1
Stanley, H. Eugene
molecules and find that it produces a major contribution to the specific heat maximum at the Widom line heat of water | orientational entropy of tetrahedral liquids | anomalies of liquid water | Widom line the Widom line TW TW (P) (19), near which different response func- tions, such as isobaric specific heat CP
New Tetrahedrally Close-Packed Structures John M. Sullivan
Sullivan, John M.
. Remember that a surface in space has (at each point) two principal curvatures k1 and k2. Because obtained when dipping a #12;tetrahedral frame into soapy water--six sheets come together into the central singularity, along four triple curves). We will define a foam mathematically as a (locally finite) collection
Search for Tetrahedral Symmetry in Nuclei:. a Short Overview
D. Curien; J. Dudek; H. Molique; L. Sengele; A. Gózdz; K. Mazurek
2011-01-01
Following a series of experiments launched by the TetraNuc collaboration to possibly demonstrate the existence of high-rank symmetries in subatomic physics, the first experimental results on the Rare Earth region appear in publications. Meanwhile an important progress has been made on the theory side strongly suggesting that the original criterion of the static tetrahedral symmetry in the form of vanishing
An Introduction to Algorithms for Constructing Conforming Delaunay Tetrahedrizations
Plotkin, Joshua B.
An Introduction to Algorithms for Constructing Conforming Delaunay Tetrahedrizations Marcelo properties and to the existence of efficient algorithms to compute and to maintain it. However, the Delaunay is represented by the vertices, edges, and facets of the tetra- hedrization. The primary goal of any algorithm
Pseudo-Tetrahedral Complexes Franz Aurenhammer and Hannes Krasser
Aurenhammer, Franz
Pseudo-Tetrahedral Complexes Franz Aurenhammer and Hannes Krasser #3; 1 Introduction A pseudo-triangulation is a cell complex in the plane whose cells are pseudo-triangles, i.e., simple polygons with exactly three, pseudo-triangulations have found their place in computational geometry; see e.g. [8, 11, 7, 1
Pseudo-Tetrahedral Complexes Franz Aurenhammer and Hannes Krasser
Aurenhammer, Franz
Pseudo-Tetrahedral Complexes Franz Aurenhammer and Hannes Krasser 1 Introduction A pseudo-triangulation is a cell complex in the plane whose cells are pseudo-triangles, i.e., simple polygons with exactly three, pseudo-triangulations have found their place in computational geometry; see e.g. [8, 11, 7, 1
The tetrahedral principle in kite design, Patrick Prosser
St Andrews, University of
1 The tetrahedral principle in kite design, revisited Patrick Prosser Kite Club of Scotland January@cs.strath.ac.uk Abstract I review an article by Alexander Graham Bell on the tertahedral principle in kite design, first a man to the moon and return him safely to earth, the atomic bomb, etc. In Bell's time the problem
Stereocontrolled Self-Assembly and Self-Sorting of Luminescent Europium Tetrahedral Cages.
Yan, Liang-Liang; Tan, Chun-Hong; Zhang, Guang-Lu; Zhou, Li-Peng; Bünzli, Jean-Claude; Sun, Qing-Fu
2015-07-01
Coordination-directed self-assembly has become a well-established technique for the construction of functional supramolecular structures. In contrast to the most often exploited transition metals, trivalent lanthanides Ln(III) have been less utilized in the design of polynuclear self-assembled structures despite the wealth of stimulating applications of these elements. In particular, stereochemical control in the assembly of lanthanide chiral cage compounds is not easy to achieve in view of the usually large lability of the Ln(III) ions. We report here the first examples of stereoselective self-assembly of chiral luminescent europium coordination tetrahedral cages and their intriguing self-sorting behavior. Two pairs of R and S ligands are designed on the basis of the pyridine-2,6-dicarboxamide coordination unit, bis(tridentate) L1 and tris(tridentate) L2. Corresponding chiral Eu4(L1)6 and Eu4(L2)4 topological tetrahedral cages are independently assembled via edge- and face-capping design strategies, respectively. The chirality of the ligand is transferred during the self-assembly process to give either ? or ? metal stereochemistry. The self-assembled cages are characterized by NMR, high-resolution ESI-TOF-MS, and in one case by X-ray crystallography. Strict control of stereoselectivity is confirmed by CD spectroscopy and NMR enantiomeric differentiation experiments. Narcissistic self-sorting is observed in the self-assembly process when two differently shaped ligands L1 and L2 are mixed. More impressively, distinct self-sorting behavior between Eu4(L1)6 and Eu4(L2)4 coordination cages is observed for the first time when racemic mixtures of ligands are used. We envisage that chiral luminescent lanthanide tetrahedral cages could be used in chiroptical probes\\sensors and enantioselective catalysis. PMID:26065490
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.
Lesson 17: Quadratic Inequalities
NSDL National Science Digital Library
2011-01-01
The lesson begins with using graphs to solve quadratic inequalities. AN equation modeling the height of a rocket is graphed along with a second equation that represents the minimum height at which the rocket can legally and safely be exploded. The intersections of the graphs provide the solution interval. A second method is then presented where the inequality is put into standard form and then solved for its x-intercepts. Interval notation and union of sets is reviewed before a purely algebraic procedure for solving the inequalities is presented. The lesson concludes with an application problem.
Use of quadratic components for buckling calculations
Dohrmann, C.R.; Segalman, D.J. [Sandia National Labs., Albuquerque, NM (United States). Structural Dynamics Dept.] [Sandia National Labs., Albuquerque, NM (United States). Structural Dynamics Dept.
1996-12-31
A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.
Solving quadratic equations using reduced unimodular quadratic forms
Denis Simon
2005-01-01
Let Q be an n × n symmetric matrix with integral entries and with detQ ?= 0, but not necesarily positive definite. We describe a generalized LLL algorithm to reduce this quadratic form. This algorithm either reduces the quadratic form or stops with some isotropic vector. It is proved to run in polynomial time. We also describe an algorithm for
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.
NASA Astrophysics Data System (ADS)
Kwack, JaeHyuk; Masud, Arif
2014-04-01
This paper presents a stabilized mixed finite element method for shear-rate dependent fluids. The nonlinear viscosity field is a function of the shear-rate and varies uniformly in space and in time. The stabilized form is developed via application of Variational Multiscale (VMS) framework to the underlying generalized Navier-Stokes equation. Linear and quadratic tetrahedral and hexahedral elements are employed with equal-order interpolations for the velocity and pressure fields. A variety of benchmark problems are solved to assess the stability and accuracy properties of the resulting method. The method is then applied to non-Newtonian shear-rate dependent flows in bifurcating artery geometry, and significant non-Newtonian fluid effects are observed. A comparative study of the proposed method shows that the additional computational costs due to the nonlinear shear-rate dependent viscosity are only ten percent more than the computational cost for a Newtonian model.
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 degrees rotation, was measured in the experiments performed. The parameters relevant for characterizing soliton collision processes were also studied in detail. Measurements were performed for various collision angles (from 0.2 to 4 degrees), phase mismatch, relative phase between the solitons and the distance to the collision point within the sample (which affects soliton formation). Both the individual and combined effects of these collision variables were investigated. Based on the research conducted, several all-optical switching scenarios were proposed.
Manfred Knebusch Specialization of Quadratic
= 2. It served me in the first place as the foundation for a theory of generic splitting of quadratic-Kahn-Karpenko- Vishik for instance. One should note that there exists a theory of (partial) generic splitting of central a specialization theory of quadratic and symmetric bilinear forms with respect to a place ~: K ! L [ 1, without
Manfred Knebusch Specialization of Quadratic
#= 2. It served me in the first place as the foundation for a theory of generic splitting of quadratic) generic splitting of central simple algebras and reductive algebraic groups, parallel to the theory during a talk by T.Y. Lam on field invariants from the theory of quadratic forms. 1 It is -- poetic
Tetrahedral Sn-silsesquioxane: synthesis, characterization and catalysis.
Beletskiy, Evgeny V; Shen, Zhongliang; Riofski, Mark V; Hou, Xianliang; Gallagher, James R; Miller, Jeffrey T; Wu, Yuyang; Kung, Harold H; Kung, Mayfair C
2014-12-25
A tetrahedral stannasilsesquioxane complex was synthesized as a racemic mixture using Sn(O(i)Pr)4 and silsesquioxanediol, and its structure was confirmed with X-ray crystallography, NMR, and EXAFS. The complex was a Lewis acid, and both anti and syn-binding with Lewis bases were possible with the formation of octahedral Sn complexes. It was also a Lewis acid catalyst active for epoxide ring opening and hydride transfer. PMID:25360661
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.
Search for Fingerprints of Tetrahedral Symmetry in $^{156}Gd$
Q. T. Doan; D. Curien; O. Stezowski; J. Dudek; K. Mazurek; A. Gozdz; J. Piot; G. Duchene; B. Gall; H. Molique; M. Richet; P. Medina; D. Guinet; N. Redon; C. Schmitt; P. Jones; R. Julin; P. Peura; S. Ketelhut; M. Nyman; U. Jakobsson; A. Maj; K. Zuber; P. Bednarczyk; N. Schunck; J. Dobaczewski; A. Astier; I. Deloncle; D. Verney; G. De Angelis; J. Gerl
2008-12-01
Theoretical predictions suggest the presence of tetrahedral symmetry as an explanation for the vanishing intra-band E2-transitions at the bottom of the odd-spin negative parity band in $^{156}Gd$. The present study reports on experiment performed to address this phenomenon. It allowed to determine the intra-band E2 transitions and branching ratios B(E2)/B(E1) of two of the negative-parity bands in $^{156}Gd$.
Hierarchical tangential vector finite elements for tetrahedra
Lars S. Andersen; John L. Volakis
1998-01-01
Tangential vector finite elements (TVFEs) overcome most of the shortcomings of node-based finite elements for electromagnetic simulations. Hierarchical TVFEs are of considerable practical interest since they allow use of effective selective field expansions where different order TVFEs are combined within a computational domain. For a tetrahedral element, this letter proposes a set of hierarchical mixed-order TVFEs up to and including
The Solution of Quadratic Equations
E. Cuthbert Atkinson
1898-01-01
IN your issue of February 24 a review appears of ``Chambers's Algebra for Schools.'' Your reviewer concludes with a lament of the probable uselessness of protesting against the method of solving quadratics by ``completing the square.''
An Investigation on Quadratic Equations.
ERIC Educational Resources Information Center
Hirst, Keith
1988-01-01
Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)
Quadratics, polynomial form in y
NSDL National Science Digital Library
ExploreMath.com
2001-01-01
Explore the graph of a quadratic of the form x = ay2 + by + c. Vary the coefficients of the equation and examine how the graph changes in response. Calculate the location of the vertex and y-intercepts.
Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems
Higham, Nicholas J.
, overdamped, weakly overdamped, quadratic matrix polynomial, quadratic matrix equation, solvent, cyclicDetecting and Solving Hyperbolic Quadratic Eigenvalue Problems Chun-Hua Guo, Nicholas J. Higham1613 DETECTING AND SOLVING HYPERBOLIC QUADRATIC EIGENVALUE PROBLEMS CHUN-HUA GUO, NICHOLAS J. HIGHAM, AND FRANC
Real Homotopies 1 Quadratic Turning Points
Verschelde, Jan
Real Homotopies 1 Quadratic Turning Points deforming real polynomials quadratic turning points 2 shooting for a turning point MCS 563 Lecture 13 Analytic Symbolic Computation Jan Verschelde, 12 February Homotopies 1 Quadratic Turning Points deforming real polynomials quadratic turning points 2 The Newtonian n
Novel biomedical tetrahedral mesh methods: algorithms and applications
NASA Astrophysics Data System (ADS)
Yu, Xiao; Jin, Yanfeng; Chen, Weitao; Huang, Pengfei; Gu, Lixu
2007-12-01
Tetrahedral mesh generation algorithm, as a prerequisite of many soft tissue simulation methods, becomes very important in the virtual surgery programs because of the real-time requirement. Aiming to speed up the computation in the simulation, we propose a revised Delaunay algorithm which makes a good balance of quality of tetrahedra, boundary preservation and time complexity, with many improved methods. Another mesh algorithm named Space-Disassembling is also presented in this paper, and a comparison of Space-Disassembling, traditional Delaunay algorithm and the revised Delaunay algorithm is processed based on clinical soft-tissue simulation projects, including craniofacial plastic surgery and breast reconstruction plastic surgery.
Structural performance of orthogonal tetrahedral truss Space-Station configurations
NASA Technical Reports Server (NTRS)
Dorsey, J. T.
1984-01-01
Two 150 kW space station configurations constructed with the orthogonal tetrahedral truss concept are described. One space station consists of a large central platform and two rotating solar wing arrays and the other consists of a long central keel with two rotating arrays. The dynamic characteristics of each configuration are obtained with and without nonstructural components present. The variation in frequencies and mass moments of inertia due to rotation of the two solar wing arrays are given for the long keel space station configuration. The structural performance of the solar wing array is assessed for cases where individual critical struts fail in the array support truss.
Search for Fingerprints of Tetrahedral Symmetry in ^{156}Gd
Doan, Q. T. [Universite Lyon 1, Villeurbanne, France; Curien, D. [CNRS, Strasbourg, France; Stezowski, O. [Universite Lyon 1, Villeurbanne, France; Dudek, J. [CNRS, Strasbourg, France; Mazurek, K. [H. Niewodniczanski Institute of Nuclear Physics (INP), Krakow, Poland; Gozdz, A. [Maria Curie-Sklodowskiej, Lublin, Poland; Piot, J. [CNRS, Strasbourg, France; Duchene, G. [CNRS, Strasbourg, France; Gall, B. [CNRS, Strasbourg, France; Molique, H. [CNRS, Strasbourg, France; Richet, M. [CNRS, Strasbourg, France; Medina, P. [CNRS, Strasbourg, France; Guinet, D. [Universite Lyon 1, Villeurbanne, France; Redon, N. [Universite Lyon 1, Villeurbanne, France; Schmitt, Ch. [Universite Lyon 1, Villeurbanne, France; Jones, P. [University of Jyvaskyla; Peura, P. [University of Jyvaskyla; Ketelhut, S. [University of Jyvaskyla; Nyman, M. [University of Jyvaskyla; Jakobsson, U. [University of Jyvaskyla; Greenlees, P. T. [University of Jyvaskyla; Julin, R. [University of Jyvaskyla; Juutinen, S. [University of Jyvaskyla; Rahkila, P. [University of Jyvaskyla; Maj, A. [H. Niewodniczanski Institute of Nuclear Physics (INP), Krakow, Poland; Zuber, K. [H. Niewodniczanski Institute of Nuclear Physics (INP), Krakow, Poland; Bednarczyk, P. [H. Niewodniczanski Institute of Nuclear Physics (INP), Krakow, Poland; Schunck, Nicolas F [ORNL; Dobaczewski, J. [Warsaw University; Astier, A. [CNRS, Orsay, France; Deloncle, I. [CNRS, Orsay, France; Verney, D. [CNRS/IN2P3, Orsay, France; De Angelis, G. [INFN, Laboratori Nazionali di Legnaro, Italy; Gerl, J. [Gesellschaft fur Schwerionenforschung (GSI), Germany
2009-01-01
Theoretical predictions suggest the presence of tetrahedral symmetry as an explanation for the vanishing intra-band E2 transitions at the bottom of the odd-spin negative-parity band in ^{156}Gd. The present study reports on experiment performed to address this phenomenon. It allowed to remove certain ambiguities related to the intra-band E2 transitions in the negative-parity bands to determine the new inter-band transitions and reduced probability ratios B(E2)/B(E1) and, for the first time, to determine the experimental uncertainties related to the latter observable.
2014-12-11
element-wise absolute value of z, and I+(z) is the indicator function of the positive orthant ... the 0-solution time is finite for all x0, we say that the sequence converges in finite time. ...... We have made these QPs publicly available as a MATLAB.
NASA Astrophysics Data System (ADS)
Lu, Yong-Ming; Lan, Ya-Qian; Xu, Yan-Hong; Su, Zhong-Min; Li, Shun-Li; Zang, Hong-Ying; Xu, Guang-Juan
2009-11-01
To investigate the relationship between topological types and molecular building blocks (MBBs), we have designed and synthesized a series of three-dimensional (3D) interpenetrating metal-organic frameworks based on different polygons or polyhedra under hydrothermal conditions, namely [Cd(bpib) 0.5(L 1)] ( 1), [Cd(bpib) 0.5(L 2)]·H 2O ( 2), [Cd(bpib) 0.5(L 3)] ( 3) and [Cd(bib) 0.5(L 1)] ( 4), where bpib=1,4-bis(2-(pyridin-2-yl)-1 H-imidazol-1-yl)butane, bib=1,4-bis(1 H-imidazol-1-yl)butane, H 2L 1=4-(4-carboxybenzyloxy)benzoic acid, H 2L 2=4,4'-(ethane-1,2-diylbis(oxy))dibenzoic acid and H 2L 3=4,4'-(1,4-phenylenebis(methylene))bis(oxy)dibenzoic acid, respectively. Their structures have been determined by single crystal X-ray diffraction analyses and further characterized by elemental analyses, IR spectra, and thermogravimetric (TG) analyses. Compounds 1- 3 display ?-Po topological nets with different degrees of interpenetration based on the similar octahedral [Cd 2(-COO) 4] building blocks. Compound 4 is a six-fold interpenetrating diamondoid net based on tetrahedral MBBs. By careful inspection of these structures, we find that various carboxylic ligands and N-donor ligands with different coordination modes and conformations, and metal centers with different geometries are important for the formation of the different MBBs. It is believed that different topological types lie on different MBBs with various polygons or polyhedra. Such as four- and six-connected topologies are formed by tetrahedral and octahedral building blocks. In addition, with the increase of carboxylic ligands' length, the degrees of interpenetration have been changed in the ?-Po topological nets. And the luminescent properties of these compounds have been investigated in detail.
Symmetric second order edge elements for triangles and tetrahedra
Akihisa Kameari
1999-01-01
A new type of second order edge elements for simplexes (triangles and tetrahedra) is proposed. The element is geometrically symmetric and the shape functions are orthogonal to each other in the integrals of the tangential components on edges. The number of nodes and edges are 14 and 24 in a tetrahedral element. The proposed elements are validated by eigenmode calculations
Encapsulation of Halocarbons in a Tetrahedral Anion Cage.
Yang, Dong; Zhao, Jie; Zhao, Yanxia; Lei, Yibo; Cao, Liping; Yang, Xiao-Juan; Davi, Martin; de Sousa Amadeu, Nader; Janiak, Christoph; Zhang, Zhibin; Wang, Yao-Yu; Wu, Biao
2015-07-20
Caged supramolecular systems are promising hosts for guest inclusion, separation, and stabilization. Well-studied examples are mainly metal-coordination-based or covalent architectures. An anion-coordination-based cage that is capable of encapsulating halocarbon guests is reported for the first time. This A4 L4 -type (A=anion) tetrahedral cage, [(PO4 )4 L4 ](12-) , assembled from a C3 -symmetric tris(bisurea) ligand (L) and phosphate ion (PO4 (3-) ), readily accommodates a series of quasi-tetrahedral halocarbons, such as the Freon components CFCl3 , CF2 Cl2 , CHFCl2 , and C(CH3 )F3 , and chlorocarbons CH2 Cl2 , CHCl3 , CCl4 , C(CH3 )Cl3 , C(CH3 )2 Cl2 , and C(CH3 )3 Cl. The guest encapsulation in the solid state is confirmed by crystal structures, while the host-guest interactions in solution were demonstrated by NMR techniques. PMID:26053734
TetSplat: Real-time Rendering and Volume Clipping of Large Unstructured Tetrahedral Meshes
TetSplat: Real-time Rendering and Volume Clipping of Large Unstructured Tetrahedral Meshes Ken: Screen shots from interactive visualization of an unstructured 275Mb mesh with more than 5 million of rendering hardware (here a P4 1.7GHz, Radeon 8700) and size of the unstructured tetrahedral mesh. Images
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…
Search for Tetrahedral Symmetry in Nuclei:. a Short Overview
NASA Astrophysics Data System (ADS)
Curien, D.; Dudek, J.; Molique, H.; Sengele, L.; Gó?d?, A.; Mazurek, K.
Following a series of experiments launched by the TetraNuc collaboration to possibly demonstrate the existence of high-rank symmetries in subatomic physics, the first experimental results on the Rare Earth region appear in publications. Meanwhile an important progress has been made on the theory side strongly suggesting that the original criterion of the static tetrahedral symmetry in the form of vanishing quadrupole moments may need to be revised to include explicitly the vibrational motion. The Actinide region seems of particular interest because of the extra stability provided by the octahedral symmetry. In this article a summary of the current experimental efforts on both the Rare-Earth and Actinide regions is given. Finally the ELMA project addressing the experimental search for the symmetries in the Actinides is briefly discussed.
Self-assembly of tetrahedral plasmonic nanoclusters for optical metafluids
NASA Astrophysics Data System (ADS)
Schade, Nicholas; Manoharan, Vinothan
2015-03-01
We direct the assembly of clusters of gold nanospheres that behave as nanoscale electromagnetic resonators. We use spherical gold nanoparticles that are exceptionally smooth, monocrystalline, and monodisperse. These particles exhibit highly reproducible scattering spectra compared with gold colloids that are available commercially. We mix these positively charged particles with negatively charged dielectric particles. The gold particles stick to the dielectric particles permanently and randomly in a process that can be modeled mathematically as ``random parking,'' a type of non-equilibrium self-assembly. By controlling the particles' sizes, stoichiometry, and interactions, we maximize the yield of tetrahedral clusters, the ideal structures for isotropic metamaterials. We measure the optical properties of these structures with dark-field spectroscopy to characterize their suitability as building blocks for a bulk, isotropic, optical metafluid.
Manfred Knebusch Specialization of Quadratic
, and therefore also K, had characteristic #= 2. It served me in the first place as the foundation for a theory a theory of (partial) generic splitting of central simple algebras and reductive algebraic groups, parallel the theory of quadratic forms. 1 It is -- poetic exaggeration allowed -- a suitable motto for this monograph
PIECEWISE QUADRATIC APPROXIMATIONS IN CONVEX ...
2010-12-11
even if the newly obtained point is inserted in I (which is possible, although not ...... As far as control of the bundle size is concerned, a classical approach (again .... towards the optimum, and the “noise” provided by the extra quadratic terms in the .... Contraints, International Journal of Electrical Power and Energy Systems,.
New quadratic baryon mass relations
Burakovsky, L.; Goldman, T. [Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)] [Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Horwitz, L.P. [School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69978 (Israel)] [School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69978 (Israel)
1997-12-01
By assuming the existence of (quasi)linear baryon Regge trajectories, we derive new quadratic Gell-Mann{endash}Okubo-type baryon mass relations. These relations are used to predict the masses of the charmed baryons absent from the baryon summary table so far, in good agreement with the predictions of many other approaches. {copyright} {ital 1997} {ital The American Physical Society}
ON QUADRATIC POLYNOMIALS. by F. Lazebnik.
Lazebnik, Felix
not exist. 3. Quadratic equations. Another most useful applications of the completion of the square in the "completed square form", and this made the finding of its minimum or maximum easy. In case when the quadratic transformation is that it allows to derive a formula for solving quadratic equations or show that no solutions
Stephen F Austin Linear, Quadratic, Polynomial,
Hubbard, Keith
the useful algebraic operation of completing the square, and how to solve quadratic equations. Then we sections--one discusses com- plex numbers (needed to solve arbitrary quadratic equations) and one dis- cusses systems of equations and matrices. 117 #12;Stephen F Austin 118 chapter 2 Linear, Quadratic
Quadratic Residues a is a quadratic residue mod m if x2
Ikenaga, Bruce
if the following equation has a solution: x2 = a (mod m) . Otherwise, a is a quadratic nonresidue mod m. Example. 8 a quadratic equation mod p has at most two solutions (Prove it!), there are exactly two. Example. x2 = 8 (mod6-21-2013 Quadratic Residues · a is a quadratic residue mod m if x2 = a (mod m). Otherwise
Quadratic fluctuation-dissipation theorem for multilayer plasmas
Golden, K.I. [Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401-1455 (United States)] [Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401-1455 (United States)
1999-01-01
The author establishes the dynamical and static quadratic fluctuation-dissipation theorems (QFDTs) for multilayer classical one-component plasmas in the absence of external magnetic fields. Areal densities and spacings between layers need not be equal. The static QFDT is used to derive the lowest-order (in coupling parameter) Mayer cluster expansion for the layer-space matrix elements of the equilibrium three-point correlation function. {copyright} {ital 1999} {ital The American Physical Society}
Quadratic fluctuation-dissipation theorem for multilayer plasmas
Kenneth I. Golden
1999-01-01
The author establishes the dynamical and static quadratic fluctuation-dissipation theorems (QFDTs) for multilayer classical one-component plasmas in the absence of external magnetic fields. Areal densities and spacings between layers need not be equal. The static QFDT is used to derive the lowest-order (in coupling parameter) Mayer cluster expansion for the layer-space matrix elements of the equilibrium three-point correlation function.
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.
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)
Quadratic algebras and integrable chains
F. Soloviev
2009-10-26
Using Krichever-Phong's universal formula, we show that a multiplicative representation linearizes Sklyanin quadratic brackets for a multi-pole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a by-product, we obtain an extension of a Sklyanin algebra in the elliptic case. Krichever-Phong's formula provides a hierarchy of symplectic structures, and we show that there exists a non-trivial cubic bracket in Sklyanin's case.
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
NASA Astrophysics Data System (ADS)
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; Charest, Marc R.; Canfield, Thomas R.; Wohlbier, John G.
2015-06-01
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 at 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.
Polyamorphism in tetrahedral substances: similarities between silicon and ice
NASA Astrophysics Data System (ADS)
Antonelli, Alex; Garcez, Karl
2015-03-01
Tetrahedral substances, such as silicon, water, germanium, and silica, share several thermodynamical anomalies. Among them, the so-called polyamorphism, i.e., the existence of more than one amorphous state, is, perhaps, the most studied one. In this work, we study the transformations between amorphs of silicon using Monte Carlo simulations. The simulations indicate that by compressing the low density amorphous state (LDA), which is obtained by quenching the liquid at high temperature, a new denser amorph is found. The transformation between these two forms of amorphous silicon displays clear hysteresis, similar to the experiment reported by McMillan et al.. However, analogously to the case of ice, our simulations indicate that upon annealing the unannealed high density amorphous silicon (uHDA) evolves to more stable forms. The annealing of uHDA at pressures on the order of 20 GPa gives rise to an even denser form, the very high density amorphous silicon (VHDA), while at much lower pressures, about 5 GPa, the uHDA transforms into a lower density form, the expanded high density amorphous silicon (eHDA). Work supported by FAPESP, CNPq, CAPES, and FAEPEX/UNICAMP.
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.
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.
Orientational order in ionic crystals containing tetrahedral ions
NASA Astrophysics Data System (ADS)
Klein, Michael L.; McDonald, Ian R.; Ozaki, Yoshiaki
1983-12-01
Molecular dynamics calculations based on atom-atom potentials and rigid nonpolarizable ions are used to study the cubic rotator phases of ammonium bromide (NH4Br). The nature of the orientational order exhibited by the ammonium ions is characterized using tetrahedral rotor functions (M?, ?=1,7). The quantities
Glutamate detection by amino functionalized tetrahedral amorphous carbon surfaces.
Kaivosoja, Emilia; Tujunen, Noora; Jokinen, Ville; Protopopova, Vera; Heinilehto, Santtu; Koskinen, Jari; Laurila, Tomi
2015-08-15
In this paper, a novel amperometric glutamate biosensor with glutamate oxidase (GlOx) immobilized directly on NH2 functionalized, platinum doped tetrahedral amorphous carbon (ta-C) film, has been successfully developed. First, we demonstrate that direct GlOx immobilization is more effective on amino-groups than on carboxyl- or hydroxyl-groups. Second, we show that anodizing and plasma treatments increase the amount of nitrogen and the proportion of protonated amino groups relative to amino groups on the aminosilane coating, which subsequently results in an increased amount of active GlOx on the surface. This effect, however, is found to be unstable due to unstable electrostatic interactions between GlOx and NH3(+). We demonstrate the detection of glutamate in the concentration range of 10µM-1mM using the NH2 functionalized Pt doped ta-C surface. The biosensor showed high sensitivity (2.9nA?M(-1)cm(-2)), low detection limit (10?M) and good storage stability. The electrode response to glutamate was linear in the concentrations ranging from 10µM to 500µM. In conclusion, the study shows that GlOx immobilization is most effective on aminosilane treated ta-C surface without any pre-treatments and the fabricated sensor structure is able to detect glutamate in the micromolar range. PMID:25966399
NASA Astrophysics Data System (ADS)
Tang, Chun-Ming; Jian, Jin-Bao
2008-10-01
Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The "active set" strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered.
Tetrahedrality and structural order for hydrophobic interactions in a coarse-grained water model.
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. PMID:25353455
Average adjacencies for tetrahedral skeleton-regular partitions
A. Plaza; M. C. Rivara
2005-01-01
For any conforming mesh, the application of a skeleton-regular partition over each element in the mesh, produces a conforming mesh such that all the topological elements of the same dimension are subdivided into the same number of child-elements. Every skeleton-regular partition has associated special constitutive (recurrence) equations. In this paper the average adjacencies associated with the skeleton-regular partitions in 3D
Gravitational Energy in Quadratic-Curvature Gravities
S. Deser; Bayram Tekin
2002-01-01
We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the ``cosmological'' Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature
Tableau-based protein substructure search using quadratic programming
Stivala, Alex; Wirth, Anthony; Stuckey, Peter J
2009-01-01
Background Searching for proteins that contain similar substructures is an important task in structural biology. The exact solution of most formulations of this problem, including a recently published method based on tableaux, is too slow for practical use in scanning a large database. Results We developed an improved method for detecting substructural similarities in proteins using tableaux. Tableaux are compared efficiently by solving the quadratic program (QP) corresponding to the quadratic integer program (QIP) formulation of the extraction of maximally-similar tableaux. We compare the accuracy of the method in classifying protein folds with some existing techniques. Conclusion We find that including constraints based on the separation of secondary structure elements increases the accuracy of protein structure search using maximally-similar subtableau extraction, to a level where it has comparable or superior accuracy to existing techniques. We demonstrate that our implementation is able to search a structural database in a matter of hours on a standard PC. PMID:19450287
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)
Implementation of a Refinement\\/Derefinement Algorithm for Tetrahedral Meshes
J. M. Gonz; R. Montenegro; J. M. Escobar; G. Montero; E. Rodr ´ iguez
To solve problems using finite element method it is necessary to obtain a good domain discretization. Once the problem geometry has been approached by an initial mesh, it must be able to adapt itself to the singularities of the numerical solution. The refinement process introduces new elements in zones of the mesh where the solution needs to be improved. The
Wortman, Kevin
Quadratic Equations and Conics A quadratic equation in two variables is an equation that's equivalent to an equation of the form p(x, y) = 0 where p(x, y) is a quadratic polynomial. Examples. · 4x2 - 3xy - 2y2 + x - y + 6 = 0 is a quadratic equation, as are x2 - y2 = 0 and x2 + y2 = 0 and x2 - 1 = 0
On ideal structure in quadratic DDS in R{sup 2}
Kutnjak, Milan [Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova 17, 2000 Maribor (Slovenia)
2008-11-13
We consider the dynamics in a special case of two-dimensional quadratic homogeneous discrete dynamical systems. It is well known (c.f. [1, 2]) that homogeneous quadratic maps are in one to one correspondence with two-dimensional commutative (nonassociative) algebras. Algebraic concepts (such as the structure of algebra and existence of special elements like idempotents and nilpotents) help us to study the dynamics of the corresponding discrete homogeneous quadratic maps. It is well-known that such systems can exhibit chaotic behavior [3], In this article we consider the influence of the existence of an algebra ideal on the dynamics of the corresponding discrete homogeneous quadratic system. We also present some examples in the plane.
3D Finite Element Meshing from Imaging Data
Yongjie Zhang; Chandrajit Bajaj; Bong-Soo Sohn
2004-01-01
This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imag- ing data. The extracted tetrahedral and hexahedral meshes are extensively used in the Finite Element Method (FEM). A top-down octree subdivision coupled with the dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging data.
Elastodynamic boundary element formulation employing discontinuous curved elements
H. R. Yerli; I. O. Deneme
2008-01-01
A boundary element formulation having discontinuous curved quadratic elements is presented for 2D elastodynamics. The first fundamental solution for static case is subtracted from and added to the first fundamental solution for dynamic case. As both kernels have the same order of singularity, the integral involving the regular expression arising from the subtraction can be calculated. H? matrix is calculated
Ikenaga, Bruce
is a root of a quadratic equation with integer coefficients. · Quadratic irrationals can be expressed. Definition. A quadratic irrational is an irrational number which is a root of a quadratic equation ax2 + bx)2 = q, r2 x2 - 2rpx + (p2 - q) = 0. This is a quadratic equation with integer coefficients, and r2
Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems
Chun-Hua Guo; Nicholas J. Higham; Françoise Tisseur
2008-01-01
Hyperbolic quadratic matrix polynomials Q(? )= ?2A + ?B + C are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are those with nonpositive eigenvalues. Neither the definition of overdamped nor any of the standard characterizations provides an efficient way to test if a given Q has this property. We show that a
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…
Existence Theorems for Some Quadratic Integral Equations
Józef Bana?; Millenia Lecko; Wagdy Gomaa El-Sayed
1998-01-01
Using the theory of measures of noncompactness, we prove a few existence theorems for some quadratic integral equations. The class of quadratic integral equations considered below contains as a special case numerous integral equations encountered in the theories of radiative transfer and neutron transport, and in the kinetic theory of gases. In particular, the well-known Chandrasekhar integral equation also belongs
Quadratic dynamics in binary number systems
Paul E. Fishback
2005-01-01
We describe the quadratic dynamics in certain two-component number systems, which like the complex numbers, can be expressed as rings of two by two real matrices. This description is accomplished using the properties of the real quadratic family and its derivative. We also demonstrate that the Mandelbrot set for any of these systems may be defined in two equivalent ways
On Quadratic Bent Functions in Polynomial Forms
Honggang Hu; Dengguo Feng
2007-01-01
In this correspondence, we construct some new quadratic bent functions in polynomial forms by using the theory of quadratic forms over finite fields. The results improve some previous work. Moreover, we solve a problem left by Yu and Gong in 2006.
Best Quadratic Approximations of Cubic Boolean Functions
, n). Key words: Bent functions; boolean functions; covering radius; lower order approximationsBest Quadratic Approximations of Cubic Boolean Functions Nicholas Kolokotronis1,2, Konstantinos of Boolean functions is treated in this paper. We focus on the case of best quadratic approximations
Single-photon quadratic optomechanics
Jie-Qiao Liao; Franco Nori
2014-09-10
We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon.
Efficient Reduced Basis Solution of Quadratically Nonlinear Diffusion
Efficient Reduced Basis Solution of Quadratically Nonlinear Diffusion Equations M. Rasty M for a steady quadratically nonlinear diffusion equation. We develop an efficient computational procedure- diction of quadratically nonlinear parametrized diffusion equations. To achieve this goal we pursue
Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition
Boyer, Edmond
parabolic partial differen- tial equation with nonlinearity having quadratic or superquadratic growthMarkovian quadratic and superquadratic BSDEs with an unbounded terminal condition Adrien Richou Abstract This article deals with the existence and the uniqueness of solutions to quadratic
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)
LETTER TO THE EDITOR: A new approach to modelling tetrahedral amorphous carbon
NASA Astrophysics Data System (ADS)
Walters, J. K.; Gilkes, K. W. R.; Wicks, J. D.; Newport, R. J.
1997-08-01
We have generated a new model for the structure of tetrahedral amorphous carbon using a modified reverse Monte Carlo modelling method. The novel feature of this approach is the definition of three different types of carbon atom, corresponding to tetrahedral, planar and linear bonding conformations. The particular strengths of the method are the large model size (3000 atoms), that all the possible arrangements of 0953-8984/9/34/001/img7 and 0953-8984/9/34/001/img8 bonds are allowed, and that no interatomic potential is required. For the first time we have determined the distribution of 0953-8984/9/34/001/img8 bonded sites within the predominantly disordered tetrahedral structure, and we find that they form polymer-like chains and small clusters which connect the 0953-8984/9/34/001/img7 bonded regions.
Reordering between tetrahedral and octahedral sites in ultrathin magnetite films grown on MgO(001)
Bertram, F.; Deiter, C. [Hamburger Synchrotronstrahlungslabor am Deutschen Elektronen-Synchrotron, Notkestr. 85, 22607 Hamburg (Germany)] [Hamburger Synchrotronstrahlungslabor am Deutschen Elektronen-Synchrotron, Notkestr. 85, 22607 Hamburg (Germany); Schemme, T.; Jentsch, S.; Wollschlaeger, J. [Fachbereich Physik, Universitaet Osnabrueck, Barbarastr. 7, 49069 Osnabrueck (Germany)] [Fachbereich Physik, Universitaet Osnabrueck, Barbarastr. 7, 49069 Osnabrueck (Germany)
2013-05-14
Magnetite ultrathin films were grown using different deposition rates and substrate temperatures. The structure of these films was studied using (grazing incidence) x-ray diffraction, while their surface structure was characterized by low energy electron diffraction. In addition to that, we performed x-ray photoelectron spectroscopy and magneto optic Kerr effect measurements to probe the stoichiometry of the films as well as their magnetic properties. The diffraction peaks of the inverse spinel structure, which originate exclusively from Fe ions on tetrahedral sites are strongly affected by the preparation conditions, while the octahedral sites remain almost unchanged. With both decreasing deposition rate as well as decreasing substrate temperature, the integrated intensity of the diffraction peaks originating exclusively from Fe on tetrahedral sites is decreasing. We propose that the ions usually occupying tetrahedral sites in magnetite are relocated to octahedral vacancies. Ferrimagnetic behaviour is only observed for well ordered magnetite films.
Reordering between tetrahedral and octahedral sites in ultrathin magnetite films grown on MgO(001)
NASA Astrophysics Data System (ADS)
Bertram, F.; Deiter, C.; Schemme, T.; Jentsch, S.; Wollschläger, J.
2013-05-01
Magnetite ultrathin films were grown using different deposition rates and substrate temperatures. The structure of these films was studied using (grazing incidence) x-ray diffraction, while their surface structure was characterized by low energy electron diffraction. In addition to that, we performed x-ray photoelectron spectroscopy and magneto optic Kerr effect measurements to probe the stoichiometry of the films as well as their magnetic properties. The diffraction peaks of the inverse spinel structure, which originate exclusively from Fe ions on tetrahedral sites are strongly affected by the preparation conditions, while the octahedral sites remain almost unchanged. With both decreasing deposition rate as well as decreasing substrate temperature, the integrated intensity of the diffraction peaks originating exclusively from Fe on tetrahedral sites is decreasing. We propose that the ions usually occupying tetrahedral sites in magnetite are relocated to octahedral vacancies. Ferrimagnetic behaviour is only observed for well ordered magnetite films.
Quality Encoding for Tetrahedral Mesh Optimization , Zhi-Quan Chenga
Xu, Kai "Kevin"
of a mesh element, a tetrahedron in our context, is measured based on its effect on interpolation error, discretization error, and the conditioning of the stiffness matrix [30]. Surface fairing has been extensively while preserving geometric features. However, surface fairing is gen- erally oblivious to the quality
Interactive Isosurface Ray Tracing of Time-Varying Tetrahedral Volumes
Utah, University of
for visualizing unstructured volumes. Index Terms--Ray Tracing, Isosurfaces, Unstructured meshes, Tetrahedra challenge for data analysis. Due to its adaptive nature and simplicity, finite element (FE) analysis has disciplines such as CFD, meteorology, geology, and astronomy. With increasingly so- phisticated simulation
Modeling of Electronic Optical System for TV Tube using Finite Element Method
Paulius Tarvydas; Alius Noreika
2003-01-01
Using finite element method model of design of electronic optical system were made. Libraries of electronic optical system components and presumable electron trajectories were made. Analysis of finite element mesh creation was completed and finite element mesh spacing was determined in the zones of presumable electron trajectories. Tetrahedral mesh was created. Partial electrical field calculations and electrical field calculations with
NASA Astrophysics Data System (ADS)
Nikitin, A. V.; Rey, M.; Tyuterev, Vl. G.
2015-03-01
A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB4 molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q)-2 type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH4 molecule is demonstrated.
Warsa, James S.; Wareing, Todd A.; Morel, Jim E. [Los Alamos National Laboratory (United States)
2002-07-15
We recently presented a method for efficiently solving linear discontinuous discretizations of the two-dimensional P{sub 1} equations on rectangular meshes. The linear system was efficiently solved with Krylov iterative methods and a novel two-level preconditioner based on a linear continuous finite element discretization of the diffusion equation. Here, we extend the preconditioned solution method to three-dimensional, unstructured tetrahedral meshes. Solution of the P{sub 1} equations forms the basis of a diffusion synthetic acceleration (DSA) scheme for three-dimensional S{sub N} transport calculations with isotropic scattering. The P{sub 1} equations and the transport equation are both discretized with isoparametric linear discontinuous finite elements so that the DSA method is fully consistent. Fourier analysis in three dimensions and computational results show that this DSA scheme is stable and very effective. The fully consistent method is compared to other 'partially consistent' DSA schemes. Results show that the effectiveness of the partially consistent schemes can degrade for skewed or optically thick mesh cells. In fact, one such scheme can degrade to the extent of being unstable even though it is both unconditionally stable and effective on rectangular grids. Results for a model application show that our fully consistent DSA method can outperform the partially consistent DSA schemes under certain circumstances.
Quantum integrability of quadratic Killing tensors
Duval, C.; Valent, G. [Centre de Physique Theorique, CNRS, Luminy, Case 907, F-13288 Marseille Cedex 9 (France); Laboratoire de Physique Theorique et des Hautes Energies, 2, Place Jussieu, F-75251 Paris Cedex 5 (France)
2005-05-01
Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a 'minimal' quantization scheme, quantum integrability is ensured for a large class of classic examples.
sensitivity analysis in convex quadratic optimization: invariant ...
Aug 20, 2004 ... Keywords: Parametric optimization; Sensitivity analysis; Quadratic opti- ... when the problem has multiple optimal (and thus degenerate) solutions, ...... present, and future, Computers and Chemical Engineering, 23, 667–. 682.
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.)
Quadratic Equations...Origins, Development and Use.
ERIC Educational Resources Information Center
McQualter, J. W.
1988-01-01
There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (YP)
Linear and quadratic programming neural network analysis
Chia-Yiu Maa; Michael A. Shanblatt
1992-01-01
Neural networks for linear and quadratic programming are analyzed. The network proposed by M.P. Kennedy and L.O. Chua (IEEE Trans. Circuits Syst., vol.35, pp.554-562, May 1988) is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems, such as the least-squares problem. For quadratic programming, the network converges either to an equilibrium or to
Thermal Expansion and Pressure Effect on the Lattice Vibration of Tetrahedrally Covalent Compounds
Toshinobu Soma; Kinya Kudo
1980-01-01
Using a phenomenological theory with the experimental pressure dependence of elastic stiffness constants and the linear interpolation formula for mode Grüneisen parameters, the thermal expansion and the pressure effect on the lattice dynamics are investigated for tetrahedrally covalent compounds. The observed data for the temperature-dependence of thermal expansion coefficients are reproduced by introducing only two parameters. One is the parameter
Cyril Gruau; Thierry Coupez
2005-01-01
In this paper we present a 3D tetrahedral, unstructured and anisotropic mesh generator that is not based on the Delaunay, frontal or octree method. Instead, it proceeds by local optimizations and uses an anisotropic shape criterion to fit a metric field.Then, we introduce a new 3D metric field that tightens the mesh around interfaces when the calculation domain is divided
NASA Astrophysics Data System (ADS)
Sanoamuang, La-Orsri; Saengphan, Nukul
2006-06-01
A new species of fairy shrimp, Streptocephalus siamensis n. sp., is described from five temporary pools in Suphan Buri and Kanchana Buri Provinces, central Thailand. It sometimes co-occurs with its congener, S. sirindhornae . This new species belongs to the subgenus Parastreptocephalus which is defined by bearing tetrahedral cysts. This is the third anostracan species reported from Thailand.
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 Chemical…
Pinnaduwa H. S. W. Kulatilake
1988-01-01
An investigation of effect of variability of strength and orientation on stability of tetrahedral wedges with two free surfaces is presented. Study was limited to potential sliding along the line of intersection of the two joint planes. Minimum rock bolt force and minimum static acceleration were considered as output stability parameters in this study. An analytical procedure which combines a
C. Sadowsky; Jonathan D. Cohen; Russell H. Taylor
2005-01-01
This paper presents a novel method for computing simulated x-ray images, or DRRs (digitally reconstructed radiographs), of tetrahedral meshes with higher-order attenuation functions. DRRs are commonly used in computer assisted surgery (CAS), with the attenuation function consisting of a voxelized CT study, which is viewed from different directions. Our application of DRRs is in intra-operative \\
Samet, Hanan
Multiresolution Tetrahedral Meshes: an Analysis and a Comparison Emanuele Danovaro, Leila De multiresolution model, that we call a multiresolution mesh. Encoding data structures for the two repre- sentations otherwise. In order to analyze volume data sets of large size and to accelerate rendering, multiresolution
Tetrahedral symmetry in Zr nuclei: calculations of low-energy excitations with Gogny interaction
NASA Astrophysics Data System (ADS)
Tagami, Shingo; Shimizu, Yoshifumi R.; Dudek, Jerzy
2015-01-01
We report on the results of the calculations of the low energy excitation patterns for three Zirconium isotopes, viz 80Zr40, 96Zr56 and 110Zr70, reported by other authors to be doubly-magic tetrahedral nuclei (with tetrahedral magic numbers Z = 40 and N = 40, 56 and 70). We employ the realistic Gogny effective interactions using three variants of their parametrization and the particle-number, parity and the angular-momentum projection techniques. We confirm quantitatively that the resulting spectra directly follow the pattern expected from the group theory considerations for the tetrahedral symmetric quantum objects. We also find out that, for all the nuclei studied, the correlation energy obtained after the angular momentum projection is very large for the tetrahedral deformation as well as other octupole deformations. The lowering of the energies of the resulting configurations is considerable, i.e. by about 10 MeV or even more, once again confirming the significance of the angular-momentum projections techniques in the mean-field nuclear structure calculations.
Verbrugge, Clark
Â 1 Â TETRAHEDRALIZATION OF SIMPLE AND NONÂSIMPLE POLYHEDRA Godfried T. Toussaint Clark Verbrugge Memorial University of Newfoundland ABSTRACT It is known that not all simple polyhedra can investigate several classes of simple and nonÂsimple polyhedra that admit such decompositions. In particular
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.
Recanati, Catherine
with electric or magnetic properties, for example with the electric dipole moment surface. The symmetrized of the potential energy surface (PES) and of the electric dipole moment surface (EDMS) of the molecule under studyIntegrity bases for covariants of tetrahedral XY4 molecules. Application to the electric dipole
Samet, Hanan
adjacent tetrahedra in a tetrahedral mesh. The tetrahedra resultfrom a recursive decomposition of a cube into six initial congru- ent tetrahedra. A new technique ispresentedfor labeling the triangularfaces and smaller tetrahedra each of which is of one of three ba- sic shapes so that all of the tetrahedra
Note on an Additive Characterization of Quadratic Residues Modulo p
Monico, Chris
if the quadratic equation x2 = a mod p has a solution. If it has no solution then a is called a quadratic nonNote on an Additive Characterization of Quadratic Residues Modulo p Chris Monico, Michele Elia, . . . , p - 1} of positive residues modulo an odd prime p is the partition into quadratic residues
LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Lim, Andrew
LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ANDREW E. B. LIM AND XUN YU differential equations (BSDEs) with a quadratic cost criteria, or backward linear-quadratic (BLQ) control differential equations (BSDEs), linear-quadratic (LQ) optimal control, Riccati equations, completion of squares
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,…
Quadratic functions with prescribed spectra Wilfried Meidl and Alev Topuzoglu
Paris-Sud XI, Université de
study quadratic Boolean functions f from F2n to F2, which are well-known to have plateaued Fourier of Fitzgerald ([2]) on degenerate quadratic forms. Keywords: Quadratic Boolean functions, s-plateaued functions, near- bent functions, self-reciprocal polynomials, linear complexity 1 Introduction We study quadratic
Tormos, Jose R.; Wiley, Kenneth L.; Wang, Yi; Fournier, Didier; Masson, Patrick; Nachon, Florian; Quinn, Daniel M.
2010-01-01
In a previous communication, kinetic ?-deuterium secondary isotope effects were reported that support a mechanism for substrate-activated turnover of acetylthiocholine by human butyrylcholinesterase (BuChE) wherein the accumulating reactant state is a tetrahedral intermediate (Tormos, J. R., et al. (2005) JACS 127, 14538–14539). In this paper additional isotope effect experiments are described with acetyl-labeled acetylthiocholines (CL3COSCH2CH2N+Me3; L = H or D) that also support accumulation of the tetrahedral intermediate in Drosophila melanogaster acetylcholinesterase (DmAChE) catalysis. In contrast to the aforementioned BuChE-catalyzed reaction, for this reaction the dependence of initial rates on substrate concentration is marked by pronounced substrate inhibition at high substrate concentrations. Moreover, kinetic ? -deuterium secondary isotope effects for turnover of acetylthiocholine depended on substrate concentration, and gave the following: D3kcat/Km = 0.95 ± 0.03, D3kcat = 1.12 ± 0.02 and D3 ? kcat = 0.97 ± 0.04. The inverse isotope effect on kcat/Km is consistent with conversion of the sp2 hybridized substrate carbonyl in the E + A reactant state into a quasi-tetrahedral transition state in the acylation stage of catalysis, whereas the markedly normal isotope effect on kcat is consistent with hybridization change from sp3 toward sp2 as the reactant state for deacylation is converted into the subsequent transition state. Transition states for Drosophila melanogaster AChE-catalyzed hydrolysis of acetylthiocholine were further characterized by measuring solvent isotope effects and determining proton inventories. These experiments indicated that the transition state for rate-determining decomposition of the tetrahedral intermediate is stabilized by multiple protonic interactions. Finally, a simple model is proposed for the contribution that tetrahedral intermediate stabilization provides to the catalytic power of acetylcholinesterase. PMID:21105647
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.
Kannan, Chellapandian; Sundaram, Thiravium; Palvannan, Thayumanavan
2008-08-30
The conventional adsorbents like activated carbon, agricultural wastes, molecular sieves, etc., used for dye adsorption are unstable in the environment for long time, and hence the adsorbed dyes again gets liberated and pollute the environment. To avoid this problem, environmentally stable adsorbent of silica and alumina should be employed for malachite green adsorption. The adsorbents were characterized by Fourier transformed infrared spectroscopy (FT-IR) to confirm the tetrahedral framework of silica and non-tetrahedral framework of alumina. The adsorption equilibrium of dye on alumina and silica were 4 and 5h, respectively, this less adsorption time on alumina might be due to the less activation energy on alumina (63.46 kJ mol(-1)) than silica (69.93 kJ mol(-1)). Adsorption increased with increase of temperature on silica, in alumina, adsorption increased up to 60 degrees C, and further increase of temperature decreased the adsorption due to the structural change of non-tetrahedral alumina in water. The optimum pH for dye adsorption on alumina was 5 and silica was 6. The dye adsorptions on both adsorbents followed pseudo-second-order kinetics. The adsorption well matched with Langmuir and Freundlich adsorption isotherms and found that adsorption capacity on alumina was more than silica. The thermodynamic studies proved that the adsorption was endothermic and chemisorptions (DeltaH degrees >40 kJ mol(-1)) on alumina and silica. Recovery of dye on alumina and silica were studied from 30 to 90 degrees C and observed that 52% of dye was recovered from alumina and only 3.5% from silica. The less recovery on silica proved the strong adsorption of dye on silica than alumina. PMID:18289784
Hu, Sheng; Tong, Ming-Liang
2005-04-01
Solvothermal reaction of CuI with flexible 1,3-bis(4-pyridyl)propane generated the first three-dimensional coordination polymer constructed with the rigid tetrahedrally connected Cu4I4 cluster unit. The net is a rare chiral triple-interpenetrated, quartz net with of vertex symbol 6(4).8(2). The solid-state luminescence spectrum displays a strong red emission band at room temperature (lambdamax= 601 nm), characteristic of the Cu4I4 cluster centers. PMID:15782250
Christiane Quesne
2007-05-17
An exactly solvable position-dependent mass Schr\\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. This example emphasizes the interest of a quadratic algebra approach to position-dependent mass Schr\\"odinger equations.
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.
A unified multigrid solver for the Navier-Stokes equations on mixed element meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.
Martin, Kimball
7 Quadratic forms in n variables In order to understand quadratic forms in n variables over Z, one is let to study quadratic forms over various rings and fields such as Q, Qp, R and Zp. This is consistent equation in Z, it is useful study the equation over other rings. Definition 7.0.8. Let R be a ring
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624
Near-field testing of the 5-meter model of the tetrahedral truss antenna
NASA Technical Reports Server (NTRS)
Kefauver, Neill; Cencich, Tom; Osborn, Jim; Osmanski, J. T.
1986-01-01
This report documents the technical results from near-field testing of the General Dynamics 5-meter model of the tetrahedral truss antenna at the Martin Marietta Denver Aerospace facility. A 5-meter square side of the tetrahedral served as the perimeter of the antenna, and a mesh surface and extensive surface contouring cord network was used to create a parabolic aperture shape to within an rms accuracy of 30 mils or better. Pattern measurements were made with offset feed systems radiating at frequencies of 7.73, 11.60, 2.27, and 4.26 (all in GHz). This report discusses the method of collecting the data, system measurement accuracy, the test data compiled, and diagostics and isolation of causes of pattern results. The technique of using near-field phase for measuring surface mechanical tolerances is included. Detailed far field antenna patterns and their implications are provided for all tests conducted.
Jalarvo, Niina H [ORNL] [ORNL; Gourdon, Olivier [ORNL] [ORNL; Bi, Zhonghe [ORNL] [ORNL; Gout, Delphine J [ORNL] [ORNL; Ohl, Michael E [ORNL] [ORNL; Paranthaman, Mariappan Parans [ORNL] [ORNL
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 activation 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.
Pleiner, Harald; Brand, Helmut R
2014-02-01
We discuss the symmetry properties as well as the dynamic behavior of various non-polar nematic liquid crystal phases with tetrahedral order. We concentrate on systems that show biaxial nematic order coexisting with octupolar (tetrahedral) order. Non-polar examples are phases with D2 and S4 symmetries, which can be characterized as biaxial nematics lacking inversion symmetry. It is this combination that allows for new features in the statics and dynamics of these phases. The D2-symmetric phase is chiral, even for achiral molecules, and shows ambidextrous chirality in all three preferred directions. The achiral S4-symmetric phase allows for ambidextrous helicity, similar to the higher-symmetric D2d-symmetric phase. Such phases are candidates for nematic phases made from banana-shaped molecules. PMID:24566665
On the triplet ground state of tetrahedral X4 clusters (X = Li, Na, K, Cu)
NASA Astrophysics Data System (ADS)
Verdicchio, Marco; Evangelisti, Stefano; Leininger, Thierry; Monari, Antonio
2012-03-01
The lowest electronic state of distorted tetrahedral X4 clusters (with X = Li, Na, K, Cu) is studied at coupled-cluster level using high-quality atomic basis sets. The ground state is found to have a triplet spin symmetry for this kind of geometry and for all the considered atomic species. The equilibrium geometries correspond to Jahn-Teller-distorted oblate tetrahedra having D2d symmetry, and tetrahedric structures are local minima on the potential-energy surfaces for the triplet states. Their energies lie between 0.2 eV (for the K4 cluster) and 0.9 eV (for Cu4) above the absolute minimum of the corresponding systems, which is a spin singlet having a rhombus geometry.
On the triplet ground state of tetrahedral X4 clusters (X = Li, Na, K, Cu).
Verdicchio, Marco; Evangelisti, Stefano; Leininger, Thierry; Monari, Antonio
2012-03-01
The lowest electronic state of distorted tetrahedral X(4) clusters (with X = Li, Na, K, Cu) is studied at coupled-cluster level using high-quality atomic basis sets. The ground state is found to have a triplet spin symmetry for this kind of geometry and for all the considered atomic species. The equilibrium geometries correspond to Jahn-Teller-distorted oblate tetrahedra having D(2d) symmetry, and tetrahedric structures are local minima on the potential-energy surfaces for the triplet states. Their energies lie between 0.2 eV (for the K(4) cluster) and 0.9 eV (for Cu(4)) above the absolute minimum of the corresponding systems, which is a spin singlet having a rhombus geometry. PMID:22401434
On orthogonality preserving quadratic stochastic operators
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-05-01
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.
Guises and disguises of quadratic divergences
NASA Astrophysics Data System (ADS)
Cherchiglia, A. L.; Vieira, A. R.; Hiller, Brigitte; Baêta Scarpelli, A. P.; Sampaio, Marcos
2014-12-01
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale ?. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Quintessence with quadratic coupling to dark matter
Boehmer, Christian G.; Chan, Nyein [Department of Mathematics and Institute of Origins, University College London, London WC1E 6BT (United Kingdom); Caldera-Cabral, Gabriela [Department of Mathematics and Institute of Origins, University College London, London WC1E 6BT (United Kingdom); Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom); Lazkoz, Ruth [Fisika Teorikoa, Euskal Herriko Unibertsitatea, 48080 Bilbao (Spain); Maartens, Roy [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom)
2010-04-15
We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.
Dongping Liu; Günther Benstetter; Edgar Lodermeier
2003-01-01
Atomic force microscope (AFM), lateral force microscope and AFM-based scratch and wear testing techniques were used to evaluate and compare the surface roughness, tribological and mechanical properties of thin (2.7–43 nm) tetrahedral amorphous carbon coatings prepared by pulsed cathodic arc discharge. It was found that surface roughness of ultrathin (2–8 nm) coatings was mainly determined by the roughness of the
Boron Kedge XANES of boron oxides: tetrahedral B–O distances and near-surface alteration
M. E. Fleet; X. Liu
2001-01-01
Synchrotron radiation boron K-edge XANES spectra collected in fluorescence yield mode are reported for monoclinic metaboric\\u000a acid [HBO2(II)], sinhalite (MgAlBO4), and a selection of boron oxides in which B is exclusively in trigonal coordination ([3]B). The anomalously high divergence of tetrahedral ([4]B–O) bond lengths in HBO2(II) and sinhalite is used to resolve fine structure at the [4]B K edge due
N. W. Khun; E. Liu
2009-01-01
Nitrogen doped tetrahedral amorphous carbon (ta-C:N) thin films were deposited on p-Si (111) substrates (1×10?3 to 6×10?3?cm) by a filtered cathodic vacuum arc technique with different nitrogen flow rates (3 and 20sccm). The ta-C:N film coated samples were used as working electrodes to detect trace heavy metals such as zinc (Zn), lead (Pb), copper (Cu) and mercury (Hg) by using
A study of pH-dependence of shrink and stretch of tetrahedral DNA nanostructures
NASA Astrophysics Data System (ADS)
Wang, Ping; Xia, Zhiwei; Yan, Juan; Liu, Xunwei; Yao, Guangbao; Pei, Hao; Zuo, Xiaolei; Sun, Gang; He, Dannong
2015-04-01
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.
A 3-D time-dependent unstructured tetrahedral-mesh SP{sub N} method
Morel, J.E.; McGhee, J.M. [Los Alamos National Lab., NM (United States); Larsen, E.W. [Michigan Univ., Ann Arbor, MI (United States). Dept. of Nuclear Engineering
1994-10-01
We have developed a 3-D time-dependent multigroup SP{sub n} method for unstructured tetrahedral meshes. The SP{sub n} equations are expressed in a canonical form which allows them to be solved using standard diffusion solution techniques in conjunction with source iteration, diffusion-synthetic acceleration, and fission-source acceleration. A computational comparison of our SP{sub n} method with an even-parity S{sub n} method is given.
P. Lemoine; J. P. Quinn; P. Maguire; J. A. McLaughlin
2004-01-01
We compared nanoindentation and nanoscratch testing of 10 and 50nm thick tetrahedral amorphous carbon (ta-C) and hydrogenated amorphous carbon (a-C:H). Raman spectroscopy shows the expected spectral features for the two carbon forms, however, luminescence from the ceramic substrate can alter the spectra. We find that hard ta-C films can blunt the diamond tip and hence use a tip area function
Mixed finite element formulation in large deformation frictional contact problem
Paris-Sud XI, Université de
Mixed finite element formulation in large deformation frictional contact problem Laurent Baillet using the 2D finite element code PLAST21 . The first contact algorithm is the classical node and compared for linear and quadratic elements. KEY WORDS: contact, mixed finite element, friction, dynamic
A novel ultrasensitive electrochemical DNA sensor based on double tetrahedral nanostructures.
Zeng, Dongdong; Zhang, Huan; Zhu, Dan; Li, Jiang; San, Lili; Wang, Zehua; Wang, Chenguang; Wang, Yunsheng; Wang, Lihua; Zuo, Xiaolei; Mi, Xianqiang
2015-09-15
Electrochemical DNA (E-DNA) sensor is an important tool for detecting DNA biomarker. In this work, we have demonstrated a novel strategy of E-DNA sensor based on DNA tetrahedral nanostructures for the sensitive detection of target DNA. In our design, thiol and biotin modified DNA tetrahedral nanostructures were used as capture and report probes respectively. The biotin-tagged three dimensional DNA tetrahedral nanostructures were employed for efficient signal amplification by capturing multiple catalytic enzymes. Such improved E-DNA sensor can sensitively detect DNA target as low as 1fM with excellent differentiation ability for even single mismatch. And a mean recovery rate of 90.57% in DNA solution extracted from human serum was obtained. We have also compared this new method of attaching catalytic enzymes with the other two typical methods: One is through biotinylated single-stranded DNA (SSDNA) and the other is through gold nanoparticles (GNPs). Results indicated that the RTSPs-based enzyme amplification system showed much better performance than the other two systems. PMID:25950940
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.
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.
NASA Astrophysics Data System (ADS)
Zhang, X. M.; Xu, G. Z.; Liu, E. K.; Liu, Z. Y.; Wang, W. H.; Wu, G. H.
2015-01-01
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 that a proper strength of tetrahedral covalent-hybridization is probably in favor to realizing the topologically insulating state with band inversion occurring at the ? point of the Brillouin zone.
D. Boulanger; R. Parrot
1987-01-01
A molecular orbital model has been elaborated to determine the orbit–lattice coupling coefficients to strains of symmetry E of the orbital triplet states of d5 ions in tetrahedral symmetry. The wave functions and energies of the monoelectronic molecular orbitals have been determined for a tetrahedral molecule MnX4 in a crystal and for a slightly distorted molecule of symmetry D2d corresponding
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.
Diagonalization of Quadratic Forms by Gauss Elimination
Charles S. Beightler; Douglass J. Wilde
1966-01-01
The La Grange linear similarity transformation (completing the square) can be used to remove all cross-product terms from a quadratic form. It is shown that the La Grange transformation may be found conveniently by adapting the well-known Gauss elimination procedure for solving linear equations. A simple algorithm for finding the inverse transformation is given. This diagonalization scheme takes much less
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…
Process setup adjustment with quadratic loss
DAN TRIETSCH
2000-01-01
A classic adjustment method, the harmonic adjustment rule, minimizes expected quadratic loss where adjustments are easy and cheap, and the items produced during the adjustment process should be as close to target as possible. This paper generalizes the harmonic adjustment rule by explicitly taking into account measurement and adjustment costs. The generalizationis static, in that adjustments are performed at predetermined
Process setup adjustment with quadratic loss
Dan Trietsch
2000-01-01
A classic adjustment method, the harmonic adjustment rule, minimizes expected quadratic loss where adjustments are easy and cheap, and the items produced during the adjustment process should be as close to target as possible. This paper generalizes the harmonic adjustment rule by explicitly taking into account measurement and adjustment costs. The generalization is static, in that adjustments are performed at
A Repository of Convex Quadratic Programming Problems
Istvan Maros; Csaba Meszaros
1997-01-01
The introduction of a standard set of linear programming problems, to be found in NETLIB\\/LP\\/DATA, had an important impact on measuring, comparing and re- porting the performance of LP solvers .Until recently the eciency of new algorith- mic developments has been measured using this important reference set .Presently, we are witnessing an ever growing interest in the area of quadratic
Multiplicative Updates for Nonnegative Quadratic Programming
Fei Sha; Yuanqing Lin; Lawrence K. Saul; Daniel D. Lee
2007-01-01
Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this paper, we study convex problems in quadratic program- ming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the
Class numbers of complex quadratic fields
Ezra Brown
1974-01-01
Congruence conditions on the class numbers of complex quadratic fields have recently been studied by various investigators, including Barrucand and Cohn, Hasse, and the author. In this paper, we study the class number of Q([radical sign] - pq), where p [reverse not equivalent] q (mod 4) are distinct primes.
MINIMAL CANONICAL DIMENSIONS OF QUADRATIC FORMS
11 11. Fifth canonical dimension 12 References 14 Date: September 2013. Key words and phrasesMINIMAL CANONICAL DIMENSIONS OF QUADRATIC FORMS NIKITA A. KARPENKO Abstract. Canonical dimension of a smooth complete connected variety is the minimal dimension of image of its rational endomorphism. The i
MINIMAL CANONICAL DIMENSIONS OF QUADRATIC FORMS
Karpenko, Nikita - Institut de MathÃ©matiques de Jussieu, UniversitÃ© Paris 7
11 11. Fifth canonical dimension 13 12. Final comments 15 References 16 Date: September 2013. RevisedMINIMAL CANONICAL DIMENSIONS OF QUADRATIC FORMS NIKITA A. KARPENKO Abstract. Canonical dimension of a smooth complete connected variety is the minimal dimension of image of its rational endomorphism. The i
Theory of the Quadratic Zeeman Effect
L. I. Schiff; H. Snyder
1939-01-01
The experiments of Jenkins and Segrè, reported in the accompanying paper, are considered theoretically. The quadratic Zeeman effect observed in absorption to large orbits in strong magnetic fields is due to the diamagnetic term in the Hamiltonian, which is proportional to the square of the vector potential and hence to the square of the magnetic field. For the alkalis, the
Block Ciphers and Systems of Quadratic Equations
Alex Biryukov; Christophe De Cannière
2003-01-01
In this paper we compare systems of multivariate poly- nomials, which completely define the block ciphers Khazad, Misty1, Kasumi, Camellia, Rijndael and Serpent in the view of a potential danger of an algebraic re-linearization attack. Keywords: Block ciphers, multivariate quadratic equations, lineariza- tion, Khazad, Misty, Camellia, Rijndael, Serpent.
A Practical Approach to Quadratic Equations.
ERIC Educational Resources Information Center
Light, Peter
1983-01-01
The usual methods for solving quadratic equations are noted to require either the use of numerical formula or curve plotting on graph paper. The method described here enables pupils to solve equations using only a 45 degree setsquare, graph paper, and a pencil for those which have both real roots and real coefficients. (Author/MP)
On quadratic integral equation of fractional orders
Mohamed Abdalla Darwish
2005-01-01
We present an existence theorem for a nonlinear quadratic integral equations of fractional orders, arising in the queuing theory and biology, in the Banach space of real functions defined and continuous on a bounded and closed interval. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tool in carrying out our proof.
Quadratic equations and monodromy evolving deformations
Yousuke Ohyama
2007-09-28
We give a basic theory on monodromy evolving deformations. proposed by Chakravarty and Ablowitz in 1996. We show that Halphen's second quadratic system can be described by monodromy evolving deformations. Our result is a generalization of the work on the DH-V system by Chakravarty and Ablowitz.
Solving Underdefined Systems of Multivariate Quadratic Equations
Nicolas Courtois; Louis Goubin; Willi Meier; Jean-daniel Tacier
2002-01-01
The security of several recent digital signature schemes is based on the difficulty of solving large systems of quadratic multivariate polynomial equations over a finite field F. This problem, sometimes called MQ, is known to be NP-hard. When the number m of equations is equal to the number n of variables, and if n< 15, Grobner base algorithms have been
Width of homoclinic zone for quadratic maps
Vassili Gelfreich; Vincent Naudot
2008-01-01
We study several families of planar quadratic diffeomorphisms near a Bogdanov-Takens bifurcation. For each family, the associate bifurcation diagram can be deduced from the interpolating flow. However, a zone of chaos confined between two lines of homoclinic bifurcation that are exponentially close to one-another is observed. The goal of this paper is to test numerically an accurate asymptotic expansion for
Energy definition for quadratic curvature gravities
Ahmet Baykal
2012-12-03
A conserved current for generic quadratic curvature gravitational models is defined, and it is shown that, at the linearized level, it corresponds to the Deser-Tekin charges. An explicit expression for the charge for new massive gravity in three dimensions is given. Some implications of the linearized equations are discussed.
Directed modified Cholesky factorizations and convex quadratic ...
2014-07-03
Jul 3, 2014 ... the quadratic coefficient matrix is positive definite but nearly singular. For the new .... Partition the permuted interval matrix Ak as: Ak = ( ?k. aT ak. Bk. ) ..... particular the column diagpert shows the average diagonal perturbation med i. (max k. (D ... Integer Global Optimization of Nonlinear Equations. Journal of ...
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.
Pak, Chongin; Kamali, Saeed; Pham, Joyce; Lee, Kathleen; Greenfield, Joshua T; Kovnir, Kirill
2013-12-26
Fragments of the superconducting FeSe layer, FeSe2 tetrahedral chains, were stabilized in the crystal structure of a new mixed-valent compound Fe3Se4(en)2 (en = ethylenediamine) synthesized from elemental Fe and Se. The FeSe2 chains are separated from each other by means of Fe(en)2 linkers. Mössbauer spectroscopy and magnetometry reveal strong magnetic interactions within the FeSe2 chains which result in antiferromagnetic ordering below 170 K. According to DFT calculations, anisotropic transport and magnetic properties are expected for Fe3Se4(en)2. This compound offers a unique way to manipulate the properties of the Fe-Se infinite fragments by varying the topology and charge of the Fe-amino linkers. PMID:24299423
Pak, Chongin; Kamali, Saeed; Pham, Joyce; Lee, Kathleen; Greenfield, Joshua T.; Kovnir, Kirill
2014-01-01
Fragments of the superconducting FeSe layer, FeSe2 tetrahedral chains, were stabilized in the crystal structure of a new mixed-valent compound Fe3Se4(en)2 (en = ethylenediamine) synthesized from elemental Fe and Se. The FeSe2 chains are separated from each other by means of Fe(en)2 linkers. Mössbauer spectroscopy and magnetometry reveal strong magnetic interactions within the FeSe2 chains which result in antiferromagnetic ordering below 170 K. According to DFT calculations, anisotropic transport and magnetic properties are expected for Fe3Se4(en)2. This compound offers a unique way to manipulate the properties of the Fe-Se infinite fragments by varying the topology and charge of the Fe-amino linkers. PMID:24299423
NASA Astrophysics Data System (ADS)
Gerlach, C. A.; Johnson, G. R.
2009-12-01
This article presents an algorithm to automatically convert distorted hexahedral elements into meshless particles during dynamic deformation. With this approach the initial mesh is composed only of elements, and the particles are generated only as needed when the elements become highly distorted. This allows the mildly distorted regions of the problem to be accurately and efficiently represented with finite elements, and the highly distorted regions to be robustly represented with meshless particles. This algorithm is an extension of a previous algorithm that converts distorted tetrahedral elements into particles. The algorithm for hexahedral elements is more complex because the faces of these elements are not planar, as they are for tetrahedral elements. Examples of high-velocity impact are included to demonstrate the capabilities of this algorithm.
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)
A quadratic assignment formulation of the molecular conformation problem
A. T. Phillips; J. B. Rosen
1994-01-01
The molecular conformation problem is discussed, and a concave quadratic global minimization approach for solving it is described. This approach is based on a quadratic assignment formulation of a discrete approximation to the original problem.
Anonymous IBE from Quadratic Residuosity with Improved Performance
Anonymous IBE from Quadratic Residuosity with Improved Performance Michael Clear , Hitesh Tewari Based Encryption, Anonymous IBE, Cocks Scheme, Quadratic Residuosity Abstract. Identity Based Encryption. Cocks constructed the first such scheme, and subsequent improvements have been made to achieve anonymity
Deflating Quadratic Matrix Polynomials with Structure Preserving Transformations
Tisseur, Francoise
polynomials, both theoretically and numerically, is to convert them into equivalent linear matrix pencilsDeflating Quadratic Matrix Polynomials with Structure Preserving Transformations Francoise Tisseur ISSN 1749-9097 #12;Deflating Quadratic Matrix Polynomials with Structure Preserving Transformations
Fundamental Frequency Determination of Stiffened Plates Using Sequential Quadratic Programming
NASA Astrophysics Data System (ADS)
Bedair, O. K.
1997-01-01
A novel approach for the determination of the fundamental frequency of stiffened plates is presented. As a first stage, the governing differential equations for the structure are derived. Then, an energy formulation is presented in which the structure is idealized as assembled plate and stiffener elements, rigidly connected at their junctions. The non-linear strain energy function of the assembled structure is then transformed into an unconstrained optimization problem and Sequential Quadratic Programming (SQP) is used to determine the magnitudes of the lowest natural frequency and the associated mode shape. Using the described algorithm, results are presented showing the variation of the natural frequency with plate/stiffener geometric parameters for various concentric and eccentric stiffening configurations.
Antonio S. de Castro
2003-11-10
The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schroedinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.
Economic Dispatch with Network Security Constraints Using Parametric Quadratic Programming
K. Aoki; T. Satoh
1982-01-01
This paper presents an efficient method to solve an economic load dispatch problem with dc load flow type network security constraints. The conventional linear programming and quadratic programming methods cannot deal with transmission losses as a quadratic form of generator outputs. In order to overcome this defect, the extension of the quadratic programming method is proposed, which is designated as
On isotropy of quadratic spaces in finite and infinite dimension
on the right hand side of the equation, which then readily establishes the fact that quadratic and bilinearOn isotropy of quadratic spaces in finite and infinite dimension Karim Johannes Becher, Detlev Hoffmann Abstract Herbert Gross asked whether there exist fields admitting anisotropic quadratic spaces
Linear and quadratic time-frequency signal representations
F. Hlawatsch; G. F. Boudreaux-Bartels
1992-01-01
A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems
Class Groups and Quadratic Diophantine R.A. Mollin
Mollin, R.A.
Class Groups and Quadratic Diophantine Equations R.A. Mollin Abstract First, we consider of the underlying real quadratic orders. This is a generalized Eisenstein criterion in the sense that the equation x words and phrases: Quadratic Diophantine equations, Continued Fractions, Central Norms, Class group
A Quadratic Gradient Equation for pricing Mortgage-Backed Securities
Monneau, Régis
A Quadratic Gradient Equation for pricing Mortgage-Backed Securities Marco Papi Institute for Applied Computing - CNR Rome (Italy) A Quadratic Gradient Equation for pricing Mortgage-Backed Securities call option on a corresponding fixed-rate bond. A Quadratic Gradient Equation for pricing Mortgage
HOW DO YOU SOLVE A QUADRATIC EQUATION? GEORGE E._ FORSYTHE
Jiang, Shidong
cs40 HOW DO YOU SOLVE A QUADRATIC EQUATION? BY GEORGE E._ FORSYTHE TECHNICAL REPORT NO. CS40 JUNE;1 \\- c. `L L t HOW DO YOU SOLVE A QUADRATIC EQUATION? bY George E. Forsythe Abstract The nature-point computation are illustrated by the formula for solving a quadratic equation. An accurate way of solving
QUADRATIC SYSTEMS OF CONSERVATION LAWS WITH GENERIC BEHAVIOR AT INFINITY
Canic, Suncica
QUADRATIC SYSTEMS OF CONSERVATION LAWS WITH GENERIC BEHAVIOR AT INFINITY SUN Å¸ CICA Å¸ CANI ' C Abstract. We identify quadratic systems of conservation laws with ``generic'' behavior at infinity, where properties at infinity that are true for an open and dense subset of the set of all planar quadratic vector
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.
Divisibility of class numbers of imaginary quadratic function fields by a fixed odd number
Banerjee, Pradipto
2011-01-01
In this paper we find a new lower bound on the number of imaginary quadratic extensions of the function field $\\mathbb{F}_{q}(x)$ whose class groups have elements of a fixed odd order. More precisely, for $q$, a power of an odd prime, and $g$ a fixed odd positive integer $\\ge 3$, we show that for every $\\epsilon >0$, there are $\\gg q^{L(1/2+\\frac{3}{2(g+1)}-\\epsilon)}$ polynomials $f \\in \\mathbb{F}_{q}[x]$ with $\\deg f=L$, for which the class group of the quadratic extension $\\mathbb{F}_{q}(x, \\sqrt{f})$ has an element of order $g$. This sharpens the previous lower bound $q^{L(1/2+\\frac{1}{g})}$ of Ram Murty. Our result is a function field analogue to a similar result of Soundararajan for number fields.
NSDL National Science Digital Library
Kris A. Warloe
2008-01-01
In this math lesson, each learner constructs a tetrahedron and describes the linear dimensions, area and volume using non?traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron, whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.
NASA Technical Reports Server (NTRS)
Roberts, Michael L. (inventor)
1993-01-01
An apparatus and method is disclosed for decelerating and absorbing impact of a re-entry vehicle suitable for payloads that are relatively light as well as payloads weighing several tons or more. The apparatus includes four inflatable legs displaced equidistantly from each other around a capsule or housing which contains a payload. The legs are inflated at a designated altitude after entering earth's atmosphere to slow the descent of the re-entry vehicle. Connected between each of the four legs are drag inducing surfaces that deploy as the legs inflate. The drag inducing surfaces are triangularly shaped with one such surface being connected between each pair of legs for a total of six drag inducing surfaces. The legs have drag inducing outer surfaces which act to slow the descent of the re-entry vehicle.
Zhu, Hai; Chi, Quan; Zhao, Yanxi; Li, Chunya; Tang, Heqing; Li, Jinlin [Key Laboratory of Catalysis and Materials Science of the State Ethnic Affairs Commission and Ministry of Education, Hubei Province, College of Chemistry and Materials Science, South-Central University for Nationalities, Wuhan 430074 (China)] [Key Laboratory of Catalysis and Materials Science of the State Ethnic Affairs Commission and Ministry of Education, Hubei Province, College of Chemistry and Materials Science, South-Central University for Nationalities, Wuhan 430074 (China); Huang, Tao, E-mail: huangt6628@yahoo.com.cn [Key Laboratory of Catalysis and Materials Science of the State Ethnic Affairs Commission and Ministry of Education, Hubei Province, College of Chemistry and Materials Science, South-Central University for Nationalities, Wuhan 430074 (China)] [Key Laboratory of Catalysis and Materials Science of the State Ethnic Affairs Commission and Ministry of Education, Hubei Province, College of Chemistry and Materials Science, South-Central University for Nationalities, Wuhan 430074 (China); Liu, Hanfan [Key Laboratory of Catalysis and Materials Science of the State Ethnic Affairs Commission and Ministry of Education, Hubei Province, College of Chemistry and Materials Science, South-Central University for Nationalities, Wuhan 430074 (China) [Key Laboratory of Catalysis and Materials Science of the State Ethnic Affairs Commission and Ministry of Education, Hubei Province, College of Chemistry and Materials Science, South-Central University for Nationalities, Wuhan 430074 (China); Institute of Chemistry, Chinese Academy of Science, Beijing 100080 (China)
2012-11-15
Graphical abstract: By using CO as a reducing agent, uniform and well-defined concave tetrahedral Pd nanocrystals were successfully synthesized. CO flow rate was the most essential for the formation of the concave tetrahedral nanostructures. The morphologies and sizes of the final products can be well controlled by adjusting the flow rate of CO. Highlights: ? By using CO as a reducing agent, concave tetrahedral Pd nanocrystals were obtained. ? CO flow rate is critical to the formation of concave tetrahedral Pd nanocrystals. ? The selective adsorption of CO on (1 1 0) facets is essential to concave Pd tetrahedra. -- Abstract: CO reducing strategy to control the morphologies of palladium nanocrystals was investigated. By using CO as a reducing agent, uniform and well-defined concave tetrahedral Pd nanocrystals with a mean size of about 55 ± 2 nm were readily synthesized with Pd(acac){sub 2} as a precursor and PVP as a stabilizer. The structures of the as-prepared Pd nanocrystals were characterized by transmission electron microscopy (TEM), X-ray powder diffraction (XRD), ultraviolet–visible (UV–vis) absorption spectroscopy and electrochemical measurements. The results demonstrated that CO was the most essential for the formation of the concave tetrahedral Pd nanostructures. The morphologies and sizes of the final products can be well controlled by adjusting the flow rate of CO. The most appropriate CO flow rate, temperature and time for the formation of the ideal concave tetrahedral Pd nanocrystals was 0.033 mL s{sup ?1}, 100 °C and 3 h, respectively.
Regular models with quadratic equation of state
S. D. Maharaj; P. Mafa Takisa
2013-01-08
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein-Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.
Stellar objects in the quadratic regime
P. Mafa Takisa; S. D. Maharaj; Subharthi Ray
2014-12-28
We model a charged anisotropic relativistic star with a quadratic equation of state. Physical features of an exact solution of the Einstein-Maxwell system are studied by incorporating the effect of the nonlinear term from the equation of state. It is possible to regain the masses, radii and central densities for a linear equation of state in our analysis. We generate masses for stellar compact objects and perform a detailed study of PSR J1614-2230 in particular. We also show the influence of the nonlinear equation of state on physical features of the matter distribution. We demonstrate that it is possible to incorporate the effects of charge, anisotropy and a quadratic term in the equation of state in modelling a compact relativistic body.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-01-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-12-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
Coherent States of Systems with Quadratic Hamiltonians
NASA Astrophysics Data System (ADS)
Bagrov, V. G.; Gitman, D. M.; Pereira, A. S.
2015-06-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schrödinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency.
Linear and quadratic programming neural network analysis.
Maa, C Y; Shanblatt, M A
1992-01-01
Neural networks for linear and quadratic programming are analyzed. The network proposed by M.P. Kennedy and L.O. Chua (IEEE Trans. Circuits Syst., vol.35, pp.554-562, May 1988) is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems, such as the least-squares problem. For quadratic programming, the network converges either to an equilibrium or to an exact solution, depending on whether the problem has constraints or not. The results also suggest an analytical approach to solve the linear system Bx =b without calculating the matrix inverse. The results are directly applicable to optimization problems with C(2) convex objective functions and linear constraints. The dynamics and applicability of the networks are demonstrated by simulation. The distance between the equilibria of the networks and the problem solutions can be controlled by the appropriate choice of a network parameter. PMID:18276458
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.
Inversion of configuration of tetrahedral BIS(4-(iminomethyl)pyrazole-5-thiolato(selenolato) nickels
Nivorozhkin, A.L.; Konstantinovskii, L.E.; Korobov, M.S.; Minkin, V.I.
1985-10-10
This paper records the process of the interconversion of enantiomeric tetrahedral structures by the dynamic-NMR method for inner-complex compounds with a chelate entity of NiN/sub 2/X/sub 2/ (X = S, Se), namely systematic series of bis(4-(iminomethyl)pyrazole-5-thiolato(selenolato) )nickels. The values of the activation barriers to interconversion are determined by the steric structure of the substituents on the coordinated nitrogen tom and increase with rise in the steric hindrance in the planar form of the complexes, which indicates that the reaction goes by the diagonal-twist mechanism.
Ryltsev, R E
2013-01-01
The local order units of dense simple liquid are typically close packed clusters (hcp, fcc and icosahedrons). We show that the fluid demonstrates the tetrahedral local order up to temperatures several orders of magnitude higher than the melting temperature and down to critical density. While the solid-like local order (hcp, fcc) disappears in the fluid at much lower temperatures and far above critical density. We find that the structure relaxation times in the supercritical fluid are much larger than ones estimated for weakly interactive gas even far above the melting line.
Tian, Jian; Motkuri, Radha K.; Thallapally, Praveen K.; McGrail, B. Peter
2010-10-19
Solvothermal assembly of a semi-rigid tetrahedral carboxylate ligand tetrakis[4-(carboxyphenyl)oxamethyl]methane acid (H4X) with Cd(II) ion in different solvent systems yields three novel metal-organic framework isomers (1-3) based on different secondary building units (SBUs). Although all three frameworks have the same dia (diamondoid) topology, complex 1 and 3 are chiral and complex 2 is achiral. One of the networks, 3 shows cross-linked three-fold interpenetration of the single dia net and exhibits permanent porosities, as confirmed by BET and selective CO2 adsorption.
QUADRATIC RECIPROCITY VIA LINEAR ALGEBRA 1. Introduction ...
2005-03-12
Gauss sum and derive from this, the law of quadratic reciprocity. 1. ... be 1 if p is a square modulo q and ?1 otherwise. The law of ... system of equations xn?j = xj, 1 ? j ? n ? 1. For n odd, we find ... case using (2.1), we solve the system a + b = (n + 1)/2, a ? b = ±1 and deduce .... a complete set of residue classes modulo mn.
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.
Numerical analysis of a quadratic matrix equation
NICHOLAS J. HIGHAM; HYUN-MIN KIM
1999-01-01
The quadratic matrix equation AX2+BX +C = 0 in n \\\\Theta n matrices arises inapplications and is of intrinsic interest as one of the simplest nonlinear matrix equations.We give a complete characterization of solutions in terms of the generalizedSchur decomposition and describe and compare various numerical solution techniques.In particular, we give a thorough treatment of functional iteration methodsbased on Bernoulli's
An alternative method on quadratic programming problems
NASA Astrophysics Data System (ADS)
Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.
2015-05-01
In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.
Ever-expanding, Isotropizing, Quadratic Cosmologies
Spiros Cotsakis; George Flessas; Peter Leach; Laurent Querella
2000-11-06
We consider some aspects of the global evolution problem of Hamiltonian homogeneous, anisotropic cosmologies derived from a purely quadratic action functional of the scalar curvature. We show that models can isotropize in the positive asymptotic direction and that quadratic diagonal Bianchi IX models do not recollapse and may be regular initially. Although the global existence and isotropization results we prove hold quite generally, they are applied to specific Bianchi models in an attempt to describe how certain dynamical properties uncommon to the general relativity case, become generic features of these quadratic universes. The question of integrability of the models is also considered. Our results point to the fact that the more general models are not integrable in the sense of Painlev\\'e and for the Bianchi IX case this may be connected to the validity of a BKL oscillatory picture on approach to the singularity in sharp contrast with other higher order gravity theories that contain an Einstein term and show a monotonic evolution towards the initial singularity.
Constrained quadratic correlation filters for target detection.
Muise, Robert; Mahalanobis, Abhijit; Mohapatra, Ram; Li, Xin; Han, Deguang; Mikhael, Wasfy
2004-01-10
A method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery is presented. The QCFs are quadratic classifiers that operate directly on the image data without 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 for detection of peaks in the outputs of multiple linear filters but choosing the most suitable among them is an error-prone task. All channels in a QCF work together to optimize the same performance metric and to produce a combined output that leads to considerable simplification of the postprocessing scheme. The QCFs that are developed involve hard constraints on the output of the filter. Inasmuch as this design methodology is indicative of the synthetic discriminant function (SDF) approach for linear filters, the filters that we develop here are referred to as quadratic SDFs (QSDFs). Two methods for designing QSDFs are presented, an efficient architecture for achieving them is discussed, and results from the Moving and Stationary Target Acquisition and Recognition synthetic aperture radar data set are presented. PMID:14735950
Zhang, Zhi-Qian
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 ...
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/, 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.
Direct observation by X-ray analysis of the tetrahedral "intermediate" of aspartic proteinases.
Veerapandian, B; Cooper, J B; Sali, A; Blundell, T L; Rosati, R L; Dominy, B W; Damon, D B; Hoover, D J
1992-03-01
We report the X-ray analysis at 2.0 A resolution for crystals of the aspartic proteinase endothiapepsin (EC 3.4.23.6) complexed with a potent difluorostatone-containing tripeptide renin inhibitor (CP-81,282). The scissile bond surrogate, an electrophilic ketone, is hydrated in the complex. The pro-(R) (statine-like) hydroxyl of the tetrahedral carbonyl hydrate is hydrogen-bonded to both active-site aspartates 32 and 215 in the position occupied by a water in the native enzyme. The second hydroxyl oxygen of the hydrate is hydrogen-bonded only to the outer oxygen of Asp 32. These experimental data provide a basis for a model of the tetrahedral intermediate in aspartic proteinase-mediated cleavage of the amide bond. This indicates a mechanism in which Asp 32 is the proton donor and Asp 215 carboxylate polarizes a bound water for nucleophilic attack. The mechanism involves a carboxylate (Asp 32) that is stabilized by extensive hydrogen bonding, rather than an oxyanion derivative of the peptide as in serine proteinase catalysis. PMID:1304340
Hong Luo; Yidong Xia; Robert Nourgaliev; Chunpei Cai
2011-06-01
A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.
Verification of the three-dimensional tetrahedral grid S{sub N} code THOR
Schunert, S. [Department of Nuclear Engineering, North Carolina State University (United States); Ferrer, R. [Studsvik Scandpower, Idaho Falls, ID (United States); Azmy, Y. [Department of Nuclear Engineering, North Carolina State University (United States)
2013-07-01
In this work current capabilities implemented in the novel, arbitrary-order, tetrahedral-grid short characteristics S{sub N} radiation transport code THOR are verified based on four benchmark problems: (1) A one-group Method of Manufactured Solution (MMS) problem on a cuboidal domain, (2) an infinite medium eigenvalue problem with up-scattering, (3) a homogeneous torus and (4) a bare cube eigenvalue problem with anisotropic scattering up to order three. The first benchmark problem exercises the various spatial discretization options available in THOR: The short characteristics method in conjunction with polynomial expansions of the source and face fluxes either using the complete or Lagrange family of arbitrary orders. Using the numerical solution's order of convergence test in the framework of a mesh refinement study, correct implementation of a selection of spatial expansion orders is demonstrated for two meshes with tetrahedral aspect ratios close to unity and 50. The second benchmark problem exercises the implementation of angular fluxes on reflective boundary faces that are implicit within a mesh sweep, and up-scattering. The third benchmark problem comprises cyclic dependencies within the mesh sweep thus exercising the algorithm devised for 'breaking' the cyclic dependencies. Finally, the fourth benchmark problem, a simple bare cube, is used to test correct implementation of the anisotropic scattering capability. For all test problems THOR obtains solutions that converge to the reference/exact solution with the expected rate thereby contributing to our confidence in the correctness of its tested features in the present implementation. (authors)
C. P. Herrero; M. Gregorkiewitz; J. Sanz; J. M. Serratosa
1987-01-01
29Si MAS-NMR spectra were obtained for vermiculite with tetrahedral composition x=Al\\/(Al+Si)=0.28, a synthetic mica with x=0.43, and margarite with x=0.5. Comparison between the observed and Monte-Carlo simulated spectra was used to test different Al-Si distribution schemes in the tetrahedral sheet. The results of this analysis are interpreted including earlier data corresponding to lower Al for Si substitutions (0.12=x=0.28), and it
Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis
2005-12-01
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.
Asymptotically safe inflation from quadratic gravity
Bonanno, Alfio
2015-01-01
Asymptotically Safe theories of gravity have recently received much attention. In this work we discuss a class of inflationary models derived from quantum-gravity modification of quadratic gravity according to the induced scaling around the non-Gaussian fixed point at very high energies. It is argued that the presence of a three dimensional ultraviolet critical surface generates operators of non-integer power of the type $R^{2-\\theta/2}$ in the effective Lagrangian, where $\\theta>0$ is a critical exponent. The requirement of a successful inflationary model in agreement with the recent Planck 2015 data puts important constraints on the strenght of this new type of couplings.
Quadratic Equation over Associative D-Algebra
Aleks Kleyn
2015-05-30
In this paper, I treat quadratic equation over associative $D$-algebra. In quaternion algebra $H$, the equation $x^2=a$ has either $2$ roots, or infinitely many roots. Since $a\\in R$, $aequation has infinitely many roots. Otherwise, the equation has roots $x_1$, $x_2$, $x_2=-x_1$. I considered different forms of the Viete's theorem and a possibility to apply the method of completing the square. Assumed the hypothesis that, in noncommutative algebra, the equation $$(x-b)(x-a)+(x-a)(x-c)=0$$ $b\
LARGE TIME SOLUTION FOR QUADRATIC SCHRODINGER EQUATIONS IN HANTAEK BAE
Yorke, James
LARGE TIME SOLUTION FOR QUADRATIC SCHR¨ODINGER EQUATIONS IN 2D AND 3D HANTAEK BAE Abstract. The aim of this paper is to establish the large time well-posedness of the quadratic Schr¨odinger equation in 2D and 3D for the solvability of (1.1), see [5]. In this paper, we consider the Schr¨odinger equation with quadratic
Runge-Kutta methods for quadratic ordinary differential equations
Arieh Iserles; Geetha Ramaswami; Mark Sofroniou
1998-01-01
Many systems of ordinary differential equations are quadratic: the derivative can be expressed as a quadratic function of\\u000a the dependent variable. We demonstrate that this feature can be exploited in the numerical solution by Runge-Kutta methods,\\u000a since the quadratic structure serves to decrease the number of order conditions. We discuss issues related to construction\\u000a design and implementation and present a
A quadratic pulse height analyzer for space applications.
NASA Technical Reports Server (NTRS)
Burtis, D. W.; Aalami, D.; Evelyn-Veere, R. H.; Sarkady, A. A.
1972-01-01
A flight-worthy pulse height analyzer that has a quadratic transfer function is described. This quadratic function permits optimum usage of the entire PHA dynamic range due to the quadratic nature of the gamma ray spectrometer's resolution vs energy. After the theoretical design discussion, the implementation of the design is examined and test results described. The analyzer is part of the University of New Hampshire gamma ray monitor for OSO-H.
V. V. Kozlov
2005-01-01
We discuss the symplectic geometry of linear Hamiltonian systems with nondegenerate Hamiltonians. These systems can be reduced to linear second-order differential equations characteristic of linear oscillation theory. This reduction is related to the problem on the signatures of restrictions of quadratic forms to Lagrangian planes. We study vortex symplectic planes invariant with respect to linear Hamiltonian systems. These planes are
Economic dispatch with network security constraints using parametric quadratic programming
Aoki, K.; Satoh, T.
1982-12-01
This paper presents an efficient method to solve an economic load dispatch problem with dc load flow type network security constraints. The conventional linear programming and quadratic programming methods cannot deal with transmission losses as a quadratic form of generator outputs. In order to overcome this defect, the extension of the quadratic programming method is proposed, which is designated as the parametric quadratic programming method. The upper bounding technique and the relaxation method are coupled with the proposed method for the purpose of computational efficiency. The test results show that the proposed method is practical for real-time applications.
Li, Gonghu; Dimitrijevic, Nada M; Chen, Le; Nichols, Jamie M; Rajh, Tijana; Gray, Kimberly A
2008-04-23
Highly photoactive, tetrahedral Ti4+ sites can be created, other than in zeolite cavities and on silica substrate, in mixed-phase TiO2 nanocomposites. The tetrahedral Ti4+ species was shown to be an intermediate formed during the thermally driven phase transformation from anatase to rutile. PMID:18370389
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 ?-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.
Theoretical study of the O? interaction with a tetrahedral Al? cluster.
Bacalis, N C; Metropoulos, A; Gross, A
2010-11-01
Employing both multireference configuration interaction (MRCI) and density functional theory (DFT) methods, we have studied the interaction of O? with a tetrahedral Al? cluster in the total spin triplet state. For a parallel to the base approach of O? facing an apex of the pyramid, the O? adsorption is hindered by a barrier. Both the MRCI and the DFT calculations show that after a small barrier, there are two local energy minima: a shallow one just above the apex atom and another deeper one below the apex atom. The latter corresponds to dissociative O? adsorption. We discuss the implications of these findings for the understanding of O? adsorption on defect sites of Al surfaces. PMID:20942497
Electrochemical switching with 3D DNA tetrahedral nanostructures self-assembled at gold electrodes.
Abi, Alireza; Lin, Meihua; Pei, Hao; Fan, Chunhai; Ferapontova, Elena E; Zuo, Xiaolei
2014-06-11
Nanomechanical switching of functional three-dimensional (3D) DNA nanostructures is crucial for nanobiotechnological applications such as nanorobotics or self-regulating sensor and actuator devices. Here, DNA tetrahedral nanostructures self-assembled onto gold electrodes were shown to undergo the electronically addressable nanoswitching due to their mechanical reconfiguration upon external chemical stimuli. That enables construction of robust surface-tethered electronic nanodevices based on 3D DNA tetrahedra. One edge of the tetrahedron contained a partially self-complementary region with a stem-loop hairpin structure, reconfigurable upon hybridization to a complementary DNA (stimulus DNA) sequence. A non-intercalative ferrocene (Fc) redox label was attached to the reconfigurable tetrahedron edge in such a way that reconfiguration of this edge changed the distance between the electrode and Fc. PMID:24802004
Near-field supersonic flow predictions by an adaptive unstructured tetrahedral grid solver
NASA Technical Reports Server (NTRS)
Djomehri, M. J.; Erickson, Larry L.
1993-01-01
Applicability of a three-dimensional solution adaptive unstructured tetrahedral Euler flow solver about generic models for near-field sonic boom pressure signature predictions is evaluated. Comparisons of computational and experimental data demonstrates the capability of the method for predicting inviscid solutions useful for high speed calculations about simple 3-D geometries. The approach has promising features and results indicate potential for application to more complex configurations. The mesh generation is based on the advancing front technique, and steady state solutions of the Euler equations are achieved by explicit time integration. Spatial discretization uses the Taylor-Galerkin approach; an alternate time integration, based on the Runge-Kutta method, is also included. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry-adaptive grid procedure has also been incorporated.
The electronic transport mechanism in amorphous tetrahedrally-coordinated carbon films
Sullivan, J.P.; Friedmann, T.A.; Dunn, R.G.; Stechel, E.B.; Schultz, P.A.
1998-02-01
The electronic transport mechanism in tetrahedrally coordinated amorphous carbon was investigated using measurements of stress relaxation, thermal evolution of electrical conductivity, and temperature dependent conductivity measurements. Stress relaxation measurements were used to determine the change in 3-fold coordinated carbon concentration, and the electrical conductivity was correlated to this change. It was found that the conductivity was exponentially proportional to the change in 3-fold concentration, indicating a tunneling or hopping transport mechanism. It was also found that the activation energy for transport decreased with increasing anneal temperature. The decrease in activation energy was responsible for the observed increase in electrical conductivity. A model is described wherein the transport in this material is described by thermally activated conduction along 3-fold linkages or chains with variable range and variable orientation hopping. Thermal annealing leads to chain ripening and a reduction in the activation energy for transport.
Giles, M.B. [Oxford Univ. Computing Lab. (United Kingdom)] [Oxford Univ. Computing Lab. (United Kingdom)
1997-04-01
This paper presents a timestep stability analysis for a class of discretisations applied to the linearised form of the Navier-Stokes equations on a 3D domain with periodic boundary conditions. Using a suitable definition of the {open_quotes}perturbation energy{close_quotes} it is shown that the energy is monotonically decreasing for both the original p.d.e. and the semi-discrete system of o.d.e.`s arising from a Galerkin discretisation on a tetrahedral grid. Using recent theoretical results concerning algebraic and generalised stability, sufficient stability limits are obtained for both global and local timesteps for fully discrete algorithms using Runge-Kutta time integration. 18 refs., 2 figs., 1 tab.
Electric dipole moments in {sup 230,232}U and implications for tetrahedral shapes
Ntshangase, S. S. [Department of Physics, University of Cape Town, Rondebosch 7700 (South Africa); iThemba LABS, P.O. Box 722, Somerset West 7129 (South Africa); Bark, R. A.; Datta, P.; Lawrie, E. A.; Lawrie, J. J.; Lieder, R. M.; Mullins, S. M. [iThemba LABS, P.O. Box 722, Somerset West 7129 (South Africa); Aschman, D. G.; Mohammed, H.; Stankiewicz, M. A. [Department of Physics, University of Cape Town, Rondebosch 7700 (South Africa); Bvumbi, S.; Masiteng, P. L.; Shirinda, O. [iThemba LABS, P.O. Box 722, Somerset West 7129 (South Africa); Department of Physics, University of the Western Cape, Bellville ZA-7535 (South Africa); Davidson, P. M.; Nieminen, P.; Wilson, A. N. [Department of Nuclear Physics, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200 (Australia); Dinoko, T. S.; Sharpey-Shafer, J. F. [Department of Physics, University of the Western Cape, Bellville ZA-7535 (South Africa); Elbasher, M. E. A. [iThemba LABS, P.O. Box 722, Somerset West 7129 (South Africa); Department of Physics, University of Stellenbosch, 7601 Matieland (South Africa); Juhasz, K. [Department of Information Technology, University of Debrecen, Egyetem ter 1, H-4032 Debrecen (Hungary)
2010-10-15
The nuclei {sup 230}U and {sup 232}U were populated in the compound nucleus reactions {sup 232}Th({alpha},6n) and {sup 232}Th({alpha},4n), respectively. Gamma rays from these nuclei were observed in coincidence with a recoil detector. A comprehensive set of in-band E2 transitions were observed in the lowest lying negative-parity band of {sup 232}U while one E2 transition was also observed for {sup 230}U. These allowed B(E1;I{sup -{yields}}I{sup +}-1)/B(E2;I{sup -{yields}}I{sup -}-2) ratios to be extracted and compared with systematics. The values are similar to those of their Th and Ra isotones. The possibility of a tetrahedral shape for the negative-parity U bands appears difficult to reconcile with the measured Q{sub 2} values for the isotone {sup 226}Ra.
R. E. Ryltsev; N. M. Chtchelkatchev
2013-09-28
The local order units of dense simple liquid are typically three dimensional (close packed) clusters: hcp, fcc and icosahedrons. We show that the fluid demonstrates the superstable tetrahedral local order up to temperatures several orders of magnitude higher than the melting temperature and down to critical density. While the solid-like local order (hcp, fcc) disappears in the fluid at much lower temperatures and far above critical density. We conclude that the supercritical fluid shows the temperature (density) driven two stage "melting" of the three dimensional local order. We also find that the structure relaxation times in the supercritical fluid are much larger than ones estimated for weakly interactive gas even far above the melting line.
Chiral discrimination for a system of tetrahedral molecules on a triangular lattice
NASA Astrophysics Data System (ADS)
Medved', I.; Huckaby, D. A.; Trník, A.; Milas, I.
2015-06-01
A tetrahedral molecule consisting of a central atom attached to four different groups exists as two non-superimposable mirror images (enantiomers). We consider a model system of such molecules adsorbed on a triangular lattice and containing an equimolar mixture of each enantiomer. By rewriting the Hamitonian in more than one way, we can obtain an m-potential in the two regions of parameter space within which the ground state configurations are finitely degenerate. We apply the rigorous Pirogov–Sinai theory to prove that at low temperatures the system in one of these regions will undergo enantiomeric phase separation into two homochiral phases, each containing a single enantiomer, and in the other region will form a racemic phase in which the two enantiomers form alternating rows in the crystal.
Liu, Fanxin; Tang, Chaojun; Zhan, Peng; Chen, Zhuo; Ma, Hongtao; Wang, Zhenlin
2014-01-01
We have demonstrated the plasmonic characteristics of an ultrathin tetrahedral amorphous carbon (ta-C) film coated with Ag nanoparticles. The simulation result shows that, under resonant and non-resonant excitations, the strongest plasmonic electric field of 1?nm ta-C coated Ag nanoparticle is not trapped within the ta-C layer but is released to its outside surface, while leaving the weaker electric field inside ta-C layer. Moreover, this outside plasmonic field shows higher intensity than that of uncoated Ag nanoparticle, which is closely dependent on the excitation wavelength and size of Ag particles. These observations are supported by the SERS measurements. We expect that the ability for ultrathin ta-C coated Ag nanoparticles as the SERS substrates to detect low concentrations of target biomolecules opens the door to the applications where it can be used as a detection tool for integrated, on-chip devices. PMID:24675437
An S{sub n} Spatial Discretization Scheme for Tetrahedral Meshes
Morel, Jim E.; Warsa, James S. [Los Alamos National Laboratory (United States)
2005-10-15
A lumped, linear discontinuous spatial discretization for S{sub n} calculations on tetrahedral meshes is described. This method is designed for applications such as thermal radiative transfer, where resistance to negative solutions and good performance in the thick diffusion limit are essential. The method described has very desirable properties in both the transport regime and the diffusion limit. In particular, the method has enhanced damping of negativities via lumping, second-order accuracy in the transport regime, and a second-order accurate symmetric positive-definite diffusion discretization in the thick diffusion limit that yields well-behaved solutions with unresolved spatial boundary layers. While it is often thought that inaccuracies result when high-aspect-ratio tetrahedra are used to resolve boundary layers, accurate solutions can in fact be computed using high-aspect-ratio tetrahedra if the shape and orientation of the tetrahedra are properly restricted in the boundary layer.
Single walled carbon nanotube network—Tetrahedral amorphous carbon composite film
NASA Astrophysics Data System (ADS)
Iyer, Ajai; Kaskela, Antti; Johansson, Leena-Sisko; Liu, Xuwen; Kauppinen, Esko I.; Koskinen, Jari
2015-06-01
Single walled carbon nanotube network (SWCNTN) was coated by tetrahedral amorphous carbon (ta-C) using a pulsed Filtered Cathodic Vacuum Arc system to form a SWCNTN—ta-C composite film. The effects of SWCNTN areal coverage density and ta-C coating thickness on the composite film properties were investigated. X-Ray photoelectron spectroscopy measurements prove the presence of high quality sp3 bonded ta-C coating on the SWCNTN. Raman spectroscopy suggests that the single wall carbon nanotubes (SWCNTs) forming the network survived encapsulation in the ta-C coating. Nano-mechanical testing suggests that the ta-C coated SWCNTN has superior wear performance compared to uncoated SWCNTN.
X-ray topography of a natural twinned diamond of unusual pseudo-tetrahedral morphology
NASA Astrophysics Data System (ADS)
Fritsch, Emmanuel; Moore, Moreton; Rondeau, Benjamin; Waggett, Richard G.
2005-06-01
The internal morphology of a natural twinned diamond was investigated using X-ray section topography. The diamond consisted of two crystals joined along a {1 1 1} plane whose remote ends were triangular {1 1 1} faces with sizes approximately 4 mm on the edge. A coating of fibrous growth obscured the morphology of the good quality diamond inside. Although the coat displayed re-entrant surfaces near the twin plane along three edges of the crystal, X-ray topography showed the inner crystal to protrude outwards along these same edges. The good quality inner core displayed the classical "spinel law" twinned octahedral morphology whereas the fibrous rim showed a typical sphalerite-like twinned tetrahedral morphology. A possible growth mechanism which could account for this is discussed.
Dynamic response of the pelvis under side impact load – a three-dimensional finite element approach
S. Majumder; A. Roychowdhury; S. Pal
2004-01-01
The pelvis is most susceptible to severe fractures in side impacts, arising from motor vehicle crashes. In recent years, car manufacturers are providing more importance to the protection of occupants in lateral impacts. This study was aimed to understand the dynamic response of the pelvis and establish its fracture threshold, using a three-dimensional finite element model, with 13,070 tetrahedral (trabecular
Discontinuous Finite Element S{sub N} Methods on 3-D Unstructured Grids
Wareing, T.A.; McGhee, J.M.; Morel, J.E.; Pautz, S.D.
1999-09-27
Discontinuous finite element methods for the S{sub N} equations on 3-D unstructured tetrahedral and hexahedral meshes are presented. Solution Techniques including Source Iteration and diffusion-synthetic acceleration are described. Numerical results are presented which demonstrate the accuracy and efficiency of these methods.
Bond-energy force-constant relationship for bent XY2, pyramidal XY3 and tetrahedral XY4 molecules
G. Thyagarajan; C. R. Sarma; M. K. Subhedar
1969-01-01
A relation between the force constants and bond energies of polyatomic molecules of bent XY2, pyramidal XY3, and tetrahedral XY4 types has been deduced by employing an approximately separable potential function for the molecules and using specific functional forms for the bonded and nonbonded interactions. To test the validity of the relation deduced, bond energies were calculated from the available
ERIC Educational Resources Information Center
Filgueiras, Carlos A. L.; Carazza, Fernando
1980-01-01
Discusses procedures, theoretical considerations, and results of an experiment involving the preparation of a tetrahedral nickel(II) complex and its transformation into an octahedral species. Suggests that fundamental aspects of coordination chemistry can be demonstrated by simple experiments performed in introductory level courses. (Author/JN)
Generation of 2D and 3D (PtS, Adamantanoid) Nets with a Flexible Tetrahedral Building Block
Tian, Jian; Motkuri, Radha K.; Thallapally, Praveen K.
2010-09-01
The self-assembly of a flexible tetrahedral linker tetrakis[4-(carboxyphenyl)oxamethyl]methane acid with various transition metals (Cu, Co and Mg) results in a 2D layered structure and 3D frameworks with PtS and adamantanoid topology. The PtS net exhibits permanent porosity as confirmed by BET and gas adsorption experiments.
Ren, Dong-Hong; Qiu, Dan; Pang, Chun-Yan; Li, Zaijun; Gu, Zhi-Guo
2015-01-14
A new class of chiral tetrahedral iron(II) cages were prepared from subcomponent self-assembly with high diastereoselectivity. The cages can be interconverted through imine exchange. The chiral cages displayed a spin transition close to room temperature, and the transition temperatures were affected by the substituent and uncoordinated solvents. PMID:25426503
Rolling element bearing diagnosis using convex hull
Sara Lioba Volpi; Marco Cococcioni; Beatrice Lazzerini; Dan Stefanescu
2010-01-01
In this paper, we compare traditional classifiers, such as Linear and Quadratic Discriminant Classifiers and neural networks, with a one-class classifier, namely, convex hull. With reference to rolling element bearing diagnosis, we show that convex hull outperforms traditional classifiers in the classification of faults and different levels of fault severity not known during the training phase.
Quadratic diophantine equations and orders in quaternion algebras
Goro Shimura
2006-01-01
We first reformulate the main theorem on quadratic Diophantine equations given in our recent book in terms of the even Clifford group. In the quaternary case the group is the multiplicative group of a quaternion algebra, and the reformulated theorem connects a class of primitive solutions of a quadratic equation with a class of an order in the algebra. In
Collisions between type II two-dimensional quadratic solitons.
Costantini, B; De Angelis, C; Barthelemy, A; Bourliaguet, B; Kermene, V
1998-03-15
We report experimental and numerical results that describe collisions between two-dimensional type II quadratic solitons excited in a KTP crystal by fundamental waves of orthogonal polarization. Our results provide experimental evidence of the possibility of both inelastic collision (when two quadratic solitons merge at input into a single soliton at output) and quasi-elastic collision. PMID:18084532
ELLIPTICAL RANGE THEOREMS FOR GENERALIZED NUMERICAL RANGES OF QUADRATIC OPERATORS
Li, Chi-Kwong
ELLIPTICAL RANGE THEOREMS FOR GENERALIZED NUMERICAL RANGES OF QUADRATIC OPERATORS CHI-KWONG LI, YIU-TUNG POON, AND NUNG-SING SZE Abstract. The classical numerical range of a quadratic operator is an elliptical disk. This result is extended to different kinds of generalized numerical ranges. In particular
June 23, 2005 THE QUADRATIC EQUATION AS SOLVED BY PERSIAN
Osler, Thomas
1 June 23, 2005 THE QUADRATIC EQUATION AS SOLVED BY PERSIAN MATHEMATICANS OF THE MIDDLE AGES mathematicians. We will look at the solution of the quadratic as viewed by two Persian mathematicians Al in Sanskrit, Pahlavi, `the classical language of Persia', Syriac and Greek [4]. Khwarazmi's most famous
THE PARALLELIZED POLLARD KANGAROO METHOD IN REAL QUADRATIC FUNCTION FIELDS
Bernstein, Daniel
THE PARALLELIZED POLLARD KANGAROO METHOD IN REAL QUADRATIC FUNCTION FIELDS ANDREAS STEIN AND EDLYN TESKE Abstract. We show how to use the parallelized kangaroo method for computing invariants in real quadratic function #12;elds. Speci#12;cally, we show how to apply the kangaroo method to the infrastructure
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…
The explicit linear quadratic regulator for constrained systems
Alberto Bemporad; Manfred Morari; Vivek Dua; Efstratios N. Pistikopoulos
2002-01-01
We present a technique to compute the explicit state-feedback solution to both the xnite and inxnite horizon linear quadratic optimal control problem subject to state and input constraints. We show that this closed form solution is piecewise linear and continuous. As a practical consequence of the result, constrained linear quadratic regulation becomes attractive also for systems with high sampling rates,
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…
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.)
Problems in Presenting Quadratics as a Unifying Topic.
ERIC Educational Resources Information Center
MacDonald, Theodore H.
1986-01-01
A sequence for teaching quadratic equations is presented. Considered are: multiplying arithmetic binomials, multiplying algebraic polynomials, reversing the process, missing terms, perfect squares, other special forms and diagrams, quadratic equations, completing the square, systematizing the process, the general form, graphing equations, and…
Improved perturbation bounds for general quadratic matrix equations
M. M. Konstantinov; P. Hr. Petkov; D. W. Gu
1999-01-01
Perturbation analysis of general algebraic quadratic matrix equations is presented, which include as particular cases the standard and descriptor algebraic matrix Riccati equations, arising in the optimal control and filtering of continuous, time-invariant, linear systems. The perturbation bounds derived are superior to the bounds, already available in the literature. They are applicable to the error analysis of general quadratic matrix
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…
Complex digital signal processing using quadratic residue number systems
R. Krishnan; G. Jullien; W. Miller
1985-01-01
Recently, the Quadratic Residue Number System (QRNS) has been introduced [4,5,6], which allows the multiplication of complex integers with two real multiplications. Restrictions on the form of the moduli can be removed if an increase in real multiplications from two to three can be tolerated; the resulting number system has been termed the Modified Quadratic Residue Number System (MQRNS). In
Semidefinite Relaxations for Non-Convex Quadratic Mixed-Integer ...
2011-11-08
Most algorithms and software tools for quadratic mixed-integer optimization ... closest vector problem (domains Z), and quadratic minimization with box con- .... The point to be separated is a pair (x0i,xii) from a positive semidefinite matrix X. By ...
Linear stability analysis of dynamical quadratic gravity
NASA Astrophysics Data System (ADS)
Ayzenberg, Dimitry; Yagi, Kent; Yunes, Nicolás
2014-02-01
We study the linear stability of dynamical, quadratic gravity, focusing on two particular subclasses (the even-parity sector, exemplified by Einstein-Dilaton-Gauss-Bonnet gravity, and the odd-parity sector, exemplified by dynamical Chern-Simons modified gravity) in the high-frequency, geometric optics approximation. This analysis is carried out by studying gravitational and scalar modes propagating on spherically symmetric and axially symmetric, vacuum solutions of the theory and finding the associated dispersion relations. These relations are solved in two separate cases (the scalar regime and the gravitational wave regime, defined by requiring the ratio of the amplitude of the perturbations to be much greater or smaller than unity) and found in both cases to not lead to exponential growth of the propagating modes, suggesting linearly stability. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.
Compact stars with quadratic equation of state
NASA Astrophysics Data System (ADS)
Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi
2015-05-01
We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.
Digital image restoration using quadratic programming.
Abdelmalek, N N; Kasvand, T
1980-10-01
The problem of digital image restoration is considered by obtaining an approximate solution to the Fredholm integral equation of the first kind in two variables. The system of linear equations resulting from the discretization of the integral equation is converted to a consistent system of linear equations. The problem is then solved as a quadratic programming problem with bounded variables where the unknown solution is minimized in the L(2) norm. In this method minimum computer storage is needed, and the repeated solutions are obtained in an efficient way. Also the rank of the consistent system which gives a best or near best solution is estimated. Computer simulated examples using spatially separable pointspread functions are presented. Comments and conclusion are given. PMID:20234627
Multiplicative updates for nonnegative quadratic programming.
Sha, Fei; Lin, Yuanqing; Saul, Lawrence K; Lee, Daniel D
2007-08-01
Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this article, we study convex problems in quadratic programming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the global minimum. The updates have a simple closed form and do not involve any heuristics or free parameters that must be tuned to ensure convergence. Despite their simplicity, they differ strikingly in form from other multiplicative updates used in machine learning. We provide complete proofs of convergence for these updates and describe their application to problems in signal processing and pattern recognition. PMID:17571937
Large-scale sequential quadratic programming algorithms
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
Quadratic algebras for three-dimensional superintegrable systems
Daskaloyannis, C., E-mail: daskalo@math.auth.gr; Tanoudis, Y. [Aristotle University of Thessaloniki, Mathematics Department (Greece)
2010-02-15
The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.
Ikenaga, Bruce
of a quadratic equation. It depends on a procedure called completing the square. Here's the idea. Suppose you can for the variable-stuff by taking the square root of both sides. Example. Solve the equation for x. (a) x2 - 49 = 0 and x = 3. Suppose you start out with a quadratic equation where you don't have a perfect square on one
Wirosoetisno, Djoko
Quadratic Forms Elliptic Curves Modular Forms Elliptic Curves vs. Modular Forms Langlands My stuff. Modular Forms Langlands My stuff Some very classical number theory Number of ways a number N can. Modular Forms Langlands My stuff Three quadratic forms(1) P(x, y, u, v) P(x, y, u, v) = x2 + xy + 3y2 + u2
Francesca Aicardi
2008-03-27
The continue fractions of quadratic surds are periodic, according to a theorem by Lagrange. Their periods may have differing types of symmetries. This work relates these types of symmetries to the symmetries of the classes of the corresponding indefinite quadratic forms. This allows to classify the periods of quadratic surds and at the same time to find, for an arbitrary indefinite quadratic form, the symmetry type of its class and the number of integer points, for that class, contained in each domain of the Poincare' model of the de Sitter world, introduced in Part I. Moreover, we obtain the same information for every class of forms representing zero, by the finite continue fraction related to a special representative of that class. We will see finally the relation between the reduction procedure for indefinite quadratic forms, defined by the continued fractions, and the classical reduction theory, which acquires a geometrical description by the results of Part I.
Aicardi, Francesca
2007-01-01
The continue fractions of quadratic surds are periodic, according to a theorem by Lagrange. Their periods may have differing types of symmetries. This work relates these types of symmetries to the symmetries of the classes of the corresponding indefinite quadratic forms. This allows to classify the periods of quadratic surds and at the same time to find, for an arbitrary indefinite quadratic form, the symmetry type of its class and the number of integer points, for that class, contained in each domain of the Poincare' model of the de Sitter world, introduced in Part I. Moreover, we obtain the same information for every class of forms representing zero, by the finite continue fraction related to a special representative of that class. We will see finally the relation between the reduction procedure for indefinite quadratic forms, defined by the continued fractions, and the classical reduction theory, which acquires a geometrical description by the results of Part I.
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.
Models for the 3D singular isotropic oscillator quadratic algebra
Kalnins, E. G., E-mail: math0236@waikato.ac.n [University of Waikato, Department of Mathematics (New Zealand); Miller, W.; Post, S. [University of Minnesota, School of Mathematics (United States)
2010-02-15
We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential-differential or differential-difference and difference-difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.
Quadratic integer programming for large scale banded matrices
NASA Technical Reports Server (NTRS)
Yan, T. Y.; Tan, H. H.
1982-01-01
This paper is concerned with the integer quadratic program where the variables are constrained to belong to a given set of discrete values. This quadratic integer program is shown to be equivalent to a problem of finding the shortest path in a particular directed graph called a trellis when the matrix is a positive-definite symmetric banded matrix. An efficient procedure for solving this shortest path problem is presented which allows the solution of the integer quadratic program. This method is particularly effective when the half-bandwidth of the matrix is significantly smaller than its dimension.
Quantitative measure of tetrahedral-sp3 geometries in amorphous phase-change alloys
NASA Astrophysics Data System (ADS)
Micoulaut, M.; Gunasekera, K.; Ravindren, S.; Boolchand, P.
2014-09-01
Phase change or Ovonic memory technology has gained much interest in the past decade as a viable solution for the rapid increase in the demand for memory storage. This unique technology, first proposed by S. Ovshinsky in 1968, is based on storing information on the crystalline and amorphous phases of a material. The most common phase-change materials (PCMs) use chalcogenide alloys such as the Ge2Sb2Te5 (GST225). However, while the structure of its crystalline phase is relatively well characterized as consisting of a rhombohedrally distorted rock-salt lattice, the corresponding amorphous phase remains still poorly understood. Here, we show that Sn119 Mössbauer spectroscopy and angular constraint counting of simulated structures can provide a quantitative measure of the sp3 tetrahedral fraction of Ge or Si cation in amorphous phase-change binary tellurides GexTe1-x and SixTe1-x. This represents the first quantitative estimate of such local structures, and reveals the fraction to be nearly 50%, while also revealing implications for the phase-change mechanism itself.
Electrical behaviour of metal/tetrahedral amorphous carbon/metal structure
NASA Astrophysics Data System (ADS)
Liu, E.; Shi, X.; Cheah, L. K.; Hu, Y. H.; Tan, H. S.; Shi, J. R.; Tay, B. K.
1999-02-01
Silicon and GaAs based devices are limited in their high-temperature applications as these materials lack high sensitivity to the temperature range above 200°C due to their small band gaps. Therefore, exploration of new materials with a high-temperature performance is necessary. Diamond-like carbon as a semiconducting material may be one of the promising candidates due to its many properties close to those of diamond. The main objective of this study is to investigate tetrahedral amorphous carbon (ta-C) film based metal-semiconductor-metal (MSM) structures targeted at high-temperature applications. The ta-C films were deposited in a filtered cathodic vacuum arc (FCVA) process. For the deposition of nitrogen-doped n-type ta-C films, N + ion beam was used to assist the doping process during deposition. Several metals of high purity, such as Cr, Ti, etc., were selected for this purpose. The high-temperature performance of MSM structures was evaluated by measuring their I- V characteristics at different temperatures up to 300°C. Al/ n-ta-C/Al structure likely shows clear Schottky behaviour among the selected metals, while Ti/ n-ta-C/Ti and Cr/ n-ta-C/Cr show typical ohmic contact behaviour in the testing temperature range.
NASA Technical Reports Server (NTRS)
Birnbaum, G.; Borysow, A.; Buechele, A.
1993-01-01
The far infrared absorption of a CH4-N2 mixture was measured at 297, 195, and 162 K from 30 to 650/cm. The spectral invariants gamma1 and alpha1, proportional, respectively, to the zeroth and first spectral moments, due to bimolecular collisions between CH4 and N2 were obtained from these data and compared with theoretical values. The theory for collision-induced dipoles between a tetrahedral and a diatomic or symmetrical linear molecule includes contributions not previously considered. Whereas the theoretical values of gamma1 are only somewhat greater than experiment at all temperatures, the theoretical values of alpha1 are significantly lower than the experimental values. From the theoretical spectral moments for the various induced dipole components, the parameters of the BC shape were computed, and theoretical spectra were constructed. Good agreement was obtained at the lower frequencies, but with increasing frequencies the theoretical spectra were increasingly less intense than the experimental spectra. Although the accuracy of the theoretical results may suffer from the lack of a reliable potential function, it does not appear that this high frequency discrepancy can be removed by any conceivable modification in the potential.
Prehna,G.; Stebbins, E.
2007-01-01
The Rho family of small GTPases represent well characterized signaling molecules that regulate many cellular functions such as actin cytoskeletal arrangement and the cell cycle by acting as molecular switches. A Rac1-GDP-Zn complex has been crystallized in space group P3{sub 2}21 and its crystal structure has been solved at 1.9 {angstrom} resolution. These trigonal crystals reveal the unexpected ability of Rac1 to coordinate Zn atoms in a tetrahedral fashion by use of its biologically relevant switch I and switch II regions. Upon coordination of zinc, the switch I region is stabilized in the GDP-bound conformation and contributes to a Rac1 trimer in the asymmetric unit. Zinc coordination causes switch II to adopt a novel conformation with a symmetry-related molecule. Additionally, zinc was found to displace magnesium from its octahedral coordination at switch I, although GDP binding remained stable. This structure represents the first reported Rac1-GDP-Zn complex, which further underscores the conformational flexibility and versatility of the small GTPase switch regions.
Prehna, G.; Stebbins, C
2007-01-01
The Rho family of small GTPases represent well characterized signaling molecules that regulate many cellular functions such as actin cytoskeletal arrangement and the cell cycle by acting as molecular switches. A Rac1-GDP-Zn complex has been crystallized in space group P3221 and its crystal structure has been solved at 1.9 {angstrom} resolution. These trigonal crystals reveal the unexpected ability of Rac1 to coordinate Zn atoms in a tetrahedral fashion by use of its biologically relevant switch I and switch II regions. Upon coordination of zinc, the switch I region is stabilized in the GDP-bound conformation and contributes to a Rac1 trimer in the asymmetric unit. Zinc coordination causes switch II to adopt a novel conformation with a symmetry-related molecule. Additionally, zinc was found to displace magnesium from its octahedral coordination at switch I, although GDP binding remained stable. This structure represents the first reported Rac1-GDP-Zn complex, which further underscores the conformational flexibility and versatility of the small GTPase switch regions.
Zhang, Lijun; Du, Mao-Hua; Singh, David J.
2010-01-01
We report the investigation of Zintl-phase Na(K){sub 8}SnSb{sub 4} and related compounds that contain SnSb{sub 4} tetrahedral anions using first principles electronic structure, Boltzmann transport, and density functional phonon calculations. We find that these compounds are narrow-gap semiconductors and there is a combination of heavy and light bands at valence band edge, which may lead to a combination of high thermopower and reasonable conductivity. High values of the thermopower are found for p-type doping within the Boltzmann transport theory. Furthermore, these materials are expected to have low thermal conductivity due to their structures that consist of a network of weakly coupled SnSb{sub 4} clusters, which leads to low phonon frequencies. In particular, we find low-frequency optical phonons that should effectively scatter the heat-carrying acoustic phonons. These results are discussed in terms of the structure, which consists of anionic clusters. Based on the results, it is suggested that such compounds may represent a useful paradigm for finding new thermoelectric materials.
Argon Implantation in Tetrahedral Amorphous Carbon Deposited by Filtered Cathodic Vacuum Arc
NASA Astrophysics Data System (ADS)
Marques, F. C.; Viana, G. A.; Motta, E. F.; Silva, D. S.; Wisnivesky, D.; Côrtes, A. D. S.; Aguiar, M. R.
2013-05-01
The implantation of argon in tetrahedral amorphous carbon (ta-C), deposited by the filtered cathodic vacuum arc technique and concurrently bombarded with argon ions (Ar+), is investigated in this study. The ta-C films were prepared with a 5-ms DC-pulsed arc, a current of 190 A, and a frequency of 3 Hz, and they were deposited on a ground substrate holder. The argon atoms were implanted into the film by simultaneously bombarding the films with a beam of Ar+ in the 0-180 eV energy range. The concentration of argon, determined by Rutherford backscattering spectroscopy, was investigated as a function of the Ar+ energy. Raman scattering spectroscopy was used to investigate the structure of the films. The stress of the films depends on the Ar+ energy and reduces significantly as a function of the annealing temperature. A study of argon effusion, ranging from room temperature up to 1000 °C, shows that the argon atoms evolve from the films at different temperatures depending on the Ar+ energy. Scanning electron microscopy revealed the formation of bubbles after argon effusion. It was observed that the structural transformations that promote the relaxation of the carbon matrix and the argon effusion are different from each other.
Petrillo, Teodolinda; O'Donohoe, Catrina A; Howe, Nicole; Malthouse, J Paul G
2012-08-01
Two new inhibitors in which the terminal ?-carboxyl groups of Z-Ala-Ala-Phe-COOH and Z-Ala-Pro-Phe-COOH have been replaced with a proton to give Z-Ala-Ala-Phe-H and Z-Ala-Pro-Phe-H, respectively, have been synthesized. Using these inhibitors, we estimate that for ?-chymotrypsin and subtilisin Carlsberg the terminal carboxylate group decreases the level of inhibitor binding 3-4-fold while a glyoxal group increases the level of binding by 500-2000-fold. We show that at pH 7.2 the effective molarities of the catalytic hydroxyl group of the active site serine are 41000-229000 and 101000-159000 for ?-chymotrypsin and subtilisin Carlsberg, respectively. It is estimated that oxyanion stabilization and the increased effective molarity of the catalytic serine hydroxyl group can account for the catalytic efficiency of the reaction. We argue that substrate binding induces the formation of a strong hydrogen bond or low-barrier hydrogen bond between histidine-57 and aspartate-102 that increases the pK(a) of the active site histidine, allowing it to be an effective general base catalyst for the formation of the tetrahedral intermediate and increasing the effective molarity of the catalytic hydroxyl group of serine-195. A catalytic mechanism for acyl intermediate formation in the serine proteases is proposed. PMID:22757750
Chen, Yuanyuan; Farquhar, Erik R.; Chance, Mark R.; Palczewski, Krzysztof; Kiser, Philip D. (Case Western)
2012-07-11
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.
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
AEM investigation of tetrahedrally coordinated Ti{sup 4+} in nickel-titanate spinel
Anderson, I.M. [Oak Ridge National Lab., TN (United States)]|[Minnesota Univ., Minneapolis, MN (United States). Dept. of Chemical Engineering and Materials Science; Bentley, J. [Oak Ridge National Lab., TN (United States); Carter, C.B. [Minnesota Univ., Minneapolis, MN (United States). Dept. of Chemical Engineering and Materials Science
1994-12-31
Stoichiometry and site distribution of metastable nickel-titanate spinel was studied with AEM. Results of EDXS and EELS agree that the metastable spinel is nonstoichiometric and titanium-deficient relative to its hypothetical endmember composition, ``Ni{sub 2}TiO{sub 4}``. The titanium deficiency has been determined by EELS to be {Delta} = 0.025 {plus_minus} 0.005. Channeling-enhanced microanalysis and ELNES studies indicate that the Ti{sup 4+} and Ni{sup 2+} cations are in tetrahedral and octahedral coordination, respectively, so that the metastable spinel has the normal cation distribution: Ti{sub l-{Delta}}[Ni{sub 2(1+{Delta})}]O{sub 4}. This is consistent with neutron powder-diffraction studies and SiO{sub 2}-solubility measurements of similar equilibrated and quenched spinel-containing specimens. Metastable nickel-titanate spinel therefore contrasts with stable stoichiometric spinels which tend to the inverse cation distribution, Me[MeTi]O{sub 4}.
Hepburn, Iain; Cannon, Robert; De Schutter, Erik
2013-01-01
We describe a novel method for calculating the quasi-static electrical potential on tetrahedral meshes, which we call E-Field. The E-Field method is implemented in STEPS, which performs stochastic spatial reaction-diffusion computations in tetrahedral-based cellular geometry reconstructions. This provides a level of integration between electrical excitability and spatial molecular dynamics in realistic cellular morphology not previously achievable. Deterministic solutions are also possible. By performing the Rallpack tests we demonstrate the accuracy of the E-Field method. Efficient node ordering is an important practical consideration, and we find that a breadth-first search provides the best solutions, although principal axis ordering suffices for some geometries. We discuss potential applications and possible future directions, and predict that the E-Field implementation in STEPS will play an important role in the future of multiscale neural simulations. PMID:24194715
A Quadratic Closure for Compressible Turbulence
Futterman, J A
2008-09-16
We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.
Optimal power flow using sequential quadratic programming
NASA Astrophysics Data System (ADS)
Nejdawi, Imad M.
1999-11-01
Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.
Local classifier weighting by quadratic programming.
Cevikalp, Hakan; Polikar, Robi
2008-10-01
It has been widely accepted that the classification accuracy can be improved by combining outputs of multiple classifiers. However, how to combine multiple classifiers with various (potentially conflicting) decisions is still an open problem. A rich collection of classifier combination procedures -- many of which are heuristic in nature -- have been developed for this goal. In this brief, we describe a dynamic approach to combine classifiers that have expertise in different regions of the input space. To this end, we use local classifier accuracy estimates to weight classifier outputs. Specifically, we estimate local recognition accuracies of classifiers near a query sample by utilizing its nearest neighbors, and then use these estimates to find the best weights of classifiers to label the query. The problem is formulated as a convex quadratic optimization problem, which returns optimal nonnegative classifier weights with respect to the chosen objective function, and the weights ensure that locally most accurate classifiers are weighted more heavily for labeling the query sample. Experimental results on several data sets indicate that the proposed weighting scheme outperforms other popular classifier combination schemes, particularly on problems with complex decision boundaries. Hence, the results indicate that local classification-accuracy-based combination techniques are well suited for decision making when the classifiers are trained by focusing on different regions of the input space. PMID:18842488
Crystal field theory and EPR parameters in D2d and C2v distorted tetrahedral copper(II) complexes
Stanislaw K. Hoffmann; Janina Goslar
1982-01-01
Calculations of the orbital energy vs tetrahedral (D2d and C2v) distortion parameters are reported for copper complexes on the assumption of constant metal-ligand distance. The possible ground states of the complexes are considered and the respective spin Hamiltonian parameters vs distortion parameters dependences are calculated. Comparison with experiment led to good agreement: the relation between the orbital splittings and dihedral
Mohanty, Debasish [ORNL; Li, Jianlin [ORNL; Abraham, Daniel P [Argonne National Laboratory (ANL); Huq, Ashfia [ORNL; Payzant, E Andrew [ORNL; Wood III, David L [ORNL; Daniel, Claus [ORNL
2014-01-01
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 Li1.2Mn0.55Ni0.15Co0.1O2 LMR composite oxide. By employing neutron powder diffraction, and temperature dependent magnetic susceptibility, we show that LSL structural rearrangement in LMR oxide occurs through a tetrahedral cation intermediate via: i) diffusion of lithium atoms from octahedral to tetrahedral sites of the lithium layer [(LiLioct LiLitet] 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 [LiTM oct LiLitet]; 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 [MnTMoct MnLitet MnLioct)]. 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.
Gong K.; Vukmirovic M.B.; Ma C.; Zhu Y.; Adzic R.R.
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 hydrothermal 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.
Reactive-power dispatch by successive quadratic programming
Quintana, V.H. (Waterloo Univ., ON (Canada)); Santos-Nieto, M. (Energy Management Systems Div., Control Data Corp., Plymouth, MN (US))
1989-09-01
In this paper the reactive-power dispatch is formulated as the minimization of real-power losses in the system, utilizing a full set of control variables: generator voltages, switchable shunt susceptances and transformer taps. The solution of the loss problem is obtained by successively solving quadratic programming problems. First- and second-order loss sensitivity coefficients are derived for the quadratic problem formulation. The derivations are based on the Jacobian method for sensitivity calculations. Sensitivity relations for the dependent constraints are based on the complete reactive-power model of the fast decoupled load flow method. The active-set projection method for quadratic programming is described and utilized as the solution algorithm for the quadratic reactive-power dispatch problems. Tests are conducted on the IEEE 30-bus and Mexican 253-bus systems. A discussion of the computer results is also presented.
Adaptive continuous-time linear quadratic Gaussian control
Duncan, Tyrone E.; Guo, L.; Pasik-Duncan, Bozenna
1999-09-01
, where Q(1), determines the quadratic form for the state in the integrand of the cost functional, A weighted least squares algorithm is modified by using a random regularization to ensure that the family of estimated models is uniformly controllable...
Optimal scaling of the ADMM algorithm for distributed quadratic ...
2014-12-11
Dec 11, 2014 ... algorithm for a class of distributed quadratic programming problems. ... Numerical simulations justify our results and highlight the benefits of optimally .... the past iterates when computing the next. ...... E. Chu, B. Peleato, and J. Eckstein, “
An Effective Branch-and-Bound Algorithm for Convex Quadratic ...
Christoph Buchheim,,,
singular, so that E(Q ,x ) may be a degenerate ellipsoid. Moreover, for ? ? R+, ...... vectors, we use the Block Korkin-Zolotarev basis reduction algorithm [16] implemented in NTL [17]. ..... by ?? modulation: the case of circulant quadratic forms.
An efficiently solvable quadratic program for stabilizing dynamic locomotion
Kuindersma, Scott
We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while ...
Regular zeros of quadratic maps and their application
Arutyunov, Aram V; Karamzin, Dmitry Yu
2011-06-30
Sufficient conditions for the existence of regular zeros of quadratic maps are obtained. Their applications are indicated to certain problems of analysis related to the inverse function theorem in a neighbourhood of an abnormal point. Bibliography: 13 titles.
Geometric Procedures for Graphing the General Quadratic Equation.
ERIC Educational Resources Information Center
DeTemple, Duane W.
1984-01-01
How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)
Effects of classroom instruction on students’ understanding of quadratic equations
Pongchawee Vaiyavutjamai
2006-01-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand,\\u000a attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data\\u000a from the students’ written responses to the equations, together with data in the form of transcripts of 36 interviews with\\u000a 18
Scale-invariant rotating black holes in quadratic gravity
Cognola, Guido; Vanzo, Luciano
2015-01-01
Black hole solutions in pure quadratic theories of gravity are interesting since they allow to formulate a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
Quadratic fluctuation-dissipation theorem: The quantum domain
G. Kalman; Xiao-Yue Gu
1987-01-01
A derivation of a general relationship between the frequency- and wave-number-dependent longitudinal quadratic response functions and the three-point dynamical structure function (the Fourier transform of the equilibrium three-point density-density correlations) is presented. This relationship is the full quadratic equivalent, valid for quantum systems of arbitrary degeneracy, of the customary (linear) fluctuation-dissipation theorem. The high-temperature limit reproduces earlier classical results, while
Quadratic function approaching method for magnetotelluric soundingdata inversion
Liangjun, Yan; Wenbao, Hu; Zhang, Keni
2004-04-05
The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.
AdS waves as exact solutions to quadratic gravity
Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram [Department of Physics, Middle East Technical University, 06531 Ankara (Turkey); Guerses, Metin [Department of Mathematics, Faculty of Sciences Bilkent University, 06800 Ankara (Turkey)
2011-04-15
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.
On active-set methods for the quadratic programming problem
NASA Astrophysics Data System (ADS)
Daryina, A. N.; Izmailov, A. F.
2012-04-01
The active-set Newton method developed earlier by the authors for mixed complementarity problems is applied to solving the quadratic programming problem with a positive definite matrix of the objective function. A theoretical justification is given to the fact that the method is guaranteed to find the exact solution in a finite number of steps. Numerical results indicate that this approach is competitive with other available methods for quadratic programming problems.
Phase recovery based on quadratic programming
NASA Astrophysics Data System (ADS)
Zhang, Quan Bing; Ge, Xiao Juan; Cheng, Ya Dong; Ni, Na
2014-11-01
Most of the information of optical wavefront is encoded in the phase which includes more details of the object. Conventional optical measuring apparatus is relatively easy to record the intensity of light, but can not measure the phase of light directly. Thus it is important to recovery the phase from the intensity measurements of the object. In recent years, the methods based on quadratic programming such as PhaseLift and PhaseCut can recover the phase of general signal exactly for overdetermined system. To retrieve the phase of sparse signal, the Compressive Phase Retrieval (CPR) algorithm combines the l1-minimization in Compressive Sensing (CS) with low-rank matrix completion problem in PhaseLift, but the result is unsatisfied. This paper focus on the recovery of the phase of sparse signal and propose a new method called the Compressive Phase Cut Retrieval (CPCR) by combining the CPR algorithm with the PhaseCut algorithm. To ensure the sparsity of the recovered signal, we use CPR method to solve a semi-definite programming problem firstly. Then apply linear transformation to the recovered signal, and set the phase of the result as the initial value of the PhaseCut problem. We use TFOCS (a library of Matlab-files) to implement the proposed CPCR algorithm in order to improve the recovered results of the CPR algorithm. Experimental results show that the proposed method can improve the accuracy of the CPR algorithm, and overcome the shortcoming of the PhaseCut method that it can not recover the sparse signal effectively.
LECTURE NOTES ON LINEAR QUADRATIC CONTROL VERSION OF 02-07-2010
Bonnans, Frédéric
quadratic problems (i.e., with a lin- ear state equation and a quadratic cost). The first section starts with the discussion of critical points of quadratic functionals, the shooting equations, and the associated RiccatiLECTURE NOTES ON LINEAR QUADRATIC CONTROL VERSION OF 02-07-2010 J. FR´ED´ERIC BONNANS Contents 1
REGULATORS OF RANK ONE QUADRATIC TWISTS CHRISTOPHE DELAUNAY AND XAVIER-FRANCOIS ROBLOT
Paris-Sud XI, Université de
) quadratic twist of E is a quadratic twist such that the sign of the func- tional equation of its LREGULATORS OF RANK ONE QUADRATIC TWISTS CHRISTOPHE DELAUNAY AND XAVIER-FRANC¸OIS ROBLOT Abstract. We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists
hp calculators HP 50g Solving for roots of polynomials and quadratics
Vetter, Frederick J.
hp calculators HP 50g Solving for roots of polynomials and quadratics The Numeric Solver Practice finding roots of polynomials and quadratics #12;hp calculators HP 50g Solving for roots of polynomials and quadratics hp calculators - 2 - HP 50g Solving for roots of polynomials and quadratics The Numeric Solver
The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry
NASA Astrophysics Data System (ADS)
Noya, Eva G.; Vega, Carlos; Doye, Jonathan P. K.; Louis, Ard A.
2010-06-01
The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values of the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centered-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centered-cubic crystal becomes more stable than the body-centered-cubic crystal, and at higher temperatures, a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centered-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centered-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centered-cubic crystal and between the fluid and the diamond crystal show that at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles.
Simple shearing flow of dry soap foams with TCP structure[Tetrahedrally Close-Packed
REINELT,DOUGLAS A.; KRAYNIK,ANDREW M.
2000-02-16
The microrheology of dry soap foams subjected to large, quasistatic, simple shearing deformations is analyzed. Two different monodisperse foams with tetrahedrally close-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Laves (C15). The elastic-plastic response is evaluated by calculating foam structures that minimize total surface area at each value of strain. The minimal surfaces are computed with the Surface Evolver program developed by Brakke. The foam geometry and macroscopic stress are piecewise continuous functions of strain. The stress scales as T/V{sup 1/3} where T is surface tension and V is cell volume. Each discontinuity corresponds to large changes in foam geometry and topology that restore equilibrium to unstable configurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a small increase in strain changes the energy profile in the neighborhood of a foam structure from a local minimum to a saddle point, which can lead to symmetry-breaking bifurcations. In general, the new foam topology associated with each stable solution branch results from a cascade of local topology changes called T1 transitions. Each T1 cascade produces different cell neighbors, reduces surface energy, and provides an irreversible, film-level mechanism for plastic yield behavior. Stress-strain curves and average stresses are evaluated by examining foam orientations that admit strain-periodic behavior. For some orientations, the deformation cycle includes Kelvin cells instead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and can even cause strain localization.
Fonseca, Gabriel Paiva; Landry, Guillaume; White, Shane; D'Amours, Michel; Yoriyaz, Hélio; Beaulieu, Luc; Reniers, Brigitte; Verhaegen, Frank
2014-10-01
Accounting for brachytherapy applicator attenuation is part of the recommendations from the recent report of AAPM Task Group 186. To do so, model based dose calculation algorithms require accurate modelling of the applicator geometry. This can be non-trivial in the case of irregularly shaped applicators such as the Fletcher Williamson gynaecological applicator or balloon applicators with possibly irregular shapes employed in accelerated partial breast irradiation (APBI) performed using electronic brachytherapy sources (EBS). While many of these applicators can be modelled using constructive solid geometry (CSG), the latter may be difficult and time-consuming. Alternatively, these complex geometries can be modelled using tessellated geometries such as tetrahedral meshes (mesh geometries (MG)). Recent versions of Monte Carlo (MC) codes Geant4 and MCNP6 allow for the use of MG. The goal of this work was to model a series of applicators relevant to brachytherapy using MG. Applicators designed for (192)Ir sources and 50?kV EBS were studied; a shielded vaginal applicator, a shielded Fletcher Williamson applicator and an APBI balloon applicator. All applicators were modelled in Geant4 and MCNP6 using MG and CSG for dose calculations. CSG derived dose distributions were considered as reference and used to validate MG models by comparing dose distribution ratios. In general agreement within 1% for the dose calculations was observed for all applicators between MG and CSG and between codes when considering volumes inside the 25% isodose surface. When compared to CSG, MG required longer computation times by a factor of at least 2 for MC simulations using the same code. MCNP6 calculation times were more than ten times shorter than Geant4 in some cases. In conclusion we presented methods allowing for high fidelity modelling with results equivalent to CSG. To the best of our knowledge MG offers the most accurate representation of an irregular APBI balloon applicator. PMID:25210788
NASA Astrophysics Data System (ADS)
Paiva Fonseca, Gabriel; Landry, Guillaume; White, Shane; D'Amours, Michel; Yoriyaz, Hélio; Beaulieu, Luc; Reniers, Brigitte; Verhaegen, Frank
2014-10-01
Accounting for brachytherapy applicator attenuation is part of the recommendations from the recent report of AAPM Task Group 186. To do so, model based dose calculation algorithms require accurate modelling of the applicator geometry. This can be non-trivial in the case of irregularly shaped applicators such as the Fletcher Williamson gynaecological applicator or balloon applicators with possibly irregular shapes employed in accelerated partial breast irradiation (APBI) performed using electronic brachytherapy sources (EBS). While many of these applicators can be modelled using constructive solid geometry (CSG), the latter may be difficult and time-consuming. Alternatively, these complex geometries can be modelled using tessellated geometries such as tetrahedral meshes (mesh geometries (MG)). Recent versions of Monte Carlo (MC) codes Geant4 and MCNP6 allow for the use of MG. The goal of this work was to model a series of applicators relevant to brachytherapy using MG. Applicators designed for 192Ir sources and 50?kV EBS were studied; a shielded vaginal applicator, a shielded Fletcher Williamson applicator and an APBI balloon applicator. All applicators were modelled in Geant4 and MCNP6 using MG and CSG for dose calculations. CSG derived dose distributions were considered as reference and used to validate MG models by comparing dose distribution ratios. In general agreement within 1% for the dose calculations was observed for all applicators between MG and CSG and between codes when considering volumes inside the 25% isodose surface. When compared to CSG, MG required longer computation times by a factor of at least 2 for MC simulations using the same code. MCNP6 calculation times were more than ten times shorter than Geant4 in some cases. In conclusion we presented methods allowing for high fidelity modelling with results equivalent to CSG. To the best of our knowledge MG offers the most accurate representation of an irregular APBI balloon applicator.
The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry.
Noya, Eva G; Vega, Carlos; Doye, Jonathan P K; Louis, Ard A
2010-06-21
The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values of the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centered-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centered-cubic crystal becomes more stable than the body-centered-cubic crystal, and at higher temperatures, a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centered-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centered-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centered-cubic crystal and between the fluid and the diamond crystal show that at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles. PMID:20572725
The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry
Eva G. Noya; Carlos Vega; Jonathan P. K. Doye; Ard A. Louis
2010-05-28
The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values for the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centred-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centred-cubic crystal becomes more stable than the body-centred-cubic crystal, and at higher temperatures a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centred-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centred-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centred-cubic crystal and between the fluid and the diamond crystal show that, at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles.
element pair for shallow-water ocean modelling
Colin J. Cotter; David A. Ham; Christopher C. Pain
We introduce a mixed discontinuous\\/continuous nite element pair for ocean mod- elling, with continuous quadratic layer thickness and discontinuous velocity. We in- vestigate the nite element pair applied to the linear shallow-water equations on an f-plane. The element pair has the property that all geostrophically balanced states which strongly satisfy the boundary conditions have discrete divergence equal to exactly zero
NSDL National Science Digital Library
2006-02-27
This company's web site features an interactive periodic chart that provides information on the elements, including a description, physical and thermal properties, abundance, isotopes, ionization energy, the element's discoverer, translations of element names into several languages, and bibliographic information on research-and-development publications involving the element. Additional information includes technical information and information on manufactured products for elemental metals, metallic compounds, and ceramic and crystalline products. The American Elements company manufactures engineered and advanced material products.
Effects of classroom instruction on students' understanding of quadratic equations
NASA Astrophysics Data System (ADS)
Vaiyavutjamai, Pongchawee; Clements, M. A. (Ken)
2006-05-01
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 transcripts of 36 interviews with 18 interviewees (a high performer, a medium performer, and a low performer from each of the six classes), were analysed. Using a rubric for assessing students' understanding, the analysis revealed that at the post-teaching stage students improved their performance on quadratic equations and had a better understanding of associated concepts than they had at the pre-teaching stage. However, many were still confused about the concepts of a variable and of a "solution" to a quadratic equation. After the lessons, most students had acquired neither an instrumental nor a relational understanding of the mathematics associated with solving elementary quadratic equations.
NASA Astrophysics Data System (ADS)
Yoo, Kwangsun
In Part I, preparation of CdS and CdSe films on various electrode materials including nanoporous TiO2 and their photoresponses were demonstrated. Both electrochemical and chemical deposition methods successfully produced Cd-chalcogenide films and post-thermal treatment was done to develop respectable photoactivity. Chemical and photo-electrochemical etching were also performed to remove impurities and increase film stability. Transparency issues for a sandwich type of a solar cell based on semiconductor thin films on a TiO 2 porous nanostructure were examined by measuring transmittances of different wavelengths of laser light. Porous TiO2 films were made from both Degussa P25 TiO2 and Ti(IV) isopropoxide sol-gels. CdSe films on both TiO2 substrates showed comparable photospectra, but the sol-gel one is more transparent and shows better net response. In Part II, electrodes of conductive nitrogen-incorporated tetrahedral amorphous carbon films (taC:N) deposited at ambient temperatures were shown to possess an extraordinary combination of the stability associated with boron-doped diamonds, yet with much enhanced electrocatalytic properties. In this study on the electrochemistry of deposited thin films of taC:N, we showed that this material demonstrates more active charge transfer properties on a variety of systems relative to the H-terminated, highly boron-doped diamond (B-diamond). Stability was shown by chlorine evolution from HCl solution for >104 times the coulombs necessary for 4e/C-atom oxidation to CO2 of a 40 nm thick taC:N film without noticeable change of the voltammetry. Cu deposition and stripping on taC:N electrodes have revealed several distinctive features comparative to other electrodes. From stationary and rotating disk voltammograms, we observed a larger nucleation overpotential of Cu deposition on a taC:N electrode, and the extraordinary Cu stripping pattern, two peak or shoulder-peak, at the position about a higher (more positive) potential than normal bulk Cu stripping peak potential, in the region of the Cu(I)/Cu(II) process. RRDE evidence clearly showed a mixed process of oxidation of Cu(0) to Cu(I) or Cu(0) to Cu(II), and, especially, the presence of Cu(II) in the product stream.
Equi-ripple design of quadratic-phase RF pulses
NASA Astrophysics Data System (ADS)
Schulte, Rolf F.; Tsao, Jeffrey; Boesiger, Peter; Pruessmann, Klaas P.
2004-01-01
An improved strategy for the design of quadratic-phase RF pulses with high selectivity and broad bandwidths using the Shinnar-Le Roux (SLR) transformation is proposed. Unlike previous implementations, the required quadratic-phase finite impulse response (FIR) filters are generated using the complex Remez exchange algorithm, which ensures an equi-ripple deviation from the ideal response function. It is argued analytically that quadratic-phase pulses are near-optimal in terms of minimising the B1-amplitude for a given bandwidth and flip angle. Furthermore, several parameter relations are derived, providing practical design guidelines. The effectiveness of the proposed design method is demonstrated by examples of excitation and saturation pulses applied in vitro and in vivo.
A class of quadratic deformations of Lie superalgebras
Peter Jarvis; Gerd Rudolph; Luke Yates
2011-06-24
We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. We derive the equivalent of the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate in detail one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
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 algebra approach to relativistic quantum Smorodinsky-Winternitz systems
Marquette, Ian [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)
2011-04-15
There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.
The generalized quadratic knapsack problem. A neuronal network approach.
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. PMID:16488117
Quadratic $n$-ary Hom-Nambu algebras
Faouzi Ammar; Sami Mabrouk; Abdenacer Makhlouf
2011-10-10
The purpose of this paper is to introduce and study quadratic $n$-ary Hom-Nambu algebras, which are $n$-ary Hom-Nambu algebras with an invariant, nondegenerate and symmetric bilinear forms that are also $\\alpha$-symmetric and $\\beta$-invariant where $\\alpha$ and $\\beta$ are twisting maps. We provide constructions of these $n$-ary algebras by using twisting principles, tensor product and T*-extension. Also is discussed their connections with representation theory and centroids. Moreover we show that one may derive from quadratic $n$-ary Hom-Nambu algebra ones of increasingly higher arities and that under suitable assumptions it reduces to a quadratic $(n-1)$-ary Hom-Nambu algebra.
The bounds of feasible space on constrained nonconvex quadratic programming
NASA Astrophysics Data System (ADS)
Zhu, Jinghao
2008-03-01
This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.
Fermionic Meixner probability distributions, Lie algebras and quadratic Hamiltonians
L. Accardi; I. Ya. Aref'eva; I. V. Volovich
2014-11-17
We introduce the quadratic Fermi algebra, which is a Lie algebra, and show that the vacuum distributions of the associated Hamiltonians define the fermionic Meixner probability distributions. In order to emphasize the difference with the Bose case, we apply a modification of the method used in the above calculation to obtain a simple and straightforward classification of the 1--dimensional Meixner laws in terms of homogeneous quadratic expressions in the Bose creation and annihilation operators. There is a huge literature of the Meixner laws but this, purely quantum probabilistic, derivation seems to be new. Finally we briefly discuss the possible multi-dimensional extensions of the above results.
FRW in quadratic form of f( T) gravitational theories
NASA Astrophysics Data System (ADS)
Nashed, G. L.
2015-07-01
We derive asymptote solution of a homogeneous and isotropic universe governed by the quadratic form of the field equation of f( T) gravity. We explain how the higher order of the torsion can provide an origin for late accelerated phase of the universe in the FRW. The solution makes the scalar torsion T to be a function of the cosmic time t. We show that for the equation of state with the scale factor represent late phase of universe. We perform the cosmological studies and show how the quadratic form of f( T) effect on the behavior of these studies.
Stability of the Quadratic Equation of Pexider Type
Soon-Mo Jung
2000-01-01
We will investigate the stability problem of the quadratic equation (1) and extend the results of Borelli and Forti, Czerwik,\\u000a and Rassias. By applying this result and an improved theorem of the author, we will also prove the stability of the quadratic\\u000a functional equation of Pexider type,f\\u000a 1 (x +y) + f2(x -y) =f\\u000a 3(x) +f\\u000a 4(y), for a large
On Evgrafov-Fedoryuk's theory and quadratic differentials
NASA Astrophysics Data System (ADS)
Shapiro, Boris
2015-02-01
The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrödinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in 1-1 -correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree d, the number of such accumulation rays can be any positive integer between (d-1) and d atopwithdelims ()2.
On the Dual of Monomial Quadratic p -ary Bent Functions
Tor Helleseth; Alexander Kholosha
2007-01-01
Considered are quadratic p-ary bent functions having the form \\u000a f(x)=Trn(a xpj+1)f(x)={\\\\rm Tr}_n(a x^{p^j+1})\\u000a . Described is the general Gold-like class of bent functions that covers all the previously known monomial quadratic cases.\\u000a Obtained is the exact value of the Walsh transform coefficients for a bent function in this class. In particular, presented\\u000a is an explicit expressions for a dual of
On Evgrafov-Fedoryuk's theory and quadratic differentials
NASA Astrophysics Data System (ADS)
Shapiro, Boris
2015-06-01
The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrödinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in -correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree the number of such accumulation rays can be any positive integer between and.
Rational quadratic Bézier curve fitting by simulated annealing technique
NASA Astrophysics Data System (ADS)
Mohamed, Najihah; Abd Majid, Ahmad; Mt Piah, Abd Rahni
2013-04-01
A metaheuristic algorithm, which is an approximation method called simulated annealing is implemented in order to have the best rational quadratic Bézier curve from a given data points. This technique is used to minimize sum squared errors in order to improve the middle control point position and the value of weight. As a result, best fitted rational quadratic Bézier curve and its mathematical function that represents all the given data points is obtained. Numerical and graphical examples are also presented to demonstrate the effectiveness and robustness of the proposed method.
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.
NASA Astrophysics Data System (ADS)
Peng, Haowei; Ndione, Paul F.; Ginley, David S.; Zakutayev, Andriy; Lany, Stephan
2015-04-01
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 Mn1 -xZnxO alloys. At Zn compositions above x ?0.3 , thin films of 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. A proof of principle is provided by initial photo-electrocatalytic device measurements, corroborating, in particular, the predicted favorable hole-transport properties of these alloys.
Peng, Haowei; Ndione, Paul F.; Ginley, David S.; Zakutayev, Andriy; Lany, Stephan
2015-05-01
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??xZnxO 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. 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
Peng, Haowei; Ndione, Paul F.; Ginley, David S.; Zakutayev, Andriy; Lany, Stephan
2015-05-01
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??xZnxO alloys. At Zn compositions above x ? 0.3, thin films of 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. A proof of principle is provided by initial photo-electrocatalytic device measurements, corroborating, in particular, the predicted favorable hole-transport properties of these alloys.
NASA Astrophysics Data System (ADS)
Brahma, Sanjoy; Datta, Biswa
2009-07-01
The partial quadratic eigenvalue assignment problem (PQEVAP) concerns the reassignment of a small number of undesirable eigenvalues of a quadratic matrix pencil, while leaving the remaining large number of eigenvalues and the corresponding eigenvectors unchanged. The problem arises in controlling undesirable resonance in vibrating structures and in stabilizing control systems. The solution of this problem requires computations of a pair of feedback matrices. For practical effectiveness, these feedback matrices must be computed in such a way that their norms and the condition number of the closed-loop eigenvector matrix are as small as possible. These considerations give rise to the minimum norm partial quadratic eigenvalue assignment problem (MNPQEVAP) and the robust partial quadratic eigenvalue assignment problem (RPQEVAP), respectively. In this paper we propose new optimization based algorithms for solving these problems. The problems are solved directly in a second-order setting without resorting to a standard first-order formulation so as to avoid the inversion of a possibly ill-conditioned matrix and the loss of exploitable structures of the original model. The algorithms require the knowledge of only the open-loop eigenvalues to be replaced and their corresponding eigenvectors. The remaining open-loop eigenvalues and their corresponding eigenvectors are kept unchanged. The invariance of the large number of eigenvalues and eigenvectors under feedback is guaranteed by a proven mathematical result. Furthermore, the gradient formulas needed to solve the problems by using the quasi-Newton optimization technique employed are computed in terms of the known quantities only. Above all, the proposed methods do not require the reduction of the model order or the order of the controller, even when the underlying finite element model has a very large degree of freedom. These attractive features, coupled with minimal computational requirements, such as solutions of small diagonal Sylvester equations make the proposed algorithms ideally suited for application to large real-life structures. Numerical results show significant improvement in feedback norms and in the condition number of the closed-loop system. Also, the closed-loop eigenvalues have acceptable accuracy.
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. PMID:25822256
Properties of holograms recorded in a material with quadratic nonlinearity
Yu. N. Denisyuk
2006-01-01
This paper discusses the properties of a hologram recorded in a medium that possesses quadratic nonlinearity when the frequencies of the nonlinear and reference waves are identical and different. It is shown theoretically and experimentally that holograms of this type can form three-dimensional images of objects. Experiments on the recording of holograms were carried out using a pulsed Nd:YAG laser
Quadratic Diophantine equations, the class number, and the massformula
Goro Shimura
2006-01-01
1. The basic setting and two ternary cases We take a finite-dimensional vector space V over a field F and take also an F -bilinear symmetric form ? : V × V ? F. We then put ?(x )= ?(x, x )f or x ? V, thus using the same letter ? for the quadratic form and the corresponding symmetric
Solving quadratically constrained least squares using black box solvers
Tony F. Chan; Julia A. Olkin; Donald W. Cooley
1992-01-01
We present algorithms for solving quadratically constrained linear least squares problems that do not necessarily require expensive dense matrix factorizations. Instead, only “black box” solvers for certain related unconstrained least squares problems, as well as the solution of two related linear systems involving the coefficient matrixA and the constraint matrixB, are required. Special structures in the problem can thus be
Least squares problems with inequality constraints as quadratic constraints
Jodi L. Mead; Rosemary A Renauty
2010-01-01
Linear least squares problems with box constraints are commonly solved to find model parameters within bounds based on physical considerations. Common algorithms include Bounded Variable Least Squares (BVLS) and the Matlab function lsqlin. Here, the goal is to find solutions to ill-posed inverse problems that lie within box constraints. To do this, we formulate the box constraints as quadratic constraints,
On Differences of Two Squares in Some Quadratic Fields
Andrej Dujella; Zrinka Franuši?
2007-01-01
It this paper, we study the problem of determining the el- ements in the rings of integers of quadratic fields Q( p d) which are rep- resentable as a dierence of two squares. The complete solution of the problem is obtained for integers d which satisfy conditions given in terms of solvability of certain Pellian equations.
Solving quadratic programming problems with linear Hopfield networks
Evgeny Dudnikov
2003-01-01
We consider a linear Hopfield network for solving quadratic programming problems with equation constraints. The problem is reduced to the solution of the ordinary linear differential equations with arbitrary square matrix. Because of some properties of this matrix the special methods are required for good convergence of the system. After some comparative study of neural network models for solving this
Solving quadratic programming problems with linear Hopfield networks
Evgeny Dudnikov
2001-01-01
We consider a linear Hopfield network for solving quadratic programming problems with equation constraints. The problem is reduced to the solution of ordinary linear differential equations with arbitrary square matrix. Because of some properties of this matrix special methods are required for good convergence of the system. After some comparative studies of neural network models for solving this problem we
Quantum electroweak symmetry breaking through loop quadratic contributions
NASA Astrophysics Data System (ADS)
Bai, Dong; Cui, Jian-Wei; Wu, Yue-Liang
2015-06-01
Based on two postulations that (i) the Higgs boson has a large bare mass mH ?mh ? 125 GeV at the characteristic energy scale Mc which defines the Standard Model (SM) in the ultraviolet region, and (ii) quadratic contributions of Feynman loop diagrams in quantum field theories are physically meaningful, we show that the SM electroweak symmetry breaking is induced by the quadratic contributions from loop effects. As the quadratic running of Higgs mass parameter leads to an additive renormalization, which distinguishes from the logarithmic running with a multiplicative renormalization, the symmetry breaking occurs once the sliding energy scale ? moves from Mc down to a transition scale ? =?EW at which the additive renormalized Higgs mass parameter mH2 (Mc / ?) gets to change the sign. With the input of current experimental data, this symmetry breaking energy scale is found to be ?EW ? 760 GeV, which provides another basic energy scale for the SM besides Mc. Studying such a symmetry breaking mechanism could play an important role in understanding both the hierarchy problem and naturalness problem. It also provides a possible way to explore the experimental implications of the quadratic contributions as ?EW lies within the probing reach of the LHC and the future Great Collider.
Quadratic assignment problems generated with the Palubetskis algorithm are degenerate
David Cyganski; Richard F. Vaz; V. Glenn Virball
1994-01-01
The quadratic assignment problem (QAP) is a combinatorial optimization problem that arises in many applications such as the allocation of processes in distributed computer systems. The QAP is NP-hard and therefore no algorithms are known for solving the QAP in polynomial time. For this reason a variety of heuristic methods have been proposed for this problem. In order to evaluate
Computing greatest common divisors and factorizations in quadratic number fields
Erich Kaltofen; Heinrich Rolletschek
1989-01-01
In a quadratic number field Q(? + + D ), D a squarefree integer, with class number 1 any algebraic integer can be decomposed uniquely into primes but for only 21 domains Euclidean algorithms are known. It was shown by Cohn (5) that for D ? -19 even remainder sequences with possibly non-decreasing norms cannot determine the GCD of arbitrary
Quantum Electroweak Symmetry Breaking Through Loop Quadratic Contributions
Dong Bai; Jian-Wei Cui; Yue-Liang Wu
2015-05-25
Based on two postulations that (i) the Higgs boson has a large bare mass $m_H \\gg m_h \\simeq 125 $ GeV at the characteristic energy scale $M_c$ which defines the standard model (SM) in the ultraviolet region, and (ii) quadratic contributions of Feynman loop diagrams in quantum field theories are physically meaningful, we show that the SM electroweak symmetry breaking is induced by the quadratic contributions from loop effects. As the quadratic running of Higgs mass parameter leads to an additive renormalization, which distinguishes from the logarithmic running with a multiplicative renormalization, the symmetry breaking occurs once the sliding energy scale $\\mu$ moves from $M_c$ down to a transition scale $\\mu =\\Lambda_{EW}$ at which the additive renormalized Higgs mass parameter $m^2_H(M_c/\\mu)$ gets to change the sign. With the input of current experimental data, this symmetry breaking energy scale is found to be $\\Lambda_{EW}\\simeq 760$ GeV, which provides another basic energy scale for the SM besides $M_c$. Studying such a symmetry breaking mechanism could play an important role in understanding both the hierarchy problem and naturalness problem. It also provides a possible way to explore the experimental implications of the quadratic contributions as $\\Lambda_{EW}$ lies within the probing reach of the LHC and the future Great Collider.
Linearizing the inverse quadratic almost ideal demand system
Toshinobu Matsuda
2007-01-01
This article investigates the linear approximation to the inverse quadratic almost ideal demand system (IQUAIDS), a recently introduced flexible functional form with potential usefulness. Linearizing this nonlinear model is of practical importance because nonstationary data, which are likely to be used in inverse demand systems, can be handled more properly in linear models. The IQUAIDS is linearized by replacing the
Linear approximations to the quadratic almost ideal demand system
Toshinobu Matsuda
2006-01-01
This paper investigates linear approximations to the recently popular quadratic almost ideal demand system (QUAIDS) by proposing a new composite variable and conducting a simulation study. The linear approximations are especially useful when one uses nonstationary time series, to which nonlinear systems are difficult to apply properly. The new composite variable performs well in combination with the price indices appropriate
Lower bounding procedure for the Asymmetric Quadratic Traveling ...
2015-02-04
a lower bound is to linearize the quadratic terms xijxjk for all (i, j),(j, k) ? A ..... Consider any cycle C. Since column Cp is the selected column to enter the basis we ..... some kind of subtour elimination constraint, we restrict the search to find a
On the quadratic convergence of the Aitken Delta2 process
V. M. Verzhbitskii; I. F. Yumanova
2011-01-01
The Aitken Delta2 method for finding fixed points of scalar mappings is interpreted as a modification of the Wegstein method. Based on this approach, conditions for the quadratic convergence of this method are obtained for various situations of convergence\\/divergence of simple iteration. An algorithm for calculating fixed points that keeps track of these situations is presented.
Nash Strategies for Dynamic Noncooperative Linear Quadratic Sequential Games
Sontag, Eduardo
by the Defense Advanced Research Project Agency (DARPA) under Contract F33615-01-C3151 issued by the AFRL introduced and researched by White in [1], but the results were based on an approximate -equilibria- gramming and linear-quadratic sequential games is seldom touched. This research was sponsored in part
The Ant System Applied to the Quadratic Assignment Problem
Vittorio Maniezzo; Alberto Colorni
1999-01-01
In recent years, there has been growing interest in algorithms inspired by the observation of natural phenomena to define computational procedures that can solve complex problems. We describe a distributed heuristic algorithm that was inspired by the observation of the behavior of ant colonies, and we propose its use for the quadratic assignment problem. The results obtained in solving several
Quadratic stabilization and tracking - Applications to the benchmark problem
NASA Technical Reports Server (NTRS)
Schmitendorf, W. E.; Dolphus, R. M.; Benson, R. W.
1992-01-01
Recent results regarding quadratic stabilization and disturbance attenuation are applied to the benchmark problem. The authors investigate the minimum achievable levels of disturbance attenuation for different disturbance inputs and controlled outputs. They then design a feedforward tracking controller which tracks step inputs while maintaining the disturbance attenuation properties of the regulator.
Cosmological Vorticity in a Gravity with Quadratic Order Curvature Couplings
J. Hwang; H. Noh
1997-10-07
We analyse the evolution of the rotational type cosmological perturbation in a gravity with general quadratic order gravitational coupling terms. The result is expressed independently of the generalized nature of the gravity theory, and is simply interpreted as a conservation of the angular momentum.
A Tight Lower Bound for the Adjacent Quadratic Assignment Problem
2014-09-23
to n locations with the minimum cost, where the cost includes a quadratic term accounting ..... then the optimal objective value of (32) is given by the solution of the ..... To do a fair comparison between RLT2 and NewRLT we reported the lower.
Minimum variance quadratic unbiased estimation of variance components
C. Radhakrishna Rao
1971-01-01
The variance of a quadratic function of the random variables in a linear model is minimized to obtain locally best unbiased estimators (MIVQUE) of variance components. Condition for such estimators to be independent of the kurtosis of the variables is given. When the variables are normally distributed, MIVQUE coincides with MINQUE under the Euclidean norm of a matrix. Conditions under
An Identity Based Encryption Scheme Based on Quadratic Residues
Clifford Cocks
2001-01-01
We present a novel public key cryptosystem in which the public key of a subscriber can be chosen to be a publicly known value,\\u000a such as his identity. We discuss the security of the proposed scheme, and show that this is related to the difficulty of solving\\u000a the quadratic residuosity problem
An Adaptation of the NICE Cryptosystem to Real Quadratic Orders
Scheidler, Renate
polynomial time. However, the security of REAL-NICE relies on the intractability of a somewhat different, such a coset may be too small to prevent an exhaustive search attack. Instead, REAL-NICE encryption hidesAn Adaptation of the NICE Cryptosystem to Real Quadratic Orders Michael J. Jacobson, Jr.1, , Renate
Estimation of wildlife populations using the quadrat method of sampling
Hribar, John Richard
1970-01-01
on the following pages follow the style of Biometrics. 1. 2 Present Status of the Problem The quadrat method of sampling has long been established as a highly satisfactory procedure for estimating plant species popula- tions. The immobility of plant life lends...
Approximation of the Quadratic Set Covering Bruno Escoffier
Paris-Sud XI, Université de
Approximation of the Quadratic Set Covering Problem§ Bruno Escoffier , Peter L. Hammer Résumé Nous Set Covering problem. This problem, which arises in many applications, is a natural generaliza- tion of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case
Quadratic stability analysis of the Takagi-Sugeno fuzzy model
Kiriakos Kiriakidis; Apostolos Grivas; Anthony Tzes
1998-01-01
The nonlinear dynamic Takagi-Sugeno fuzzy model with offset terms is analyzed as a perturbed linear system. A sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model. The criterion accepts a convex programming formulation of reduced computational cost compared to the common Lyapunov matrix approach. Parametric robust control techniques suggest
An experiment in rotational motion with linear and quadratic drag
B. G. Thompson; P. A. Smith
2004-01-01
We describe a study of velocity-dependent drag in rotational motion that is suitable for an undergraduate laboratory experiment. Using standard teaching-laboratory equipment to obtain the data, we found that a drag force that is linear in the angular speed describes the data very well; however, the model residuals reveal that quadratic drag is also present. When a combined model is
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.
DIMACS Technical Report 9940 Camel Sequences and Quadratic Residues
DIMACS Technical Report 9940 Camel Sequences and Quadratic Residues by V. Gurvich 1 DIMACS generate them, will be called the camel distributions and camel sequences, respectively upcamel and downcamel. For example, the first sequence above is downcamel, and the second one is upcamel. Camel sequences have
Monotonic solutions of a quadratic integral equation of fractional order
Józef Bana?; Beata Rzepka
2007-01-01
In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112–119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with
Linear and Quadratic Change: A Problem from Japan
ERIC Educational Resources Information Center
Peterson, Blake E.
2006-01-01
In the fall of 2003, the author conducted research on the student teaching process in Japan. The basis for most of the lessons observed was rich mathematics problems. Upon returning to the US, the author used one such problem while teaching an algebra 2 class. This article introduces that problem, which gives rise to both linear and quadratic…
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…
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.
Homotopy analysis method for quadratic Riccati differential equation
Yue Tan; Saeid Abbasbandy
2008-01-01
In this paper, the quadratic Riccati differential equation is solved by means of an analytic technique, namely the homotopy analysis method (HAM). Comparisons are made between Adomian’s decomposition method (ADM), homotopy perturbation method (HPM) and the exact solution and the homotopy analysis method. The results reveal that the proposed method is very effective and simple.
Feasibility Testing for Systems of Real Quadratic Equations
Alexander I. Barvinok
1993-01-01
We consider the problem of deciding whether a given system of quadratic homogeneous equations over the reals has nontrivial\\u000a solution. We design an algorithm which, for a fixed number of equations, uses a number of arithmetic operations bounded by\\u000a a polynomial in the number of variables only.
Neural net solutions to fuzzy problems: The quadratic equation
J. J. Buckley; E. Eslami
1997-01-01
This paper continues our research on using neural nets to solve fuzzy equations. After outlining our general method of employing neural nets to solve fuzzy problems we concentrate on solving the fuzzy quadratic equation. We show how neural nets can produce both real, and complex, fuzzy number solutions.
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.
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…
Feasibility testing for systems of real quadratic equations
Alexander I. Barvinok
1992-01-01
We consider the problem of deciding whether a given system of quadratic homogeneous equations over the reals has non-trivial solution. We design an approximative algorithm whose complexity is polynomial in the number of variables and exponential in the number of equations. Some applications to general systems of polynomial equations and inequalities over the reals are discussed.
Monotonic solutions of a quadratic integral equation of Volterra type
A. Martinon
2004-01-01
We study a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval. With the help of a suitable measure of noncompactness, we show that the mentioned integral equation has monotonic solutions.
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)
On a bi-quadratic functional equation and its stability
Won-Gil Park; Jae-Hyeong Bae
2005-01-01
In this paper, we obtain the general solution and the generalized Hyers–Ulam stability of the bi-quadratic functional equation f(x+y,z+w)+f(x+y,z-w)+f(x-y,z+w)+f(x-y,z-w)=4[f(x,z)+f(x,w)+f(y,z)+f(y,w)].
Quadratic-Argument Approach to the Davey-Stewartson Equations
Xiaoping Xu
2008-12-10
The Davey-Stewartson equations are used to describe the long time evolution of a three-dimensional packets of surface waves. Assuming that the argument functions are quadratic in spacial variables, we find in this paper various exact solutions modulo the most known symmetry transformations for the Davey-Stewartson equations.
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.
Adaptive Memory Tabu Search for Binary Quadratic Programs
Fred Glover; Gary A. Kochenberger; Bahram Alidaee
1998-01-01
Recent studies have demonstrated the effectiveness of applying adaptive memory tabu search procedures to combinatorial optimization problems. In this paper we describe the development and use of such an approach to solve binary quadratic programs. Computational experience is reported, showing that the approach optimally solves the most difficult problems reported in the literature. For challenging problems of limited size, which
REPRESENTATION BY INTEGRAL QUADRATIC FORMS -A RAINER SCHULZE-PILLOT
Schulze-Pillot, Rainer
REPRESENTATION BY INTEGRAL QUADRATIC FORMS - A SURVEY RAINER SCHULZE-PILLOT Introduction form (1.1) q(x) = 1 2 t xSx on Z m given by S. We may equivalently consider a lattice L = L m j=1 Ze j j )) attached to q and the basis (e 1 ; : : : ; e m ) of L. We will also consider the situation
FIVE SQUARES IN ARITHMETIC PROGRESSION OVER QUADRATIC FIELDS
González, Enrique
FIVE SQUARES IN ARITHMETIC PROGRESSION OVER QUADRATIC FIELDS ENRIQUE GONZ´ALEZ-JIM´ENEZ AND XAVIER) there is a non-constant arithmetic progression of five squares. This is carried out by translating the problem that the only non-constant arithmetic progression of five squares over Q( 409), up to equivalence, is 72 , 132
Complex digital signal processing using quadratic residue number systems
RAMASAMY KRISHNAN; GRAH-AM A. JULLIEN; WILLIAM C. MILLER
1986-01-01
Recently, the quadratic residue number system (QRNS) has been introduced [6], [7] which allows the multiplication of complex integers with two real multiplications. The restriction is that the number system has either all prime moduli of the form 4K + 1, or composite numbers with prime factors of that form. If an increase in real multiplications from two to three
Learning to Rank and Quadratic Assignment Thomas Mensink
Paris-Sud XI, Université de
Learning to Rank and Quadratic Assignment Thomas Mensink TVPA - XRCE & LEAR - INRIA Grenoble it is common practice to learn a classifier per annotation label, and the labels are then ranked by the classification score. Following the development of the structured SVM framework [1, 2], learning ranking
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…
Efficient quadratic detection in perturbed arrays via Fourier transform techniques
Anil M. Rao; Douglas L. Jones
2001-01-01
Matched-field beamforming used in combination with a generalized likelihood ratio test is the most common detector structure in array processing situations. Unfortunately, various array perturbations caused by phase, calibration, propagation effects, or modeling errors can cause the sensor observations to become only partially correlated, limiting the performance of traditional matched-field beamformers that assume perfect coherence of the signal wavefronts. Quadratic
DISCRETE CALCULUS OF VARIATIONS FOR QUADRATIC LAGRANGIANS. CONVERGENCE ISSUES
Smouch, Laurent
is a preliminary discussion of convergence of y(t), uniformly locally in ]a, b[, as tends 0 for stationary. In this paper we work with lagrangians of the shape L(x, x) and L(x, x) where L : Cd Ã? Cd C is a quadratic
Constructions of Quadratic Bent Functions in Polynomial Forms
Nam Yul Yu; Guang Gong
2006-01-01
In this correspondence, the constructions and enumerations of all bent functions represented by a polynomial form of , are presented for special cases of . Using an iterative approach, the construction of bent functions of variables with degree is also provided using the constructed quadratic bent functions.
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION KARIM JOHANNES BECHER AND DAVID B. LEEP Abstract. The radical of a field consists of all is constructed where the natural analogue to the square-class e* *xact sequence for the radical fails
A parallel algorithm for constrained concave quadratic global minimization
A. T. Phillips; J. B. Rosen
1988-01-01
The global minimization of large-scale concave quadratic problems over a bounded polyhedral set using a parallel branch and bound approach is considered. The objective function consists of both a concave part (nonlinear variables) and a strictly linear part, which are coupled by the linear constraints. These large-scale problems are characterized by having the number of linear variables much greater than
Solving quadratic programming problems by delayed projection neural network.
Yang, Yongqing; Cao, Jinde
2006-11-01
In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network. PMID:17131675
Semismooth Newton method for quadratic programs with bound constraints
NASA Astrophysics Data System (ADS)
Daryina, A. N.; Izmailov, A. F.
2009-10-01
Convex quadratic programs with bound constraints are proposed to be solved by applying a semismooth Newton method to the corresponding variational inequality. Computational experiments demonstrate that, for strongly convex problems, this approach can be considerably more efficient than more traditional approaches.
Sequential quadratic programming for large-scale nonlinear optimization
NASA Astrophysics Data System (ADS)
Boggs, Paul T.; Tolle, Jon W.
2000-12-01
The sequential quadratic programming (SQP) algorithm has been one of the most successful general methods for solving nonlinear constrained optimization problems. We provide an introduction to the general method and show its relationship to recent developments in interior-point approaches, emphasizing large-scale aspects.
A Note on Stable Quadratic Polynomials over Fields of Characteristic Two
Omran Ahmadi; Claude Shannon
2009-01-01
In this note, first we show that there is no stable quadratic polynomial over finite fields of characteristic two and then show that there exist stable quadratic polynomials over function fields of characteristic two.
FIBER OPTIC POINT QUADRAT SYSTEM FOR IMPROVED ACCURACY IN VEGETATION SAMPLING
An automated, fiber optic point quadrat system for vegetation sampling is described. Because the effective point diameter of the system never exceeds 25um it minimizes the substantial errors which can arise with conventional point quadrats. Automatic contact detection eliminates ...
Multi-Quadratic Dynamic Programming Procedure of - Preserving Denoising for Medical Images
NASA Astrophysics Data System (ADS)
Pham, C. T.; Kopylov, A. V.
2015-05-01
In this paper, we present a computationally efficient technique for edge preserving in medical image smoothing, which is developed on the basis of dynamic programming multi-quadratic procedure. Additionally, we propose a new non-convex type of pair-wise potential functions, allow more flexibility to set a priori preferences, using different penalties for various ranges of differences between the values of adjacent image elements. The procedure of image analysis, based on the new data models, significantly expands the class of applied problems, and can take into account the presence of heterogeneities and discontinuities in the source data, while retaining high computational efficiency of the dynamic programming procedure and Kalman filterinterpolator. Comparative study shows, that our algorithm has high accuracy to speed ratio, especially in the case of high-resolution medical images.
NASA Astrophysics Data System (ADS)
Gallardo, Luis A.; Meju, Max A.; Pérez-Flores, Marco A.
2005-04-01
Although a comparative analysis of multiple images of a physical target can be useful, a joint image reconstruction approach should provide better interpretative elements for multi-spectral images. We present a generalized image reconstruction algorithm for the simultaneous reconstruction of band-limited images based on the novel cross-gradients concept developed for geophysical imaging. The general problem is formulated as the search for those images that stay within their band limits, are geometrically similar and satisfy their respective data in a least-squares sense. A robust iterative quadratic programming scheme is used to minimize the resulting objective function. We apply the algorithm to synthetic data generated using linear mathematical functions and to comparative geophysical test data. The resulting images recovered the test targets and show improved structural semblance between the reconstructed images in comparison to the results from two other conventional approaches.
NSDL National Science Digital Library
Mr. Wall
2008-12-09
You have been assigned an element during class. Your mission is to research information about your element. Create a Word document with the title of your element. Save your work regularly! Next, use the resources on this page to find and record the following information in your word document. (Hint: copy and paste the questions into your word document, then answer them.) See It s Elemental for electron configuration - ...
Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay
Shengyuan Xu; James Lam; Chengwu Yang
2001-01-01
This paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete-time systems with state delay. The system under consideration involves state time delay and time-varying norm-bounded parameter uncertainties appearing in all the matrices of the state-space model. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix
Technology Transfer Automated Retrieval System (TEKTRAN)
Trace elements are defined as mineral elements that occur in living systems in micrograms per gram of body weight or less. Trace elements of greatest practical concern in human health are iodine, iron and zinc. Suggestive evidence is emerging that cobalt (as vitamin B12), copper, selenium, boron and...
On a finite dynamic element method for free vibration analysis of structures
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1976-01-01
This paper explores the concept of finite dynamic elements involving higher order dynamic correction terms in the associated stiffness and mass matrices. Such matrices are then developed for a rectangular prestressed membrane element. Next, efficient analysis techniques for the eigenproblem solution of the resulting quadratic matrix equations are described in detail. These are followed by suitable numerical examples which indicate that employment of such dynamic elements in conjunction with an efficient quadratic matric solution technique will result in a most significant economy in the free vibration analysis of structures.
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
The first chapter in the twelfth unit of this SMSG series deals with the following topics involving quadratic functions: parabolas, translations of the parabola, completing the square, solving quadratic equations, "falling body" functions, and the use of quadratics in solving other equations. The chapter on statistics discusses cumulative and…
Optical gap solitons in nonresonant quadratic media Takeshi Iizuka1,2
of quadratic solitons because the equation for the dc field can be integrated explicitly, leading medium with a quadratic (2) nonlinear response. To derive the coupled-mode equations for the waveOptical gap solitons in nonresonant quadratic media Takeshi Iizuka1,2 and Yuri S. Kivshar2 1
ccsd-00008676,version1-13Sep2005 Quadratic Quantum Hamiltonians revisited
Boyer, Edmond
is a survey concerning exact useful formulas for time dependent Schr¨odinger equations with quadratic quadratic Schr¨odinger equation and Gaus- sian Coherent States. It is well known and clearccsd-00008676,version1-13Sep2005 Quadratic Quantum Hamiltonians revisited Monique Combescure IPNL
ECS 178 Course Notes THE ANALYTIC FORM OF THE QUADRATIC BEZIER CURVE
California at Davis, University of
the curve is quadratic, and that it is really a parabola. Developing the Equation of the CurveECS 178 Course Notes THE ANALYTIC FORM OF THE QUADRATIC BEZIER CURVE Kenneth I. Joy Institute We are working with the quadratic B´ezier curve, and have discovered that our initial divide- and
ECS 178 Course Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT
California at Davis, University of
by Chaikin's Algorithm [?]. The Matrix Equation for the Quadratic Uniform B-Spline Curve Given a setECS 178 Course Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT Kenneth I. Joy Institute for Data method for a quadratic uniform B-spline curve and show that the refinement is exactly that speci- fied
On-Line Geometric Modeling Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT
California at Davis, University of
that specified by Chaikin's Algorithm [1]. The Matrix Equation for the Quadratic Uniform B-Spline Curve GivenOn-Line Geometric Modeling Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT Kenneth I. Joy the refinement method for a quadratic uniform B-spline curve and show that the refinement is exactly
Applicability of quadratic and threshold models to motion discrimination in the rabbit retina
Norberto M. Grzywacz; F. R. Amthor; L. A. Mistler
1990-01-01
Computational and behavioral studies suggest that visual motion discrimination is based on quadratic nonlinearities. This raises the question of whether the behavior of motion sensitive neurons early in the visual system is actually quadratic. Theoretical studies show that mechanisms proposed for retinal directional selectivity do not behave quadratically at high stimulus contrast. However, for low contrast stimuli, models for these
Alignment-orientation conversion by quadratic Zeeman effect: Analysis and observation for Te2
Auzinsh, Marcis
Alignment-orientation conversion by quadratic Zeeman effect: Analysis and observation for Te2 I. P momenta into orientation due to quadratic correction to Zeeman effect. Circularity rate up to 0 of the quadratic correction to the Zeeman effect in diatomic mol- ecules. In particular, we direct now our
Article Submitted to IMA Journal of Numerical Analysis On a quadratic matrix equation associated
Guo, Chun-Hua
Article Submitted to IMA Journal of Numerical Analysis On a quadratic matrix equation associated 0A2, Canada (chguo@math.uregina.ca) Abstract We study the quadratic matrix equation X2 - EX - F = 0, where E is diagonal and F is an M-matrix. Quadratic matrix equations of this type arise in noisy Wiener
REMARKS ON THE CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL QUADRATIC (FRACTIONAL) HEAT EQUATION
Boyer, Edmond
REMARKS ON THE CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL QUADRATIC (FRACTIONAL) HEAT EQUATION LUC quadratic (fractional) heat equation: ut = D2 x u u2 , t (0, T), x R or T, with 0 introduced by Bejenaru-Tao [1] for a one-dimensional quadratic Schr¨odinger equation. This approach is based