Discontinuous Galerkin Method on Tetrahedral Elements for
Twente, Universiteit
Discontinuous Galerkin Method on Tetrahedral Elements for Aeroacoustics #12;Discontinuous Galerkin, The Netherlands #12;DISCONTINUOUS GALERKIN METHOD ON TETRAHEDRAL ELEMENTS FOR AEROACOUSTICS PROEFSCHRIFT ter equations in dimensionless form . . . . . . . . . 32 3 Discontinuous Galerkin formulation 35 3
Tadepalli, Srinivas C; Erdemir, Ahmet; Cavanagh, Peter R
2011-08-11
Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation. PMID:21742332
Implementation and Verification of a Nodally-Integrated Tetrahedral Element in FEBio
Utah, University of
Implementation and Verification of a Nodally-Integrated Tetrahedral Element in FEBio Steve A. Maas Abstract: Finite element simulations in computational biomechanics commonly require the discretization and time consuming using hexahedral elements. Automatic meshing algorithms exist for tetrahedral elements
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.
1999-01-01
This report documents a collection of papers on a family of uniform strain tetrahedral finite elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral Finite Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform strain and enhanced uniform strain formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.
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.
NASA Technical Reports Server (NTRS)
Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.
1992-01-01
A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.
Quadratic finite elements and incompressible viscous flows.
Dohrmann, Clark R.; Gartling, David K.
2005-01-01
Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.
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.
A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids
NASA Astrophysics Data System (ADS)
Hu, Jun; Zhang, ShangYou
2015-02-01
A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed, where the stress is approximated by symmetric $H(\\d)$-$P_k$ polynomial tensors and the displacement is approximated by $C^{-1}$-$P_{k-1}$ polynomial vectors, for all $k\\ge 4$. Numerical tests are provided.
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.
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)
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.
The quadratic MITC plate and MITC shell elements in plate bending
Phill-Seung Lee; Klaus-Jürgen Bathe
2010-01-01
The analysis of plates can be achieved using the quadratic MITC plate or MITC shell elements. The plate elements have a strong mathematical basis and have been shown to be optimal in their convergence behavior, theoretically and numerically. The shell elements have not (yet) been analyzed mathematically in depth for their rates of convergence, with the plate\\/shell thickness varying, but
Ho, Philip Wai-Sun
1977-01-01
to a finite number of degrees of freedom, the exact strain energy may never be achieved consequently. To ensure convergence to the correct result, several conditions have to 8 be satisfied. (1) The displacement functiou chosen should not produce... are used. The second type of distortion can always be corrected within the program and therefore, will not be considered here. 1-4 Several authors have discussed the stiffening effect of a dis- 1 torted isoparametric element. Henshell and others used...
D. Lefebvre; J. Peraire; K. Morgan
1993-01-01
We present a method based on time differencing and a least squares finite element approximation for the solution of the compressible Euler equations. The scheme is implicit and unconditionally stable and has been implemented using both linear and quadratic triangular elements in two dimensions. The method is based upon the minimization of the L2 norm of the equation residuals at
X. HAN; G. R. LIU; K. Y. LAM; T. OHYOSHI
2000-01-01
A novel method is presented for investigating elastic waves in functionally graded material (FGM) plates excited by plane pressure waves. The FGM plate is first divided into quadratic layer elements (QLEs). A general solution for the equation of motion governing the QLE has been derived. The general solution is then used together with the boundary and continuity conditions to obtain
Parallel Anisotropic Tetrahedral Adaptation
NASA Technical Reports Server (NTRS)
Park, Michael A.; Darmofal, David L.
2008-01-01
An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domain-decomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.
Analysis of periodic 3D viscous flows using a quadratic discrete Galerkin boundary element method
NASA Astrophysics Data System (ADS)
Chan, Chiu Y.; Beris, Antony N.; Advani, Suresh G.
1994-05-01
A discrete Galerkin boundary element technique with a quadratic approximation of the variables was developed to simulate the three-dimensional (3D) viscous flow established in periodic assemblages of particles in suspensions and within a periodic porous medium. The Batchelor's unit-cell approach is used. The Galerkin formulation effectively handles the discontinuity in the traction arising in flow boundaries with edges or corners, such as the unit cell in this case. For an ellipsoidal dilute suspension over the range of aspect ratio studied (1 to 54), the numerical solutions of the rotational velocity of the particles and the viscosity correction were found to agree with the analytic values within 0.2% and 2% respectively, even with coarse meshes. In a suspension of cylindrical particles the calculated period of rotation agreed with the experimental data. However, Burgers' predictions for the correction to the suspension viscosity were found to be 30% too low and therefore the concept of the equivalent ellipsoidal ratio is judged to be inadequate. For pressure-driven flow through a fixed bed of fibers, the prediction on the permeability was shown to deviate by as much as 10% from the value calculated based on approximate permeability additivity rules using the corresponding values for planar flow past a periodic array of parallel cylinders. These applications show the versatility of the technique for studying viscous flows in complicated 3D geometries.
NSDL National Science Digital Library
2014-09-18
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
Tufts University
2013-01-01
Working in teams of four, learners 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. Investigating questions encourage learners to reflect about the engineering and manufacturing process. Activity contains recommended resources about the history of kites and their construction.
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.
Omid Z. Mehdizadeh; Marius Paraschivoiu
2005-01-01
A three-dimensional finite element method has been implemented to predict the transmission loss of a packed muffler and a parallel baffle silencer for a given frequency range. Iso-parametric quadratic tetrahedral elements have been chosen due to their flexibility and accuracy in modeling geometries with curved surfaces. For accurate physical representation, perforated plates are modeled with complex acoustic impedance while absorption
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
Tao Lü; Jing Lu
2002-01-01
Splitting extrapolation for solving second order elliptic systems with curved boundary in Rd by using isoparametric d-quadratic element Q2 is presented, which is a new technique for solving large scale scientific and engineering problems in parallel. By means of domain decomposition, a large scale multidimensional problem with curved boundary is turned into many discrete problems involving several grid parameters. The
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.
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, K.; 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.
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…
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.
Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees
Bronson, Jonathan; Levine, Joshua A.; Whitaker, Ross
2014-01-01
We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach. PMID:24356365
NASA Astrophysics Data System (ADS)
Accardi, Luigi; Dhahri, Ameur
2010-02-01
We construct the quadratic analog of the boson Fock functor. While in the first order (linear) case all contractions on the 1-particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. The encouraging fact is that it contains, as proper subgroups (i.e., the contractions), all the gauge transformations of second kind and all the a.e. invertible maps of Rd into itself leaving the Lebesgue measure quasi-invariant (in particular, all diffeomorphism of Rd). This allows quadratic two-dimensional quantization of gauge theories, of representations of the Witt group (in fact it continuous analog), of the Zamolodchikov hierarchy, and much more. Within this semigroup we characterize the unitary and the isometric elements and we single out a class of natural contractions.
Tunneling states of a tetrahedral molecule in a tetrahedral field
NASA Astrophysics Data System (ADS)
Ozaki, Yoshiaki; Kataoka, Yosuke; Okada, Kenkichi; Yamamoto, Tsunenobu
1980-11-01
Accuracies of the rotational eigenvalues and eigenvectors of a tetrahedral molecule in a tetrahedral field are examined. Calculations are made in two ways: one is in terms of a set of free rotor functions and the other in the use of the pocket state method by Hüller and Kroll [J. Chem. Phys. 63, 4495 (1975)]. If the basis set consists of the free rotor functions up to the eighth order, the former method is superior to the latter as long as the potential strength does not exceed 40B, B being the rotational constant. Hüller and Raich's criterion for the accuracy of the free rotor function method [J. Chem. Phys. 71, 3851 (1979)] is shown to have limited application.
Single molecule spectroscopy of tetrahedral oligophenylenevinylene molecules
Buratto, Steve
Single molecule spectroscopy of tetrahedral oligophenylenevinylene molecules Melissa A. Summers form 17 July 2002 Abstract We probe the fluorescence from single molecules of a new class of tetrahedral oligo(phenylenevinylene) (OPV) molecules. Our results show that the tetrahedral molecules contain
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
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.
Au40: A Large Tetrahedral Magic Cluster
Jiang, Deen [ORNL; Walter, Michael [University of Freiburg, Germany
2011-01-01
40 is a magic number for tetrahedral symmetry predicted in both nuclear physics and the electronic jellium model. We show that Au{sub 40} could be such a magic cluster from density functional theory-based basin hopping for global minimization. The putative global minimum found for Au{sub 40} has a twisted pyramid structure, reminiscent of the famous tetrahedral Au{sub 20}, and a sizable HOMO-LUMO gap of 0.69 eV, indicating its molecular nature. Analysis of the electronic states reveals that the gap is related to shell closings of the metallic electrons in a tetrahedrally distorted effective potential.
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.
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…
NSDL National Science Digital Library
2011-01-01
Completing the square is applied to the general quadratic to derive the quadratic formula. Before an area application example is given there is a quick review of the four methods that have been presented for solving quadratic equations. Complex numbers are introduced before the discriminant is presented.
Hamiltonian Tetrahedralizations with Steiner Points Francisco Escalona
Urrutia, Jorge
(S), interior points. A tetrahedralization T of S is a partition of Conv(S) into tetrahedra with vertices in S such that: 1. The tetrahedra only intersect at points, lines or faces. 2. The tetrahedra do not contain T of S, we define DT , the dual graph of T , to be the graph whose vertex set is the tetrahedra
Distorted tetrahedral shapes of nematic vesicles
NASA Astrophysics Data System (ADS)
Son Nguyen, Thanh; Selinger, Jonathan
2013-03-01
In membranes with internal orientational or crystalline order, there is a geometric coupling between 2D internal order and 3D shape. Nonuniformity in internal order tends to induce curvature, and curvature provides an effective potential acting on internal order. For a closed vesicle with nematic liquid-crystalline order, there must be a total topological charge of +2, which normally occurs as four defects of +1/2 each. Previous research has suggested that these four defects form a regular tetrahedron, leading to a tetrahedral shape of the vesicle, which may be useful in colloidal crystals for photonic applications. Here, we develop an explicit model to calculate energies of defect structures in nematic vesicles. When the liquid-crystal interaction energy is a purely 2D intrinsic interaction, we find that the perfect tetrahedral shape is stable only up to a maximum interaction strength (Frank constant), where it changes to an elongated rectangular configuration. When the interaction energy is a 3D extrinsic and intrinsic interaction, the perfect tetrahedral shape is never stable; the vesicle is a distorted tetrahedron for small Frank constant and a highly elongated rectangle for larger Frank constant. These results show the difficulty in designing tetrahedral structures.
Hybrid Adaptation Method and Directional Viscous Multigrid with Prismatic-Tetrahedral Meshes
V. Parthasarathy; Y. Kallinderis; K. Nakajima
1995-01-01
A solution adaptive scheme with directionalmultigrid for viscous computations on hybrid gridsis presented. The flow domain is discretized withprismatic and tetrahedral elements. The use of hybridgrid enables the solver to compute accuratesolutions with relatively less memory requirementthan a fully unstructured grid. Further, employingprisms to discretize the full Navier-Stokes equationsand tetrahedra for Euler equations rendersthe solver equation-adaptive. A hybrid grid adaptation...
Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality
Bronson, Jonathan R.; Levine, Joshua A.; Whitaker, Ross T.
2013-01-01
Summary We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity. PMID:25309969
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.
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.
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
Pseudo-fivefold diffraction symmetries in tetrahedral packing.
Lee, Stephen; Henderson, Ryan; Kaminsky, Corey; Nelson, Zachary; Nguyen, Jeffers; Settje, Nick F; Schmidt, Joshua Teal; Feng, Ji
2013-07-29
We review the way in which atomic tetrahedra composed of metallic elements pack naturally into fused icosahedra. Orthorhombic, hexagonal, and cubic intermetallic crystals based on this packing are all shown to be united in having pseudo-fivefold rotational diffraction symmetry. A unified geometric model involving the 600-cell is presented: the model accounts for the observed pseudo-fivefold symmetries among the different Bravais lattice types. The model accounts for vertex-, edge-, polygon-, and cell-centered fused-icosahedral clusters. Vertex-centered and edge-centered types correspond to the well-known pseudo-fivefold symmetries in Ih and D5h quasicrystalline approximants. The concept of a tetrahedrally-packed reciprocal space cluster is introduced, the vectors between sites in this cluster corresponding to the principal diffraction peaks of fused-icosahedrally-packed crystals. This reciprocal-space cluster is a direct result of the pseudosymmetry and, just as the real-space clusters, can be rationalized by the 600-cell. The reciprocal space cluster provides insights for the Jones model of metal stability. For tetrahedrally-packed crystals, Jones zone faces prove to be pseudosymmetric with one another. Lower and upper electron per atom bounds calculated for this pseudosymmetry-based Jones model are shown to accord with the observed electron counts for a variety of Group 10-12 tetrahedrally-packed structures, among which are the four known Cu/Cd intermetallic compounds: CdCu2, Cd3Cu4, Cu5Cd8, and Cu3Cd10. The rationale behind the Jones lower and upper bounds is reviewed. The crystal structure of Zn11Au15Cd23, an example of a 1:1 MacKay cubic quasicrystalline approximant based solely on Groups 10-12 elements is presented. This compound crystallizes in Im3 (space group no. 204) with a = 13.842(2)?Å. The structure was solved with R1 = 3.53?%, I > 2?; = 5.33?%, all data with 1282/0/38 data/restraints/parameters. PMID:23780731
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,
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.
Measure of disorder in tetrahedrally bonded semiconductors
Sundari, S. Tripura; Raghavan, G. [Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102 (India)
2005-06-13
A measure of crystalline order in tetrahedrally bonded semiconductors is proposed based on optical response. This measure is obtained from the <111> critical point structure in the dielectric spectra. This descriptor is sensitive to the nature and extent of disorder in specimens and distinguishes differences in medium and short-order present in amorphous materials. Application to Ar{sup +}-irradiated Si specimens yields the threshold amorphization dose and this technique is sensitive to structural changes which occur as a function of irradiation fluence both above and beyond the amorphization threshhold. Systematic variations are also obtained in hydrogenated amorphous-Si. The general validity of the method is indicated.
Field emission from tetrahedral amorphous carbon
Satyanarayana, B.S.; Hart, A.; Milne, W.I.; Robertson, J. [Engineering Department, Cambridge University, Cambridge CB2 1PZ (United Kingdom)] [Engineering Department, Cambridge University, Cambridge CB2 1PZ (United Kingdom)
1997-09-01
Field emission has been measured from a series of tetrahedrally bonded amorphous carbon (ta-C) films produced by the filtered cathodic vacuum arc. The threshold field and current densities achievable have been studied as a function of their sp{sup 3} content and of nitrogen incorporation. Typical undoped ta-C films are found to have a threshold field of 10{endash}20 V/{mu}m, decreasing with increasing sp{sup 3} content, and optimally nitrogen doped films exhibit threshold fields as low as 3{endash}5 V/{mu}m. {copyright} {ital 1997 American Institute of Physics.}
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
A bicontinuous tetrahedral structure in a liquid-crystalline lipid
NASA Astrophysics Data System (ADS)
Longley, William; McIntosh, Thomas J.
1983-06-01
The structure of most lipid-water phases can be visualized as an ordered distribution of two liquid media, water and hydrocarbons, separated by a continuous surface covered by the polar groups of the lipid molecules1. In the cubic phases in particular, rod-like elements are linked into three-dimensional networks1,2. Two of these phases (space groups Ia3d and Pn3m) contain two such three-dimensional networks mutually inter-woven and unconnected. Under the constraints of energy minimization3, the interface between the components in certain of these `porous fluids' may well resemble one of the periodic minimal surface structures of the type described mathematically by Schwarz4,5. A structure of this sort has been proposed for the viscous isotropic (cubic) form of glycerol monooleate (GMO) by Larsson et al.6 who suggested that the X-ray diagrams of Lindblom et al.7 indicated a body-centred crystal structure in which lipid bilayers might be arranged as in Schwarz's octahedral surface4. We have now found that at high water contents, a primitive cubic lattice better fits the X-ray evidence with the material in the crystal arranged in a tetrahedral way. The lipid appears to form a single bilayer, continuous in three dimensions, separating two continuous interlinked networks of water. Each of the water networks has the symmetry of the diamond crystal structure and the bilayer lies in the space between them following a surface resembling Schwarz's tetrahedral surface4.
Quadratic spline subroutine package
Rasmussen, L.A.
1982-01-01
A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)
Tetrahedrally coordinated half-metallic antiferromagnets
NASA Astrophysics Data System (ADS)
Nakao, Masao
2006-11-01
We explore the electronic structures of transition-metal-based chalcopyrites TMX2 ( X=S , Se, and Te) to establish a concept of half-metallic antiferromagnets (HM-AFM’s) within the class of tetrahedrally coordinated ternary systems. Using a full-potential muffin-tin approach and the spin-polarized density functional method, we find two series of HM-AFM’s: CrFeX2 and VCoX2 , where two constituent magnetic ions in a unit cell have antialigned local moments that cancel exactly by virtue of the integer filling of one spin channel. The bonding nature is interpreted in terms of the “ghost-bond-orbital model”; the T - X bonds are covalent while the M - X bonds are ionic, suggesting the magnetic interaction in each bond is due to ferromagnetic double exchange and antiferromagnetic superexchange, respectively, in the conventional scheme.
Optical Quadratic Measure Eigenmodes
Michael Mazilu; Joerg Baumgartl; Sebastian Kosmeier; Kishan Dholakia
2010-07-13
We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of their interaction with matter. In this manner we may decompose the respective fields into optical quadratic measure eigenmodes (QME). Key applications include the optimization of the size of a focused spot, the transmission through photonic devices, and the structured illumination of photonic and plasmonic structures. We verify the validity of the QME approach through a particular experimental realization where the size of a focused optical field is minimized using a superposition of Bessel beams.
Accardi, Luigi; Dhahri, Ameur [Volterra Center, University of Roma Tor Vergata, Via Columbia 2, 00133 Roma (Italy)
2009-12-15
We give a necessary and sufficient condition for the existence of a quadratic exponential vector with test function in L{sup 2}(R{sup d}) intersection L{sup {infinity}}(R{sup d}). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique different from the one used by Accardi et al. [Quantum Probability and Infinite Dimensional Analysis, Vol. 25, p. 262, (2009)], we also extend, to a more general class of test functions, the explicit form of the scalar product between two such vectors.
The Rise and Fall of Anomalies in Tetrahedral Liquids
Waldemar Hujo; B. Shadrack Jabes; Varun K. Rana; Charusita Chakravarty; Valeria Molinero
2011-07-28
The thermodynamic liquid-state anomalies and associated structural changes of the Stillinger-Weber family of liquids are mapped out as a function of the degree of tetrahedrality of the interaction potential, focusing in particular on tetrahedrality values suitable for modeling C, H2O, Si, Ge and Sn. We show that the density anomaly, associated with a rise in molar volume on isobaric cooling, emerges at intermediate tetrahedralities (e.g. Ge, Si and H2O) but is absent in the low (e.g. Sn) and high (e.g. C) tetrahedrality liquids. The rise in entropy on isothermal compression associated with the density anomaly is related to the structural changes in the liquid using the pair correlation entropy. An anomalous increase in the heat capacity on isobaric cooling exists at high tetrahedralities but is absent at low tetrahedralities (e.g. Sn). Structurally, this heat capacity anomaly originates in a sharp rise in the fraction of four-coordinated particles and local tetrahedral order in the liquid as its structure approaches that of the tetrahedral crystal.
Updates to Multi-Dimensional Flux Reconstruction for Hypersonic Simulations on Tetrahedral Grids
NASA Technical Reports Server (NTRS)
Gnoffo, Peter A.
2010-01-01
The quality of simulated hypersonic stagnation region heating with tetrahedral meshes is investigated by using an updated three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. An earlier implementation of this algorithm provided improved symmetry characteristics on tetrahedral grids compared to conventional reconstruction methods. The original formulation however displayed quantitative differences in heating and shear that were as large as 25% compared to a benchmark, structured-grid solution. The primary cause of this discrepancy is found to be an inherent inconsistency in the formulation of the flux limiter. The inconsistency is removed by employing a Green-Gauss formulation of primitive gradients at nodes to replace the previous Gram-Schmidt algorithm. Current results are now in good agreement with benchmark solutions for two challenge problems: (1) hypersonic flow over a three-dimensional cylindrical section with special attention to the uniformity of the solution in the spanwise direction and (2) hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problems provide a sensitive indicator for algorithmic effects on heating. Additional simulations on a sharp, double cone and the shuttle orbiter are then presented to demonstrate the capabilities of the new algorithm on more geometrically complex flows with tetrahedral grids. These results provide the first indication that pure tetrahedral elements utilizing the updated, three-dimensional, upwind reconstruction algorithm may be used for the simulation of heating and shear in hypersonic flows in upwind, finite volume formulations.
Robert O. Curtis; David D. Marshall
Quadratic mean diameter is the measure of average tree diameter conventionally used in forestry, rather than arithmetic mean diameter. The historical and practical reasons for this convention are reviewed. West. J. Appl. For. 15(3):137-139. Average diameter is a widely used stand statistic that appears in virtually all yield tables, simulator outputs, stand summaries, and much inventory data. To most people,
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.
J. Killingbeck
1979-01-01
The hydrogen-atom quadratic Zeeman effect is treated by several techniques, and a new perturbation approach is suggested which involves numerical solution of a radial equation based on the s part of the potential. The low-field results appear to be more accurate than those of previous workers.
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]…
Martin Kaser; P. M. Mai; Michael Dumbser
2007-01-01
We present a new method for near-source ground-motion calculations due to earthquake rupture on potentially geometrically complex faults. Following the recently introduced Discontinuous Galerkin approach with local time stepping on tetrahedral meshes, we use piecewise polynomial approximations of the unknown variables inside each element and achieve the same approximation order in time and space due to the new ADER time
NASA Technical Reports Server (NTRS)
Homemdemello, Luiz S.
1992-01-01
An assembly planner for tetrahedral truss structures is presented. To overcome the difficulties due to the large number of parts, the planner exploits the simplicity and uniformity of the shapes of the parts and the regularity of their interconnection. The planning automation is based on the computational formalism known as production system. The global data base consists of a hexagonal grid representation of the truss structure. This representation captures the regularity of tetrahedral truss structures and their multiple hierarchies. It maps into quadratic grids and can be implemented in a computer by using a two-dimensional array data structure. By maintaining the multiple hierarchies explicitly in the model, the choice of a particular hierarchy is only made when needed, thus allowing a more informed decision. Furthermore, testing the preconditions of the production rules is simple because the patterned way in which the struts are interconnected is incorporated into the topology of the hexagonal grid. A directed graph representation of assembly sequences allows the use of both graph search and backtracking control strategies.
Preliminary design of a large tetrahedral truss/hexagonal heatshield panel aerobrake
NASA Technical Reports Server (NTRS)
Dorsey, John T.; Mikulas, Martin M., Jr.
1989-01-01
An aerobrake structural concept is introduced which consists of two primary components: (1) a lightweight erectable tetrahedral support truss; and (2) sandwich hexagonal heatshield panels which, when attached to the truss, form a continuous impermeable aerobraking surface. Generic finite element models and a general analysis procedure to design tetrahedral truss/hexagonal heatshield panel aerobrakes is developed, and values of the aerobrake design parameters which minimize mass and packaging volume for a 120-foot-diameter aerobrake are determined. Sensitivity of the aerobrake design to variations in design parameters is also assessed. The results show that a 120-foot-diameter aerobrake is viable using the concept presented (i.e., the aerobrake mass is less than or equal to 15 percent of the payload spacecraft mass). Minimizing the aerobrake mass (by increasing the number of rings in the support truss) however, leads to aerobrakes with the highest part count.
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.
Periodic superstructures in tetrahedrally bonded homopolymers
NASA Astrophysics Data System (ADS)
Saxena, Avadh; Cao, Wenwu
1988-10-01
Using a lattice sum over single bipolaron potentials displaced by periodicity d, we have analytically obtained a solution for a bipolaron lattice for a tetrahedrally bonded homopolymer within the continuum model of Rice and Phillpot. This solution is used to derive the band structure, which consists of two bipolaron bands symmetrically located about the middle of the band gap in addition to the conduction and valence bands. The electronic density of states, chemical potential ?, and the energy of formation of a bipolaron lattice are also calculated as a function of the bipolaron density ?b. The bipolaron chemical potential lies between the conduction-band edge and the upper edge of the upper bipolaron band, indicating that the bipolaron lattice is energetically the most favorable charge configuration at low ?b. In the strict weak-coupling limit (infinite momentum cutoff ?) the bipolaron-bipolaron interaction is found to be repulsive and varies with bipolaron density as (1/?b)exp(-2/?b?p), ?p being the bipolaron characteristic length. Thus, the bipolaron lattice is stable only in the range 0
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.
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
Tetrahedral Meshing of Volumetric Medical Images Respecting Image Edges
Michal Špan?l; P?emysl Kršek; Miroslav Švub; Vít Štancl
\\u000a In this paper, a variational tetrahedral meshing approach is used to adapt a tetrahedral mesh to the underlying CT volumetric\\u000a data so that image edges are well approximated in the mesh. Afterwards, tetrahedra in the mesh are classified into regions\\u000a whose image characteristics are similar. Three different clustering schemes are proposed to classify tetrahedra, while the\\u000a clustering scheme viewing the
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 ...
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.
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
THE GENERATION OF TETRAHEDRAL MESH MODELS FOR NEUROANATOMICAL MRI
Lederman, Carl; Joshi, Anand; Dinov, Ivo; Vese, Luminita; Toga, Arthur; Van Horn, John Darrell
2010-01-01
In this article, we describe a detailed method for automatically generating tetrahedral meshes from 3D images having multiple region labels. An adaptively sized tetrahedral mesh modeling approach is described that is capable of producing meshes conforming precisely to the voxelized regions in the image. Efficient tetrahedral construction is performed minimizing an energy function containing three terms: a smoothing term to remove the voxelization, a fidelity term to maintain continuity with the image data, and a novel elasticity term to prevent the tetrahedra from becoming flattened or inverted as the mesh deforms while allowing the voxelization to be removed entirely. The meshing algorithm is applied to structural MR image data that has been automatically segmented into 56 neuroanatomical sub-divisions as well as on two other examples. The resulting tetrahedral representation has several desirable properties such as tetrahedra with dihedral angles away from 0 and 180 degrees, smoothness, and a high resolution. Tetrahedral modeling via the approach described here has applications in modeling brain structure in normal as well as diseased brain in human and non-human data and facilitates examination of 3D object deformations resulting from neurological illness (e.g. Alzheimer’s Disease), development, and/or aging. PMID:21073968
A comparison of tetrahedral mesh improvement techniques
Freitag, L.A.; Ollivier-Gooch, C. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
1996-12-01
Automatic mesh generation and adaptive refinement methods for complex three-dimensional domains have proven to be very successful tools for the efficient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more difficult to compute. Fortunately, the shape of the elements can be improved through several mechanisms, including face-swapping techniques that change local connectivity and optimization-based mesh smoothing methods that adjust grid point location. The authors consider several criteria for each of these two methods and compare the quality of several meshes obtained by using different combinations of swapping and smoothing. Computational experiments show that swapping is critical to the improvement of general mesh quality and that optimization-based smoothing is highly effective in eliminating very small and very large angles. The highest quality meshes are obtained by using a combination of swapping and smoothing techniques.
Assembly of tetrahedral gold nanoclusters from binary colloidal mixtures
NASA Astrophysics Data System (ADS)
Schade, Nicholas B.; ``Peter''sun, Dazhi; Holmes-Cerfon, Miranda C.; Chen, Elizabeth R.; Gehrels, Emily W.; Fan, Jonathan A.; Gang, Oleg; Manoharan, Vinothan N.
2013-03-01
We experimentally investigate the structures that form when colloidal gold nanospheres cluster around smaller spheres. We use nanoparticles coated with complementary DNA sequences to assemble the clusters, and we observe them under electron microscopy. Previous experiments using polystyrene microspheres indicate that a 90% yield of tetrahedral clusters is possible near a critical diameter ratio; random sphere parking serves as a useful model for understanding this phenomenon. Here we examine how this approach can be scaled down by an order of magnitude in size, using gold building blocks. We study how this method can be used to assemble tetrahedral plasmonic resonators in order to create a bulk, isotropic, optical metamaterial.
Molecular origin of auxetic behavior in tetrahedral framework silicates.
Alderson, Andrew; Evans, Kenneth E
2002-11-25
Recent analytical models for the Poisson's ratios (nu(ij)) of tetrahedral frameworks are applied to alpha-cristobalite and alpha-quartz for the first time. Rotation and dilation of the SiO4 tetrahedral subunits are considered. Each mechanism leads to negative nu(31) values, whereas negative and positive values are possible when they act concurrently. The concurrent model is in excellent agreement with experiment and explains the dichotomy between negative and positive nu(31) values in alpha-cristobalite and alpha-quartz, respectively. The predicted strain-dependent trends confirm those from molecular modeling. PMID:12485081
Molecular Origin of Auxetic Behavior in Tetrahedral Framework Silicates
NASA Astrophysics Data System (ADS)
Alderson, Andrew; Evans, Kenneth E.
2002-11-01
Recent analytical models for the Poisson's ratios (?ij) of tetrahedral frameworks are applied to ?-cristobalite and ?-quartz for the first time. Rotation and dilation of the SiO4 tetrahedral subunits are considered. Each mechanism leads to negative ?31 values, whereas negative and positive values are possible when they act concurrently. The concurrent model is in excellent agreement with experiment and explains the dichotomy between negative and positive ?31 values in ?-cristobalite and ?-quartz, respectively. The predicted strain-dependent trends confirm those from molecular modeling.
A quadratic analog-to-digital converter
NASA Technical Reports Server (NTRS)
Harrison, D. C.; Staples, M. H.
1980-01-01
An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.
Tetrahedral Models of Learning: Application to College Reading.
ERIC Educational Resources Information Center
Nist, Sherrie L.
J. D. Bransford's tetrahedral model of learning considers four variables: (1) learning activities, (2) characteristics of the learner, (3) criterial tasks, and (4) the nature of the materials. Bransford's model provides a research-based theoretical framework that can be used to teach, model, and have students apply a variety of study strategies to…
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
PIECEWISE QUADRATIC APPROXIMATIONS IN CONVEX ...
2010-12-11
For instance, the recent [31] uses a different model ...... Fortunately, increasing ? and/or ? is a reaction to the fact that the ? obtained by ..... Piecewise quadratic approximations in convex numerical optimization. 25 name n function. 1 CB2. 2.
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.
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)
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.
FUNCTION DIGRAPHS OF QUADRATIC MAPS MODULO p Christie L. Gilbert
Reiter, Clifford A.
FUNCTION DIGRAPHS OF QUADRATIC MAPS MODULO p Christie L. Gilbert 8 Gerome Avenue, Burlington, NJ(u(x)) denote the function digraph which has Zm as vertices and edges of the form (x,u(x)) where x is an element of Zm. This digraph geometrically represents the function u(x) and paths correspond to iteration of u
FUNCTION DIGRAPHS OF QUADRATIC MAPS MODULO p Christie L. Gilbert
Storey, John D.
FUNCTION DIGRAPHS OF QUADRATIC MAPS MODULO p Christie L. Gilbert 8 Gerome Avenue, Burlington, NJ,4]. In particular, let fdm(u(x)) denote the function digraph which has Zm as vertices and edges of the form (x,u(x)) where x is an element of Zm. This digraph geometrically represents the function u(x) and paths
Quadratic Randomized Lower Bound for the Knapsack Problem \\Lambda
Grigoriev, Dima
to the ele ment distinctness problem. In [BKL93], [GKMS96] a linear depth RCT was constructed for a similar]). This example shows that the still open problem of complexity of an RCT for the element distinctness problemQuadratic Randomized Lower Bound for the Knapsack Problem \\Lambda Dima Grigoriev y Marek Karpinski
Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis
NASA Technical Reports Server (NTRS)
Thompson, P. M.
1979-01-01
Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.
Interactive point-based rendering of higher-order tetrahedral data.
Zhou, Yuan; Garland, Michael
2006-01-01
Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, such solutions may often be expressed using non-linear basis functions. Certain solution techniques, such as discontinuous Galerkin methods, may even produce non-conforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to non-conforming meshes. We introduce a point-based visualization system for interactive rendering of large, potentially non-conforming, tetrahedral meshes. We propose methods for adaptively sampling points from non-linear solution data and for decimating points at run time to fit GPU memory limits. Because these are streaming processes, memory consumption is independent of the input size. We also present an order-independent point rendering method that can efficiently render volumes on the order of 20 million tetrahedra at interactive rates. PMID:17080856
Tetrahedral order in homologous disaccharide-water mixtures.
Branca, C; Maccarrone, S; Magazù, S; Maisano, G; Bennington, S M; Taylor, J
2005-05-01
The present work aims at evidencing the "kosmotrope" nature of trehalose through the analysis of inelastic neutron scattering measurements on trehalose and sucrose water solutions at different temperatures. Neutron spectra were collected by using the spectrometer MARI at the ISIS pulsed neutron source of the Rutherford Appleton Laboratory (Chilton, UK). To study the structural modifications induced on the tetrahedral hydrogen-bond network of water by homologous disaccharides, as a first step, the vibrational properties of pure water at different temperatures have been investigated. In particular, the temperature behavior of the intramolecular OH stretching mode has been analyzed. Successively, the vibrational properties for pure water have been compared with those of the sugar water solutions focusing the attention on the tetrahedral network-forming tendency. Finally, the obtained findings have been compared with previous Raman scattering evidences, and the results interpreted in the frame of recent molecular dynamics simulation works. PMID:15910051
Tetrahedrally coordinated carbonates in Earth’s lower mantle
NASA Astrophysics Data System (ADS)
Boulard, Eglantine; Pan, Ding; Galli, Giulia; Liu, Zhenxian; Mao, Wendy L.
2015-02-01
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.
An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA
NASA Technical Reports Server (NTRS)
Djomehri, M. Jahed; Erickson, Larry L.
1994-01-01
A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.
Solving Quadratic Equations by Factoring
NSDL National Science Digital Library
2012-08-06
This video explains how to solve quadratic equations with the factoring method. In 4 minutes 23 seconds, the two narrators explain in detail the steps required. Additionally, how these equations relate to objects and events in the real world such as roller coasters is covered.
Water and other tetrahedral liquids: order, anomalies and solvation
NASA Astrophysics Data System (ADS)
Shadrack Jabes, B.; Nayar, Divya; Dhabal, Debdas; Molinero, Valeria; Chakravarty, Charusita
2012-07-01
In order to understand the common features of tetrahedral liquids with water-like anomalies, the relationship between local order and anomalies has been studied using molecular dynamics simulations for three categories of such liquids: (a) atomistic rigid-body models for water (TIP4P, TIP4P/2005, mTIP3P, SPC/E), (b) ionic melts, BeF2 (TRIM model) and SiO2 (BKS potential) and (c) Stillinger-Weber liquids parametrized to model water (mW) and silicon. Rigid-body, atomistic models for water and the Stillinger-Weber liquids show a strong correlation between tetrahedral and pair correlation order and the temperature for the onset of the density anomaly is close to the melting temperature. In contrast, the ionic melts show weaker and more variable degrees of correlation between tetrahedral and pair correlation metrics, and the onset temperature for the density anomaly is more than twice the melting temperature. In the case of water, the relationship between water-like anomalies and solvation is studied by examining the hydration of spherical solutes (Na+, Cl-, Ar) in water models with different temperature regimes of anomalies (SPC/E, TIP4P and mTIP3P). For both ionic and nonpolar solutes, the local structure and energy of water molecules is essentially the same as in bulk water beyond the second-neighbour shell. The local order and binding energy of water molecules are not perturbed by the presence of a hydrophobic solute. In the case of ionic solutes, the perturbation is largely localized within the first hydration shell. The binding energies for the ions are strongly dependent on the water models and clearly indicate that the geometry of the partial charge distributions, and the associated multipole moments, play an important role. However the anomalous behaviour of the water network has been found to be unimportant for polar solvation.
Water and other tetrahedral liquids: order, anomalies and solvation.
Jabes, B Shadrack; Nayar, Divya; Dhabal, Debdas; Molinero, Valeria; Chakravarty, Charusita
2012-07-18
In order to understand the common features of tetrahedral liquids with water-like anomalies, the relationship between local order and anomalies has been studied using molecular dynamics simulations for three categories of such liquids: (a) atomistic rigid-body models for water (TIP4P, TIP4P/2005, mTIP3P, SPC/E), (b) ionic melts, BeF(2) (TRIM model) and SiO(2) (BKS potential) and (c) Stillinger-Weber liquids parametrized to model water (mW) and silicon. Rigid-body, atomistic models for water and the Stillinger-Weber liquids show a strong correlation between tetrahedral and pair correlation order and the temperature for the onset of the density anomaly is close to the melting temperature. In contrast, the ionic melts show weaker and more variable degrees of correlation between tetrahedral and pair correlation metrics, and the onset temperature for the density anomaly is more than twice the melting temperature. In the case of water, the relationship between water-like anomalies and solvation is studied by examining the hydration of spherical solutes (Na(+), Cl(-), Ar) in water models with different temperature regimes of anomalies (SPC/E, TIP4P and mTIP3P). For both ionic and nonpolar solutes, the local structure and energy of water molecules is essentially the same as in bulk water beyond the second-neighbour shell. The local order and binding energy of water molecules are not perturbed by the presence of a hydrophobic solute. In the case of ionic solutes, the perturbation is largely localized within the first hydration shell. The binding energies for the ions are strongly dependent on the water models and clearly indicate that the geometry of the partial charge distributions, and the associated multipole moments, play an important role. However the anomalous behaviour of the water network has been found to be unimportant for polar solvation. PMID:22739063
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.
uv Studies of Tetrahedral Bonding in Diamondlike Amorphous Carbon
Merkulov, V.I.; Lannin, J.S. [Department of Physics, Penn State University, University Park, Pennsylvania 16802 (United States)] [Department of Physics, Penn State University, University Park, Pennsylvania 16802 (United States); Munro, C.H.; Asher, S.A. [Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (United States)] [Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (United States); Veerasamy, V.S.; Milne, W.I. [Engineering Department, University of Cambridge, Cambridge CB2 1PZ (United Kingdom)] [Engineering Department, University of Cambridge, Cambridge CB2 1PZ (United Kingdom)
1997-06-01
We report ultraviolet (uv) Raman scattering studies of hydrogen-free, diamondlike amorphous carbon thin films with a wide range of tetrahedral bonding. The uv Raman spectra are shown to provide direct evidence for the presence of sp{sup 3}-bonded C atoms in these materials. The experimental results are found to be in excellent agreement with theoretical predictions and contribute to an improved understanding of the mechanism by which the diamondlike fraction develops within the amorphous carbon network. {copyright} {ital 1997} {ital The American Physical Society}
Quadratic Optimization Problems Arising in Computer Vision
Gallier, Jean
Quadratic Optimization Problems Arising in Computer Vision Jean Gallier Special Thanks to Jianbo a fundamental problem. Unfortunately, I proved Jean Gallier (Upenn) Quadratic Optimization Problems March 23. Jean Gallier (Upenn) Quadratic Optimization Problems March 23, 2011 2 / 61 #12;Perverse Cohomology
Quadratic Optimization Problems Arising in Computer Vision
Gallier, Jean
Quadratic Optimization Problems Arising in Computer Vision Jean Gallier Special Thanks to Jianbo a fundamental problem. Unfortunately, I proved Jean Gallier (Upenn) Quadratic Optimization Problems March 23. Jean Gallier (Upenn) Quadratic Optimization Problems March 23, 2011 2 / 78 #12;Perverse Cohomology
Quadratic bosonic and free white noises
Piotr Sniady
2003-03-20
We discuss the meaning of renormalization used for deriving quadratic bosonic commutation relations introduced by Accardi and find a representation of these relations on an interacting Fock space. Also, we investigate classical stochastic processes which can be constructed from noncommutative quadratic white noise. We postulate quadratic free white noise commutation relations and find their representation on an interacting Fock space.
A Quadratic Programming Bibliography - Optimization Online
2001-02-27
Feb 27, 2001 ... quadratic programming methods for nonlinear programming, nor to those on ... system of the quadratic programming problem by an approximate system of smaller rank. ..... predictive control via multiparametric quadratic programming. ...... This paper presents a neural-network computational scheme with ...
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 Â· a is a quadratic residue mod m if x2 = a (mod m). Otherwise
Transport properties of tetrahedral, network-forming ionic melts.
Agarwal, Manish; Ganguly, Abir; Chakravarty, Charusita
2009-11-19
Molecular dynamics simulations of liquid silica and beryllium fluoride are performed using the van Beest-Kramer-van Santen and transferable rigid ion model potentials, respectively, in order to compare transport properties. The ionic conductivity (sigma), shear viscosity (eta) and ionic self-diffusivities (D(+/-)) are computed over a fairly wide range of temperatures and densities and deviations from Arrhenius behavior along different isochores is studied. The Stokes-Einstein relation is shown to hold over the entire range of state points, though the effective hydrodynamic radius shows small variations due to thermal fluctuations, compression, and local tetrahedral order. Several alternative tests of the Nernst-Einstein relation are implemented which show that significant network-formation in the anomalous regime leads to a breakdown of this relationship. The relaxation times, tau(sigma) and tau(M), associated with the decay of the charge-flux and pressure ACFs respectively, are computed. In the anomalous regime, as the tetrahedral network formation progresses, tau(M) increases rapidly while tau(sigma) shows very little variation, indicating a decoupling of charge and momentum transport processes. PMID:19860439
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 Zeeman effect in positronium
G. Feinberg; A. Rich; J. Sucher
1990-01-01
The orbital muL.B and diamagnetic A2 interactions of electrons and positrons with an external magnetic field lead to a small quadratic Zeeman shift in the L=0, mS=+\\/-1 states of positronium, which, unlike the mS=0 states, are not affected by the usual, spin-induced Zeeman shifts. For the n=1 states, this shift would be about 2 kHz in a field of 1000
Quadratic Optimization of Impedance Control
Rolf Johansson; Mark W. Spong
1994-01-01
This paper presents algorithms for continuous-time quadratic optimization of impedance control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are found by solving an algebraic matrix equation. System stability is investigated according to Lyapunov function theory, and it is shown that global asymptotic stability holds. The solution results in design parameters in the form of square
Shan, Xiao; Connor, J N L
2012-11-26
A previous paper by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392) reported the surprising result that four simple parametrized S matrices can reproduce the forward-angle glory scattering of the H + D(2)(v(i)=0,j(i)=0) ? HD(v(f)=3,j(f)=0) + D reaction, whose differential cross section (DCS) had been computed in a state-of-the-art scattering calculation for a state-of-the-art potential energy surface. Here, v and j are vibrational and rotational quantum numbers, respectively, and the translational energy is 1.81 eV. This paper asks the question: Can we replace the analytic functions (of class C(?)) used by Shan-Connor with simpler mathematical functions and still reproduce the forward-angle glory scattering? We first construct S matrix elements (of class C(0)) using a quadratic phase and a piecewise-continuous pre-exponential factor consisting of three pieces. Two of the pieces are constants, with one taking the value N (a real normalization constant) at small values of the total angular momentum number, J; the other piece has the value 0 at large J. These two pieces are joined at intermediate values of J by either a straight line, giving rise to the linear parametrization (denoted param L), or a quadratic curve, which defines the quadratic parametrization (param Q). We find that both param L and param Q can reproduce the glory scattering for center-of-mass reactive scattering angles, ?(R) ? 30°. Second, we use a piecewise-discontinuous pre-exponential factor and a quadratic phase, giving rise to a step-function parametrization (param SF) and a top-hat parametrization (param TH). We find that both param SF and param TH can reproduce the forward-angle scattering, even though these class C(-1) parametrizations are usually considered too simplistic to be useful for calculations of DCSs. We find that an ultrasimplistic param THz, which is param TH with a phase of zero, can also reproduce the glory scattering at forward angles. The S matrix elements for param THz are real and consist of five nonzero equal values, given by S(J) = 0.02266, for the window, J = 21(1)25. Param THz is sufficiently simple that we can derive closed forms for the partial wave scattering amplitude, f(?(R)), and the near-side (N) and far-side (F) subamplitudes. We show that window representations of f(?(R)) provide important insights into the range of J values that contribute to the reaction dynamics. Other theoretical techniques used are NF theory for the analysis of DCSs and full and NF local angular momentum theory, in both cases including up to three resummations of f(?(R)) before making the NF decomposition. Finally, we investigate the accuracy of various semiclassical glory theories for the DCS of param L. By varying one phase parameter for param L, we show that the uniform semiclassical approximation is accurate from ?(R) = 0° to close to ?(R) = 180°. Our approach is an example of a "weak" form of Heisenberg's S matrix program, which does not use a potential energy surface(s); rather it focuses on the properties of the S matrix. Our method is easy to apply to DCSs from experimental measurements or from computer simulations. PMID:22876759
Quadratic algebra contractions and 2nd order superintegrable systems
Ernest G. Kalnins; Willard Miller Jr
2014-01-04
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces we show that the free quadratic algebras generated by the 1st and 2nd order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.
Diamagnetic Anisotropy of Silicates Composed of Tetrahedral Networks
NASA Astrophysics Data System (ADS)
Uyeda, Chiaki; Ohtawa, Kouichi; Okita, Kazuyuki
2000-04-01
Small diamagnetic anisotropy, (??) DIA, on the order of 10-9 to 10-10 emu/g was detected for four silicates by the use of the field-induced harmonic-oscillation method in the high-temperature region. The measured ??-T relations were effective to separate the ?? component caused by the paramagnetic impurity ions. The obtained maximum (??) DIA values between two magnetic principal axes are (2.1±0.1)×10-9 emu/g [b-a axes] for orthoclase, (3.5±0.1)×10-9 emu/g [b-a axes] for petalite, (0.8±0.1)×10-9 emu/g [a-c axes] for scapolite and (3.8±0.1)×10-9 emu/g [a-c axes] for apophyllite. The (Si,Al)O4 tetrahedral frameworks composing the crystal structures of the silicates are considered to be the origin of the observed (??) DIA values.
Grid-characteristic method on unstructured tetrahedral meshes
NASA Astrophysics Data System (ADS)
Muratov, M. V.; Petrov, I. B.; Sannikov, I. V.; Favorskaya, A. V.
2014-05-01
The goal of this paper is to develop a grid-characteristic method intended for high-performance computer systems and implemented on unstructured tetrahedral hierarchical meshes with the use of a multiple time step and high-order interpolation, including interpolation with a limiter, piecewise parabolic interpolation, and monotone interpolation. The method is designed for simulating complex three-dimensional dynamical processes in heterogeneous media. It involves accurately stated contact conditions and produces physically correct solutions of problems in seismology and seismic exploration. Hierarchical meshes make it possible to take into account numerous inhomogeneous inclusions (cracks, cavities, etc.) and to solve problems in a real-life formulation. The grid-characteristic method enables the use of a multiple time step. As a result, the computation time is considerably reduced and the efficiency of the method is raised. The method is parallelized on a computer cluster with an optimal use of system resources.
Nuclear Tetrahedral Symmetry: Possibly Present Throughout the Periodic Table
J. Dudek; A. Gozdz; N. Schunck; M. Miskiewicz
2002-05-21
More than half a century after the fundamental, spherical shell structure in nuclei has been established, theoretical predictions indicate that the shell-gaps comparable or even stronger than those at spherical shapes may exist. Group-theoretical analysis supported by realistic mean-field calculations indicate that the corresponding nuclei are characterized by the $T_d^D$ ('double-tetrahedral') group of symmetry, exact or approximate. The corresponding strong shell-gap structure is markedly enhanced by the existence of the 4-dimensional irreducible representations of the group in question and consequently it can be seen as a geometrical effect that does not depend on a particular realization of the mean-field. Possibilities of discovering the corresponding symmetry in experiment are discussed.
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…
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
A Streaming Language Implementation of the Discontinuous Galerkin Finite Element Method
Dally, William J.
StreamFEM A Streaming Language Implementation of the Discontinuous Galerkin Finite Element Method(MHD)Linear(Euler)Linear(MHD) Quadratic(Euler) Quadratic(MHD)Cubic(Euler)Cubic(MHD) Element Type (Equation Type) Sustained GFLOPS LRF BW(MHD)Linear(Euler)Linear(MHD)Quadratic(Euler)Quadratic(MHD) Cubic(Euler) Cubic(MHD) Element Type (Equation Type) Sustained GFLOPS Ops / mem access A DG Finite
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)
RELIABLE SOLUTION OF CONVEX QUADRATIC PROGRAMS ...
2011-01-28
Key words. active set, convex, homotopy method, parametric quadratic programming ... impluse response design, optimal power flow, economic dispatch, etc. Several ... *Interdisciplinary Center for Scientific Computing, Heidelberg University, ...
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. Â· 4x2 - 3xy - 2y2 + x - y + 6 = 0 is a quadratic equation, as are x2 - y2 = 0 and x2 + y2 = 0 and x2 - 1 = 0
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
Quadratic Zeeman effect in positronium
Feinberg, G. (Department of Physics, Columbia University, New York, New York 10027 (USA)); Rich, A. (Department of Physics, University of Michigan, Ann Arbor, Michigan 48109 (USA)); Sucher, J. (Department of Physics, University of Maryland, College Park, Maryland 20742 (USA) Astronomy, University of Maryland, College Park, Maryland 20742 (USA))
1990-04-01
The orbital {mu}{sub {ital L}}{center dot}{ital B} and diamagnetic {ital A}{sup 2} interactions of electrons and positrons with an external magnetic field lead to a small quadratic Zeeman shift in the {ital L}=0, {ital m}{sub {ital S}}={plus minus}1 states of positronium, which, unlike the {ital m}{sub {ital S}}=0 states, are not affected by the usual, spin-induced Zeeman shifts. For the {ital n}=1 states, this shift would be about 2 kHz in a field of 1000 G. These additional shifts are the same in all spin states for {ital L}=0 but do depend on {ital n}.
Single-photon quadratic optomechanics
Liao, Jie-Qiao; Nori, Franco
2014-01-01
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. PMID:25200128
Quadratic Equations: From Factored to Standard Form
NSDL National Science Digital Library
2011-01-01
This activity leads students to understand the utility in the factored form of a quadratic equation. Students then express quadratic equations in standard form in the corresponding factored form. The activity is concluded with four critical-thinking questions. website: http://www.mathedpage.org/ copyright information: http://www.mathedpage.org/rights.html
Binary Quadratic Forms: A Historical View
ERIC Educational Resources Information Center
Khosravani, Azar N.; Beintema, Mark B.
2006-01-01
We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…
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 stability with real and complex perturbations
A. Packard; J. Doyle
1990-01-01
It is shown that the equivalence between real and complex perturbations in the context of quadratic stability to linear, fractional, unstructured perturbations does not hold when the perturbations are block structured. For a limited class of problems, quadratic stability in the face of structured complex perturbations is equivalent to a particular class of scaled norms, and hence appropriate synthesis techniques,
Natural frequency of uniform and optimized tetrahedral truss platforms
NASA Technical Reports Server (NTRS)
Wu, K. Chauncey; Lake, Mark S.
1994-01-01
Qualitative and quantitative estimates for the fundamental frequency of uniform and optimized tetrahedral truss platforms are determined. A semiempirical equation is developed for the frequency of free-free uniform trusses as a function of member material properties, truss dimensions, and parasitic (nonstructural) mass fraction Mp/Mt. Optimized trusses with frequencies approximately two times those of uniform trusses are determined by varying the cross-sectional areas of member groups. Trusses with 3 to 8 rings, no parasitic mass, and member areas up to 25 times the minimum area are optimized. Frequencies computed for ranges of both Mp/Mt and the ratio of maximum area to minimum area are normalized to the frequency of a uniform truss with no parasitic mass. The normalized frequency increases with the number of rings, and both frequency and the ratio of maximum area to minimum area decrease with increasing Mp/Mt. Frequency improvements that are achievable with a limited number of member areas are estimated for a 3-ring truss by using Taguchi methods. Joint stiffness knockdown effects are also considered. Comparison of optimized and baseline uniform truss frequencies indicates that tailoring can significantly increase structural frequency; maximum gains occur for trusses with low values of Mp/Mt. This study examines frequency trends for ranges of structural parameters and may be used as a preliminary design guide.
Ikenaga, Bruce
is a root of a quadratic equation with integer coefficients. Â· 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
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)
Lu Yongming; Lan Yaqian; Xu Yanhong [Institute of Functional Material Chemistry, Key Laboratory of Polyoxometalate Science of Ministry of Education, Faculty of Chemistry, Northeast Normal University, Changchun 130024 (China); Su Zhongmin, E-mail: zmsu@nenu.edu.c [Institute of Functional Material Chemistry, Key Laboratory of Polyoxometalate Science of Ministry of Education, Faculty of Chemistry, Northeast Normal University, Changchun 130024 (China); Li Shunli, E-mail: lishunli@yahoo.c [Institute of Functional Material Chemistry, Key Laboratory of Polyoxometalate Science of Ministry of Education, Faculty of Chemistry, Northeast Normal University, Changchun 130024 (China); Zang Hongying; Xu Guangjuan [Institute of Functional Material Chemistry, Key Laboratory of Polyoxometalate Science of Ministry of Education, Faculty of Chemistry, Northeast Normal University, Changchun 130024 (China)
2009-11-15
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){sub 0.5}(L{sup 1})] (1), [Cd(bpib){sub 0.5}(L{sup 2})].H{sub 2}O (2), [Cd(bpib){sub 0.5}(L{sup 3})] (3) and [Cd(bib){sub 0.5}(L{sup 1})] (4), where bpib=1,4-bis(2-(pyridin-2-yl)-1H-imidazol-1-yl)butane, bib=1,4-bis(1H-imidazol-1-yl)butane, H{sub 2}L{sup 1}=4-(4-carboxybenzyloxy)benzoic acid, H{sub 2}L{sup 2}=4,4'-(ethane-1,2-diylbis(oxy))dibenzoic acid and H{sub 2}L{sup 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 alpha-Po topological nets with different degrees of interpenetration based on the similar octahedral [Cd{sub 2}(-COO){sub 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 alpha-Po topological nets. And the luminescent properties of these compounds have been investigated in detail. - Graphical abstract: A series of three-dimensional interpenetrating metal-organic frameworks based on different polygons or polyhedra has been synthesized. The crystal structures and topological analysis of these compounds, along with a systematic investigation of the relationship between topological types and molecular building blocks, will be discussed.
Magnetoelectronic properties of Gd-implanted tetrahedral amorphous carbon
NASA Astrophysics Data System (ADS)
Zeng, Li; Zutz, H.; Hellman, F.; Helgren, E.; Ager, J. W., III; Ronning, C.
2011-10-01
The structural, electronic, magnetic, and magnetoelectronic properties of tetrahedral amorphous carbon (ta-C) thin films doped with gadolinium via ion implantation (ta-C1-x:Gdx, x = 0.02 ˜ 0.20) have been studied, both as prepared and after annealing, with Xe-implanted samples as control samples. Gd implantation causes significant increases in electrical conductivity, showing that Gd adds carriers as in other rare earth-semiconductor systems. Gd also provides a large local moment from its half-filled f shell. Carrier-mediated Gd-Gd interactions are strong but very frustrated, causing a spin-glass state < 10 K for higher x. An enormous negative magnetoresistance (about -103 at 3 K in a 70-kOe field for x = 0.088) is observed at low T (<30 K), an indication of carrier-moment interactions that cause magnetic disorder-induced localization and consequent magnetic field-induced delocalization as Gd moments align with the magnetic field. Gd implantation causes substantial changes in Raman intensity, associated with conversion of C-C bonds into Raman inactive bonds, which induce further graphitization after annealing. The changing nature of the C-C bonding with increasing x or with annealing causes the electrical transport properties to depend on Gd concentration x with a nonmonotonic dependence. Systematic but nonmonotonic trends are seen on comparing the magnetic and magnetotransport properties of Gd-doped a-C, a-Si, and a-Ge matrices, suggesting that electron concentration and band gap play separate important roles.
Schwarz and multilevel methods for quadratic spline collocation
Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
Ken-ichiro Arita; Yasunori Mukumoto
2014-05-09
Shell structures in single-particle energy spectra are investigated against regular tetrahedral type deformation using radial power-law potential model. Employing a natural way of shape parametrization which interpolates sphere and regular tetrahedron, we find prominent shell effects at rather large tetrahedral deformations, which bring about shell energies much larger than the cases of spherical and quadrupole type shapes. We discuss the semiclassical origin of these anomalous shell structures using periodic orbit theory.
ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS
. 2.Essential dimension Let k be a field. We will write Fieldskfor the category of field extensions ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS PATRICK BROSNANy, ZINOVY REICHSTEINy, AND ANGELO VISTOLIz Abstract. We prove that the essential
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)
PRIMES AND QUADRATIC RECIPROCITY ANGELICA WONG
May, J. Peter
PRIMES AND QUADRATIC RECIPROCITY ANGELICA WONG Abstract. We discuss number theory with the ultimate xi yp-i . It suffices to show that each term of the expansion Date: August 11, 2008. 1 #12;2 ANGELICA
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,…
REAL SYMMETRIC QUADRATIC MODEL UPDATING THAT PRESERVES POSITIVE DEFINITENESS AND NO SPILL-OVER
, electrical oscillation, vibro-acoustics, fluid dynamics, signal processing, and finite element model of some polynomials in general and quadratic eigenvalue problems (QEP) in particular can be found in the seminal books of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543. (matchudl
NLPQLP: A Fortran Implementation of a Sequential Quadratic Programming Algorithm with Distributed
Schittkowski, Klaus
problem collection of Bongartz et al. [8]. About 80 test problems based on a Finite Element formulationNLPQLP: A Fortran Implementation of a Sequential Quadratic Programming Algorithm with Distributed.schittkowski@uni-bayreuth.de Web: http://www.klaus-schittkowski.de Date: May, 2010 Abstract The Fortran subroutine NLPQLP solves
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.
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.
Tetrahedral-mesh-based computational human phantom for fast Monte Carlo dose calculations
NASA Astrophysics Data System (ADS)
Yeom, Yeon Soo; Jeong, Jong Hwi; Han, Min Cheol; Kim, Chan Hyeong
2014-06-01
Although polygonal-surface computational human phantoms can address several critical limitations of conventional voxel phantoms, their Monte Carlo simulation speeds are much slower than those of voxel phantoms. In this study, we sought to overcome this problem by developing a new type of computational human phantom, a tetrahedral mesh phantom, by converting a polygonal surface phantom to a tetrahedral mesh geometry. The constructed phantom was implemented in the Geant4 Monte Carlo code to calculate organ doses as well as to measure computation speed, the values were then compared with those for the original polygonal surface phantom. It was found that using the tetrahedral mesh phantom significantly improved the computation speed by factors of between 150 and 832 considering all of the particles and simulated energies other than the low-energy neutrons (0.01 and 1 MeV), for which the improvement was less significant (17.2 and 8.8 times, respectively).
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
Edge element computations of eddy currents in laminated materials
Yueqiang Liu; A. Bondeson; R. Bergstrom; M. G. Larson; K. Samuelsson
2003-01-01
We studied different types of edge elements in three-dimensional computations of power dissipation in laminated conductors. The standard, lowest order (mixed first and zeroth order) basis on tetrahedral grids produces inaccurate results and grossly overestimates the losses. However, on hexahedral grids, aligned with the laminations, the standard edge elements give much more accurate results. If the grid cannot be aligned
On the relation between hydrogen bonds, tetrahedral order and molecular mobility in model water
NASA Astrophysics Data System (ADS)
Pereyra, Rodolfo Guillermo; Bermúdez di Lorenzo, Aleida J.; Malaspina, David C.; Carignano, Marcelo A.
2012-06-01
We studied by molecular dynamics simulations the relation existing between the lifetime of hydrogen bonds, the tetrahedral order and the diffusion coefficient of model water. We tested four different models: SPC/E, TIP4P-Ew, TIP5P-Ew and Six-Site, these last two having sites explicitly resembling the water lone pairs. While all the models perform reasonably well at ambient conditions, their behavior is significantly different for temperatures below 270 K. The models with explicit lone-pairs have a longer hydrogen bond lifetime, a better tetrahedral order and a smaller diffusion coefficient than the models without them.
Tetrahedral occupancy in the Pd-D system observed by in situ neutron powder diffraction
NASA Astrophysics Data System (ADS)
Pitt, M. P.; MacA. Gray, E.
2003-11-01
The crystallography of the Pd-Dx system has been studied by in situ neutron powder diffraction at 309 °C, in the supercritical region, and, after quenching in the pure ? phase to 50 °C, in the two-phase region at 50 °C. Rietveld profile analysis of the supercritical diffraction patterns showed that 14% of D interstitials were occupying tetrahedral interstices, in sharp contrast to previous studies at lower temperatures. Tetrahedral occupancy was maintained through the two-phase region at 50 °C. These results are discussed in the light of first-principles total-energy calculations of hydrogen states in palladium.
Instabilities of quadratic band crossing points
NASA Astrophysics Data System (ADS)
Uebelacker, Stefan; Honerkamp, Carsten
2011-03-01
The variation of the orbital composition of bands around band crossing points near the Fermi level can generate interesting effects. In particular, rather simple interactions can give rise to the spontaneous formation of topological insulating phases (S. Raghu et al., Phys. Rev. Lett. 100, 156401 (2008)). In contrast with Dirac points, quadratic band crossing points offer the advantage of a nonzero density of states at the crossing point, and instabilities occur already at small interaction strengths. Here, we present results of functional renormalization group calculations for models with a quadratic band crossing point and discuss the possibilities for nontrivial insulating phases induced by local interactions.
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.
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.
A Streaming Language Implementation of the Discontinuous Galerkin Finite Element Method
Dally, William J.
StreamFEM A Streaming Language Implementation of the Discontinuous Galerkin Finite Element Method(MHD)Linear(Euler)Linear(MHD)Quadratic(Euler)Quadratic(MHD) Cubic(Euler) Cubic(MHD) Element Type (Equation Type) Sustained GFLOPS Ops / mem access A DG Finite Element Method for Conservation Laws Â·Scalar Advection (1 PDE) Â·Euler Equations (4 PDEs
Formation of pyramid elements for hexahedra to tetrahedra transitions
OWEN,STEVEN J.; SAIGAL,SUNIL
2000-02-24
New algorithms are proposed for the modification of a mixed hexahedra-tetrahedra element mesh to maintain compatibility by the insertion of pyramid elements. Several methods for generation of the pyramids are presented involving local tetrahedral transformations and/or node insertion near the hex/tet interface. Local smoothing and topological operations improve the quality of the transition region. Results show superior performance of the resulting elements in a commercial finite element code over non-conforming interface conditions.
Cyclotomic Matrices over Quadratic Integer Rings
Sheldon, Nathan D.
Cyclotomic Matrices over Quadratic Integer Rings Gary Greaves Thesis submitted to the University's problem is usually stated in terms of a geometric constraint on the zeros of polynomials having integer integer symmetric matrix A we define its associated polynomial as RA(z) := zn A(z + 1/z). A Hermitian
Copositivity and constrained fractional quadratic problems
2011-11-16
The lower bounds based on this technique can be favorably com- pared with bounds ... pendent term, then this problem can be formulated as a fractional quadratic program ...... as a similar rational grid will contain an exponential in n number of points, if, e.g., T .... Furthermore, by Euler's homogeneity theorem,. 0=¯
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…
Factoring pq2 with Quadratic Forms
Nguyen, Phong Q.
is exactly the case for the so-called NICE family of public-key cryptosystems based on quadratic fields [OU98], Takagi's fast RSA variants [Tak98], and the large family (surveyed in [BTV04 s with s squarefree) is a classical problem in algorithmic number theory (cf. [AM94]), because it is polynomial
Factoring pq2 with Quadratic Forms
Boyer, Edmond
is exactly the case for the so-called NICE family of public-key cryptosystems based on quadratic fields [OU98], Takagi's fast RSA variants [Tak98], and the large family (surveyed in [BTV04 (cf. [AM94]), because it is polynomial-time equivalent to determining the ring of integers of a number
Instabilities of quadratic band crossing points
Stefan Uebelacker; Carsten Honerkamp
2011-01-01
The variation of the orbital composition of bands around band crossing points near the Fermi level can generate interesting effects. In particular, rather simple interactions can give rise to the spontaneous formation of topological insulating phases (S. Raghu et al., Phys. Rev. Lett. 100, 156401 (2008)). In contrast with Dirac points, quadratic band crossing points offer the advantage of a
Fuzzy quadratic minimum spanning tree problem
Lu, Mei
Fuzzy quadratic minimum spanning tree problem Jinwu Gao *, Mei Lu Department of Mathematical the effectiveness of the genetic algorithm. Ã? 2004 Published by Elsevier Inc. Keywords: Minimum spanning tree; Fuzzy programming; Genetic algorithm; Credibility measure 1. Introduction The minimum spanning tree (MST) problem
1 Splitting Patterns of Excellent Quadratic Forms
Rehmann, Ulf
is infinite or a power of 2, an* *d that fields exist having a prescribed power of 2 as its level (cf. 3 that a generic splitting fie* *ld of such an algebra D splits precisely those division algebras which represent * * 2 which occur for the quadratic forms qL := q L with L running through all fie* *ld extensions
ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS
Brosnan, Patrick
. Fakhruddin for helpful correspondence. 2. Essential dimension Let k be a field. We will write Fieldsk write ed G for ed FG and ed(G; p) for ed(FG; p). Essential dimension was originally introducedESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS PATRICK BROSNAN , ZINOVY REICHSTEIN
ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS
ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS PATRICK BROSNAN + , ZINOVY REICHSTEIN + , AND ANGELO VISTOLI # Abstract. We prove that the essential dimension of the spinor group Spin n grows of classes of evenÂdimensional forms in W(K); cf. [Lam73]. By abuse of notation, we will write q # I a (K
EFFICIENT AND CHEAP BOUNDS FOR (STANDARD) QUADRATIC ...
2005-07-08
The main tools employed in the conception and analysis of most bounds are ... objective function into a sum of two quadratic functions, each of which is easy to minimize. ...... Now let us take a fresh look at vertex optimality. As before, we start.
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.
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.
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
Quadratic trend analysis and heartbeat detection
Stefan Wiens; Stephen N. Palmer
2001-01-01
In heartbeat detection tasks based on the Method of Constant Stimuli (MCS), subjects judge the simultaneity between their heartbeats and stimuli presented at six intervals ranging from 0 to 500 ms after the R-waves on an electrocardiogram. Because research suggests that subjects do not perceive stimuli at 0 or 500 ms as simultaneous, individual performance was indexed with quadratic trend
Decision making with fuzzy quadratic programming
W. Cui; D. I. Blockley
1990-01-01
Decision making in civil engineering systems necessarily involves imprecise data. Fuzzy linear programming (FLP) has been used to deal with imprecision in parameter definitions. In this paper, it is argued that present methods of FLP can be improved upon by using a new method of fuzzy quadratic programming (FQP) which enables the modelling of independent fuzzy parameters. Several numerical examples
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
Semiclassical mechanics of the quadratic Zeeman effect
Kristin D. Krantzman; John A. Milligan; D. Farrelly
1992-01-01
A comprehensive approach to semiclassical quantization of the quadratic Zeeman effect in the hydrogen atom (QZE) is presented which utilizes the connection between the Kepler system and the four-dimensional harmonic oscillator. Past attempts to quantize the QZE have encountered problems associated with singularities arising because of a classical separatrix. Here, a uniform semiclassical quantization scheme that passes smoothly through the
EMBEDDABILITY OF QUADRATIC FORMS IN PFISTER FORMS
Âembeddable over F (resp. over an extension of F ; resp. over a purely transcendental extension of F ). We study transcendental extension of the field F . As an application, we show that for certain ``generic'' quadratic forms transcendental, and anisotropic forms stay anisotropic over purely transcendental extensions, hence W (F (#)/F
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.
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.
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.
Lattice thermal expansion for normal tetrahedral compound semiconductors
Omar, M.S. [Department of Physics, College of Science, University of Salahaddin, Arbil, Iraqi Kurdistan (Iraq)]. E-mail: dr_m_s_omar@yahoo.com
2007-02-15
The cubic root of the deviation of the lattice thermal expansion from that of the expected value of diamond for group IV semiconductors, binary compounds of III-V and II-VI, as well as several ternary compounds from groups I-III-VI{sub 2}, II-IV-V{sub 2} and I-IV{sub 2}V{sub 3} semiconductors versus their bonding length are given straight lines. Their slopes were found to be 0.0256, 0.0210, 0.0170, 0.0259, 0.0196, and 0.02840 for the groups above, respectively. Depending on the valence electrons of the elements forming these groups, a formula was found to correlate all the values of the slopes mentioned above to that of group IV. This new formula which depends on the melting point and the bonding length as well as the number of valence electrons for the elements forming the compounds, will gives best calculated values for lattice thermal expansion for all compounds forming the groups mentioned above. An empirical relation is also found between the mean ionicity of the compounds forming the groups and their slopes mentioned above and that gave the mean ionicity for the compound CuGe{sub 2}P{sub 3} in the range of 0.442.
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. PMID:25747072
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.
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.
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
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
Tetrahedral occupancy in the Pd-D system observed by in situ neutron powder diffraction
M. P. Pitt; E. Mac A. Gray
2003-01-01
The crystallography of the Pd-Dx system has been studied by in situ neutron powder diffraction at 309 °C, in the supercritical region, and, after quenching in the pure beta phase to 50 °C, in the two-phase region at 50 °C. Rietveld profile analysis of the supercritical diffraction patterns showed that 14% of D interstitials were occupying tetrahedral interstices, in sharp
Tetrahedral occupancy in the Pd-D system observed by in situ neutron powder diffraction
M. P. Pitt; E. Mac A. Gray
2003-01-01
The crystallography of the Pd-Dx system has been studied by in situ neutron powder diffraction at 309 °C, in the supercritical region, and, after quenching in the pure ? phase to 50 °C, in the two-phase region at 50 °C. Rietveld profile analysis of the supercritical diffraction patterns showed that 14% of D interstitials were occupying tetrahedral interstices, in sharp
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…
Aging of Tetrahedral Structure in a Lennard-Jones Glass1 Gianguido C. CIANCI2
Weeks, Eric R.
Aging of Tetrahedral Structure in a Lennard-Jones Glass1 Gianguido C. CIANCI2 and Eric R. WEEKS3,4 Summary We study the aging of a glassy Lennard-Jones binary mixture with molecular dy- namics simulations. We follow the evolution of the packing as a function of the system's age tw, the time passed since
Mixed-metal chalcogenide tetrahedral clusters with an exo-polyhedral metal fragment.
Yuvaraj, K; Roy, Dipak Kumar; Anju, V P; Mondal, Bijnaneswar; Varghese, Babu; Ghosh, Sundargopal
2014-12-01
The reaction of metal carbonyl compounds with group 6 and 8 metallaboranes led us to report the synthesis and structural characterization of several novel mixed-metal chalcogenide tetrahedral clusters. Thermolysis of arachno-[(Cp*RuCO)2B2H6], 1, and [Os3(CO)12] in the presence of 2-methylthiophene yielded [Cp*Ru(CO)2(?-H){Os3(CO)9}S], 3, and [Cp*Ru(?-H){Os3(CO)11}], 4. In a similar fashion, the reaction of [(Cp*Mo)2B5H9], 2, with [Ru3(CO)12] and 2-methylthiophene yielded [Cp*Ru(CO)2(?-H){Ru3(CO)9}S], 5, and conjuncto-[(Cp*Mo)2B5H8(?-H){Ru3(CO)9}S], 6. Both compounds 3 and 5 can be described as 50-cve (cluster valence electron) mixed-metal chalcogenide clusters, in which a sulfur atom replaces one of the vertices of the tetrahedral core. Compounds 3 and 5 possess a [M3S] tetrahedral core, in which the sulfur is attached to an exo-metal fragment, unique in the [M3S] metal chalcogenide tetrahedral arrangements. All the compounds have been characterized by mass spectrometry, IR, and (1)H, (11)B and (13)C NMR spectroscopy in solution, and the solid state structures were unequivocally established by crystallographic analysis of compounds 3, 5 and 6. PMID:25317933
Automated Tetrahedral Mesh Generation for CFD Analysis of Aircraft in Conceptual Design
NASA Technical Reports Server (NTRS)
Ordaz, Irian; Li, Wu; Campbell, Richard L.
2014-01-01
The paper introduces an automation process of generating a tetrahedral mesh for computational fluid dynamics (CFD) analysis of aircraft configurations in early conceptual design. The method was developed for CFD-based sonic boom analysis of supersonic configurations, but can be applied to aerodynamic analysis of aircraft configurations in any flight regime.
NASA Technical Reports Server (NTRS)
Gnoffo, Peter A.
2009-01-01
The quality of simulated hypersonic stagnation region heating on tetrahedral meshes is investigated by using a three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. Two test problems are investigated: hypersonic flow over a three-dimensional cylinder with special attention to the uniformity of the solution in the spanwise direction and hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problem provides a sensitive test for algorithmic effects on heating. This investigation is believed to be unique in its focus on three-dimensional, rotated upwind schemes for the simulation of hypersonic heating on tetrahedral grids. This study attempts to fill the void left by the inability of conventional (quasi-one-dimensional) approaches to accurately simulate heating in a tetrahedral grid system. Results show significant improvement in spanwise uniformity of heating with some penalty of ringing at the captured shock. Issues with accuracy near the peak shear location are identified and require further study.
NASA Astrophysics Data System (ADS)
Alderson, A.; Evans, K. E.
Analytical expressions are derived for the Poisson's ratios associated with a three-dimensional network of regular, corner-sharing tetrahedra in which: (1) the tetrahedra are assumed to be rigid and free to rotate relative to each other; (2) the tetrahedra are assumed to maintain shape and orientation but are free to change size (dilate); (3) tetrahedral rotation and dilation are assumed to act concurrently. The structure has a primitive unit cell containing four tetrahedra and is analogous to the molecular structure of ?-cristobalite. Strain-dependent variations in Poisson's ratio are also predicted by the models. For deformation due to tetrahedral rotation the network is found to exhibit negative Poisson's ratios in each of the three principal directions, with the magnitude of the Poisson's ratio being dependent on the angle of rotation of the tetrahedra. The behaviour of the Poisson's ratio is isotropic in the transverse plane, but anisotropic elsewhere. In the dilation model negative Poisson's ratios equal to -1 are observed for uniaxial loading in any of the principal directions, with the value being constant irrespective of tetrahedral size. The model for concurrent tetrahedral rotation and dilation allows positive as well as negative Poisson's ratios, with the values determined by the framework geometry and relative strengths of the two mechanisms. The concurrent model also offers a design route to materials and structures having ultrahigh Young's moduli.
Photoluminescence of Tetrahedral Quantum-Dot Quantum Wells Vladimir A. Fonoberov,1,2
Fonoberov, Vladimir
Photoluminescence of Tetrahedral Quantum-Dot Quantum Wells Vladimir A. Fonoberov,1,2 Evghenii P within a nonadiabatic approach a quantitative interpretation of the photoluminescence spectrum in the photoluminescence spectrum is attributed to interface optical phonons. We also show that the experimental value
Physica E 26 (2005) 6366 Photoluminescence of tetrahedral quantum-dot quantum wells
Fonoberov, Vladimir
Physica E 26 (2005) 63Â66 Photoluminescence of tetrahedral quantum-dot quantum wells V-adiabatic approach a quantitative interpretation of the photoluminescence (PL) spectrum of a single CdS/HgS/CdS QDQW Keywords: Photoluminescence; Excitons; ExcitonÂphonon interaction; Quantum-dot quantum wells; Non
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)
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.
Candel, A.; Kabel, A.; Lee, L.; Li, Z.; Limborg, C.; Ng, C.; Prudencio, E.; Schussman, G.; Uplenchwar, R.; Ko, K.; /SLAC
2009-06-19
Over the past years, SLAC's Advanced Computations Department (ACD), under SciDAC sponsorship, has developed a suite of 3D (2D) parallel higher-order finite element (FE) codes, T3P (T2P) and Pic3P (Pic2P), aimed at accurate, large-scale simulation of wakefields and particle-field interactions in radio-frequency (RF) cavities of complex shape. The codes are built on the FE infrastructure that supports SLAC's frequency domain codes, Omega3P and S3P, to utilize conformal tetrahedral (triangular)meshes, higher-order basis functions and quadratic geometry approximation. For time integration, they adopt an unconditionally stable implicit scheme. Pic3P (Pic2P) extends T3P (T2P) to treat charged-particle dynamics self-consistently using the PIC (particle-in-cell) approach, the first such implementation on a conformal, unstructured grid using Whitney basis functions. Examples from applications to the International Linear Collider (ILC), Positron Electron Project-II (PEP-II), Linac Coherent Light Source (LCLS) and other accelerators will be presented to compare the accuracy and computational efficiency of these codes versus their counterparts using structured grids.
Nonperturbative dynamical-group approach to the quadratic Zeeman effect
Gerry, C.C.; Laub, J.
1985-12-01
In this paper we consider the quadratic Zeeman effect from the point of view of scaling variational method based on the SO(4,2) dynamical group of the point Coulomb problem. In this formulation, the tilting angle is treated as a variational parameter. We scale a linear combination of the SO(4,2) basis states, solving numerically for the eigenvalues by diagonalization of the resulting matrix representation of the effective Hamiltonian. The SO(4,2) formulation has the advantage that the basis states form a complete set without the inclusion of continuum states, and furthermore, all matrix elements are calculated algebraically. The method is shown to be valid for field strengths at least as high as 10/sup 10/ G and possibly up to 10/sup 12/ G.
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
A Quadratic Gradient Equation for pricing Mortgage-Backed Securities
Monneau, RÃ©gis
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
THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY
Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...
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, an uncontrolled BSDE, and an uncontrolled forward stochastic differential equation (SDE), while the second
Higgsed Stueckelberg vector and Higgs quadratic divergence
NASA Astrophysics Data System (ADS)
Demir, Durmu? Ali; Karahan, Canan Nurhan; Korutlu, Beste
2015-01-01
Here we show that, a hidden vector field whose gauge invariance is ensured by a Stueckelberg scalar and whose mass is spontaneously generated by the Standard Model Higgs field contributes to quadratic divergences in the Higgs boson mass squared, and even leads to its cancellation at one-loop when Higgs coupling to gauge field is fine-tuned. In contrast to mechanisms based on hidden scalars where a complete cancellation cannot be achieved, stabilization here is complete in that the hidden vector and the accompanying Stueckelberg scalar are both free from quadratic divergences at one-loop. This stability, deriving from hidden exact gauge invariance, can have important implications for modeling dark phenomena like dark matter, dark energy, dark photon and neutrino masses. The hidden fields can be produced at the LHC.
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.
Coherent States of Systems with Quadratic Hamiltonians
NASA Astrophysics Data System (ADS)
Bagrov, V. G.; Gitman, D. M.; Pereira, A. S.
2015-03-01
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.
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
NASA Astrophysics Data System (ADS)
Mafa Takisa, P.; Maharaj, S. D.; Ray, Subharthi
2014-12-01
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.
Linear and quadratic sufficiency and commutativity
NASA Astrophysics Data System (ADS)
Ferreira, Sandra S.; Ferreira, Dário; Nunes, Célia
2012-09-01
Given a mixed model let T be the orthogonal projection matrix on the range space spanned by the mean vector. If the model has variance-covariance matrix ?2V we use commutative Jordan algebras to show that Ty is both linear sufficient and linear complete and that Ty, y'V+y with V+ the Moore-Penrose inverse of V is quadratic sufficient whenever T and V commute.
Instabilities of quadratic band crossing points
Stefan Uebelacker; Carsten Honerkamp
2011-01-01
Using a functional renormalization-group approach, we study interaction-driven instabilities in quadratic band crossing point two-orbital models in two dimensions, extending a previous study of Sun [Phys. Rev. Lett.PRLTAO0031-900710.1103\\/PhysRevLett.103.046811 103, 046811 (2009)]. The wave-vector dependence of the Bloch eigenvectors of the free Hamiltonian causes interesting instabilities toward spin-nematic, quantum anomalous Hall, and quantum spin Hall states. In contrast with other known
Extended Decentralized Linear-Quadratic-Gaussian Control
NASA Technical Reports Server (NTRS)
Carpenter, J. Russell
2000-01-01
A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.
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
Monotone and convex quadratic spline interpolation
NASA Technical Reports Server (NTRS)
Lam, Maria H.
1990-01-01
A method for producing interpolants that preserve the monotonicity and convexity of discrete data is described. It utilizes the quadratic spline proposed by Schumaker (1983) which was subsequently characterized by De Vore and Yan (1986). The selection of first order derivatives at the given data points is essential to this spline. An observation made by De Vore and Yan is generalized, and an improved method to select these derivatives is proposed. The resulting spline is completely local, efficient, and simple to implement.
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 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.
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
Quadratic optimization in ill-posed problems
NASA Astrophysics Data System (ADS)
Ben Belgacem, F.; Kaber, S.-M.
2008-10-01
Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.
Quadratic Gabor filters for object detection.
Weber, D M; Casasent, D P
2001-01-01
We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. For detection, the creation of macro filters (linear combinations of multiple single filters) allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized. The fusion parameters to combine the Gabor filter outputs are optimized using an extended piecewise quadratic neural network (E-PQNN). We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We present preliminary results obtained for an infrared (IR) vehicle detection problem. PMID:18249613
Quadratic Programming for Allocating Control Effort
NASA Technical Reports Server (NTRS)
Singh, Gurkirpal
2005-01-01
A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.
Ga?Se bond lengths and EXAFS phase-shifts in tetrahedrally coordinated compounds
NASA Astrophysics Data System (ADS)
Antonioli, G.; Lottici, P. P.
1990-04-01
We report on a study by the EXAFS (Extended X-ray Absorption Fine Structure) spectroscopy of the Ga?Se bond lengths in different tetrahedrally coordinated compounds having different degree of internal distortions: the chalcopyrite CuGaSe 2, the defect chalcopyrites CdGa 2Se 4 and ZnGa 2Se 4 and the defective cubic compound Ga 2Se 3. The NN distances have been calculated from EXAFS data on Ga K-edge, using CuGaSe 2 as reference system for the EXAFS phase shifts. A comparison with theoretical phase shifts is presented. We have found essentially the same Ga?Se distance in all crystals: the result supports the validity of the CTB (conservation of tetrahedral bond) model.
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.
Miao, Peng; Wang, Bidou; Chen, Xifeng; Li, Xiaoxi; Tang, Yuguo
2015-03-25
MicroRNAs are not only important regulators of a wide range of cellular processes but are also identified as promising disease biomarkers. Due to the low contents in serum, microRNAs are always difficult to detect accurately . In this study, an electrochemical biosensor for ultrasensitive detection of microRNA based on tetrahedral DNA nanostructure is developed. Four DNA single strands are engineered to form a tetrahedral nanostructure with a pendant stem-loop and modified on a gold electrode surface, which largely enhances the molecular recognition efficiency. Moreover, taking advantage of strand displacement polymerization, catalytic recycling of microRNA, and silver nanoparticle-based solid-state Ag/AgCl reaction, the proposed biosensor exhibits high sensitivity with the limit of detection down to 0.4 fM. This biosensor shows great clinical value and may have practical utility in early diagnosis and prognosis of certain diseases. PMID:25738985
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.
O'Connell, T P; Malthouse, J P
1995-01-01
Subtilisin and delta-chymotrypsin have been alkylated using 2-13C-enriched benzyloxycarbonylglycylglycylphenylalanylchloromethane. A single signal due to the 13C-enriched carbon was detected in both the intact subtilisin and delta-chymotrypsin derivatives. The signal titrated from 98.9 p.p.m. to 103.6 p.p.m. with a pKa value of 6.9 in the subtilisin derivative and it is assigned to a tetrahedral adduct formed between the hydroxy group of serine-221 and the inhibitor. The signal in the delta-chymotrypsin derivative titrated from 98.5 p.p.m. to 103.2 p.p.m. with a pKa value of 8.92 and it is assigned to a tetrahedral adduct formed between the hydroxy group of serine-195 and the inhibitor. In both derivatives the titration shift is assigned to the formation of the oxyanion of the tetrahedral adduct. delta-Chymotrypsin has been inhibited by benzyloxycarbonylphenylalanylchloromethane and two signals due to 13C-enriched carbons were detected. One of these signals titrated from 98.8 p.p.m. to 103.6 p.p.m. with a pKa value of 9.4 and it was assigned in the same way as in the previous delta-chymotrypsin derivative. The second signal had a chemical shift of 204.5 +/- 0.5 p.p.m. and it did not titrate from pH 3.5 to 9.0. This signal was assigned to alkylated methionine-192. We discuss how subtilisin and chymotrypsin could stabilize the oxyanion of tetrahedral adducts. PMID:7733869
M. Bonelli; A. C. Ferrari; A. Fioravanti; A. Li Bassi; A. Miotello; P. M. Ossi
2002-01-01
: Tetrahedral amorphous carbon films have been produced by pulsed laser deposition, at a wavelength of 248 nm, ablating highly\\u000a oriented pyrolytic graphite at room temperature, in a 10-2 Pa vacuum, at fluences ranging between 0.5 and 35 Jcm-2. Both (100) Si wafers and wafers covered with a SiC polycrystalline interlayer were used as substrates. Film structure was\\u000a investigated by
Wareing, T.A.; Parsons, D.K. [Los Alamos National Lab., NM (United States); Pautz, S. [Texas A and M Univ., College Station, TX (United States). Dept. of Nuclear Engineering
1997-12-31
Recently, a new state-of-the-art discrete-ordinates code, ATTILA, was developed. ATTILA provides the capabilities to solve geometrically complex 3-D transport problems by using an unstructured tetrahedral mesh. In this paper we describe the application of ATTILA to a 3-D reactor pressure vessel dosimetry problem. We provide numerical results from ATTILA and the Monte Carlo code, MCNP. The results demonstrate the effectiveness and efficiency of ATTILA for such calculations.
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung; Chang, Chau-Lyan; Yen, Joseph C.
2013-01-01
In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.
A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TETRAHEDRAL DOMAINS
Fu, Zhisong; Kirby, Robert M.; Whitaker, Ross T.
2014-01-01
Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper presents a parallel algorithm for solving the eikonal equation on fully unstructured tetrahedral meshes. The method is appropriate for the type of fine-grained parallelism found on modern massively-SIMD architectures such as graphics processors and takes into account the particular constraints and capabilities of these computing platforms. This work builds on previous work for solving these equations on triangle meshes; in this paper we adapt and extend previous two-dimensional strategies to accommodate three-dimensional, unstructured, tetrahedralized domains. These new developments include a local update strategy with data compaction for tetrahedral meshes that provides solutions on both serial and parallel architectures, with a generalization to inhomogeneous, anisotropic speed functions. We also propose two new update schemes, specialized to mitigate the natural data increase observed when moving to three dimensions, and the data structures necessary for efficiently mapping data to parallel SIMD processors in a way that maintains computational density. Finally, we present descriptions of the implementations for a single CPU, as well as multicore CPUs with shared memory and SIMD architectures, with comparative results against state-of-the-art eikonal solvers. PMID:25221418
A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TETRAHEDRAL DOMAINS.
Fu, Zhisong; Kirby, Robert M; Whitaker, Ross T
2013-01-01
Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper presents a parallel algorithm for solving the eikonal equation on fully unstructured tetrahedral meshes. The method is appropriate for the type of fine-grained parallelism found on modern massively-SIMD architectures such as graphics processors and takes into account the particular constraints and capabilities of these computing platforms. This work builds on previous work for solving these equations on triangle meshes; in this paper we adapt and extend previous two-dimensional strategies to accommodate three-dimensional, unstructured, tetrahedralized domains. These new developments include a local update strategy with data compaction for tetrahedral meshes that provides solutions on both serial and parallel architectures, with a generalization to inhomogeneous, anisotropic speed functions. We also propose two new update schemes, specialized to mitigate the natural data increase observed when moving to three dimensions, and the data structures necessary for efficiently mapping data to parallel SIMD processors in a way that maintains computational density. Finally, we present descriptions of the implementations for a single CPU, as well as multicore CPUs with shared memory and SIMD architectures, with comparative results against state-of-the-art eikonal solvers. PMID:25221418
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.
Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis. Final Report
NASA Technical Reports Server (NTRS)
Thompson, P. M.
1980-01-01
Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.
Finite dynamic element formulation for a plane triangular element
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1979-01-01
Higher order correction terms for the stiffness and inertia matrices associated with a triangular plane stress-strain finite dynamic element are developed in detail. Numerical results are presented which indicate that the adoption of these matrices along with a suitable quadratic matrix eigenproblem solver effects a significant economy in the free vibration solution of structure when compared with the analysis based on the usual finite element procedure. Finally, a FORTRAN IV computer program listing of the various relevant matrices is given.
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.
Discrete wave propagation in quadratically nonlinear media
NASA Astrophysics Data System (ADS)
Iwanow, Robert
Discrete models are used in describing various microscopic phenomena in many branches of science, ranging from biology through chemistry to physics. Arrays of evanescently coupled, equally spaced, identical waveguides are prime examples of optical structures in which discrete dynamics can be easily observed and investigated. As a result of discretization, these structures exhibit unique diffraction properties with no analogy in continuous systems. Recently nonlinear discrete optics has attracted a growing interest, triggered by the observation of discrete solitons in AlGaAs waveguide arrays reported by Eisenberg et al. in 1998. So far, the following experiments involved systems with third order nonlinearities. In this work, an experimental investigation of discrete nonlinear wave propagation in a second order nonlinear medium is presented. This system deserves particular attention because the nonlinear process involves two or three components at different frequencies mutually locked by a quadratic nonlinearity, and new degrees of freedom enter the dynamical process. In the first part of dissertation, observation of the discrete Talbot effect is reported. In contrast to continuous systems, where Talbot self-imaging effect occurs irrespective of the pattern period, in discrete configurations this process is only possible for a specific set of periodicities. The major part of the dissertation is devoted to the investigation of soliton formation in lithium niobate waveguide arrays with a tunable cascaded quadratic nonlinearity. Soliton species with different topology (unstaggered---all channels in-phase, and staggered---neighboring channels with a pi relative phase difference) are identified in the same array. The stability of the discrete solitons and plane waves (modulational instability) are experimentally investigated. In the last part of the dissertation, a phase-insensitive, ultrafast, all-optical spatial switching and frequency conversion device based on quadratic waveguide array is demonstrated. Spatial routing and wavelength conversion of milliwatt signals is achieved without pulse distortions.
Plane torsion waves in quadratic gravitational theories
O. V. Babourova; B. N. Frolov; E. A. Klimova
1998-05-03
The definition of the Riemann-Cartan space of the plane wave type is given. The condition under which the torsion plane waves exist is found. It is expressed in the form of the restriction imposed on the coupling constants of the 10-parametric quadratic gravitational Lagrangian. In the mathematical appendix the formula for commutator of the variation operator and Hodge operator is proved. This formula is applied for the variational procedure when the gravitational field equations are obtained in terms of the exterior differential forms.
Semiclassical mechanics of the quadratic Zeeman effect
Krantzman, K.D.; Milligan, J.A. (Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024-1569 (United States)); Farrelly, D. (Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300 (United States))
1992-03-01
A comprehensive approach to semiclassical quantization of the quadratic Zeeman effect in the hydrogen atom (QZE) is presented which utilizes the connection between the Kepler system and the four-dimensional harmonic oscillator. Past attempts to quantize the QZE have encountered problems associated with singularities arising because of a classical separatrix. Here, a uniform semiclassical quantization scheme that passes smoothly through the separatrix is developed using classical perturbation theory. This method accounts for the topologically distinct kinds of dynamics that arise in the QZE, and provides good estimates of tunneling splittings. Extension to the quantization of arbitrarily-high-order classical perturbation expansions is straightforward.
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.
Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Kim, Seonghoon; Sohn, Jason W
2015-02-21
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. PMID:25615567
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
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
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
NSDL National Science Digital Library
Illuminations National Council of Teachers of Mathematics
2009-05-12
Students construct "a tetrahedron and describe the linear, 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." (from NCTM Illuminations)
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.
LARGE TIME SOLUTION FOR QUADRATIC SCHRODINGER EQUATIONS IN HANTAEK BAE
Yorke, James
LARGE TIME SOLUTION FOR QUADRATIC SCHRÂ¨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 SchrÂ¨odinger equation in 2D and 3D for the solvability of (1.1), see [5]. In this paper, we consider the SchrÂ¨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
Statistical Cosmology with Quadratic Density Fields
Peter Watts; Peter Coles
2002-08-15
Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations grow linearly. During this phase the Gaussian character of the fluctuations is preserved. Later on, when the fluctuations have amplitude of order the mean density or larger, non-linear effects cause departures from Gaussianity. In Fourier space, non-linearity is responsible for coupling Fourier modes and altering the initially random distribution of phases that characterizes Gaussian initial conditions. In this paper we investigate some of the effects of quadratic non-linearity on basic statistical properties of cosmological fluctuations. We demonstrate how this form of non-linearity can affect asymptotic properties of density fields such as homogeneity, ergodicity, and behaviour under smoothing. We also show how quadratic density fluctuations give rise to a particular relationship between the phases of different Fourier modes which, in turn, leads to the generation of a non-vanishing bispectrum. We thus elucidate the relationship between higher-order power spectra and phase distributions.
UNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS 1
UNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS 1 Ian R. Petersen Jan C. Willems School of Electrical Engineering, Australian Defence Force Academy, Campbell, 2600, Australia, Phone +61
A study of the stabilization of tetrahedral adducts by trypsin and delta-chymotrypsin.
Finucane, M D; Malthouse, J P
1992-01-01
delta-Chymotrypsin has been alkylated by 1-13C- and 2-13C-enriched tosylphenylalanylchloromethane. In the intact inhibitor derivative, signals due to the 1-13C- and 2-13C-enriched carbon atoms have chemical shifts which titrate from 55.10 to 59.50 p.p.m. and from 99.10 to 103.66 p.p.m. respectively with similar pKa values of 8.99 and 8.85 respectively. These signals are assigned to a tetrahedral adduct formed between the hydroxy group of serine-195 and the inhibitor. An additional signal at 58.09 p.p.m. and at 204.85 p.p.m. in the 1-13C- and 2-13C-enzyme-inhibitor derivatives respectively does not titrate when the pH is changed and it is assigned to alkylated methionine-192. On denaturation/autolysis of the 1-13C-enriched enzyme-inhibitor derivative these signals associated with the intact inhibitor derivative are no longer detected, and a new signal, which titrates from 56.28 to 54.84 p.p.m. with a pKa of 5.26, is detected. The titration shift of this signal is assigned to the deprotonation of the imidazolium cation of alkylated histidine-57 in the denatured/autolysed enzyme-inhibitor derivative. Model compounds which form stable hydrates and hemiketals in aqueous solutions have been synthesized. By comparing the 13C titration shifts of these model compounds with those of the 13C enriched trypsin- and delta-chymotrypsin-inhibitor derivatives, we deduce that, in both of the intact enzyme-inhibitor derivatives, the zwitterionic tetrahedral adduct containing the imidazolium cation of histidine-57 and the hemiketal oxyanion predominates at alkaline pH values. It is estimated that in both the trypsin and delta-chymotrypsin-inhibitor derivatives the concentration of this zwitterionic tetrahedral adduct is 10,000-fold greater than it would be in water. We conclude that the pKa of the oxyanion of the hemiketal in the presence of the imidazolium cation of histidine-57 is 7.9 and 8.9 in the trypsin and delta-chymotrypsin-inhibitor derivatives respectively and that the pKa of the imidazolium cation of histidine-57 is greater than 7.9 and greater than 8.9 when the oxyanion is present as its conjugate acid, whereas, when the oxyanion is present, the pKa of the imidazolium cation is greater than 11 in both enzyme-inhibitor derivatives. We discuss how these enzymes preferentially stabilize zwitterionic tetrahedral adducts in the intact enzyme-inhibitor derivatives and how they could stabilize similar tetrahedral intermediates during catalysis. It is suggested that substrate binding could raise the pKa of the imidazolium cation of histidine-57 before tetrahedral-intermediate formation which would explain the enhanced nucleophilicity of the hydroxy group of serine-195.(ABSTRACT TRUNCATED AT 400 WORDS) PMID:1417749
A study of the stabilization of tetrahedral adducts by trypsin and delta-chymotrypsin.
Finucane, M D; Malthouse, J P
1992-09-15
delta-Chymotrypsin has been alkylated by 1-13C- and 2-13C-enriched tosylphenylalanylchloromethane. In the intact inhibitor derivative, signals due to the 1-13C- and 2-13C-enriched carbon atoms have chemical shifts which titrate from 55.10 to 59.50 p.p.m. and from 99.10 to 103.66 p.p.m. respectively with similar pKa values of 8.99 and 8.85 respectively. These signals are assigned to a tetrahedral adduct formed between the hydroxy group of serine-195 and the inhibitor. An additional signal at 58.09 p.p.m. and at 204.85 p.p.m. in the 1-13C- and 2-13C-enzyme-inhibitor derivatives respectively does not titrate when the pH is changed and it is assigned to alkylated methionine-192. On denaturation/autolysis of the 1-13C-enriched enzyme-inhibitor derivative these signals associated with the intact inhibitor derivative are no longer detected, and a new signal, which titrates from 56.28 to 54.84 p.p.m. with a pKa of 5.26, is detected. The titration shift of this signal is assigned to the deprotonation of the imidazolium cation of alkylated histidine-57 in the denatured/autolysed enzyme-inhibitor derivative. Model compounds which form stable hydrates and hemiketals in aqueous solutions have been synthesized. By comparing the 13C titration shifts of these model compounds with those of the 13C enriched trypsin- and delta-chymotrypsin-inhibitor derivatives, we deduce that, in both of the intact enzyme-inhibitor derivatives, the zwitterionic tetrahedral adduct containing the imidazolium cation of histidine-57 and the hemiketal oxyanion predominates at alkaline pH values. It is estimated that in both the trypsin and delta-chymotrypsin-inhibitor derivatives the concentration of this zwitterionic tetrahedral adduct is 10,000-fold greater than it would be in water. We conclude that the pKa of the oxyanion of the hemiketal in the presence of the imidazolium cation of histidine-57 is 7.9 and 8.9 in the trypsin and delta-chymotrypsin-inhibitor derivatives respectively and that the pKa of the imidazolium cation of histidine-57 is greater than 7.9 and greater than 8.9 when the oxyanion is present as its conjugate acid, whereas, when the oxyanion is present, the pKa of the imidazolium cation is greater than 11 in both enzyme-inhibitor derivatives. We discuss how these enzymes preferentially stabilize zwitterionic tetrahedral adducts in the intact enzyme-inhibitor derivatives and how they could stabilize similar tetrahedral intermediates during catalysis. It is suggested that substrate binding could raise the pKa of the imidazolium cation of histidine-57 before tetrahedral-intermediate formation which would explain the enhanced nucleophilicity of the hydroxy group of serine-195.(ABSTRACT TRUNCATED AT 400 WORDS) PMID:1417749
Preliminary design of a large tetrahedral truss/hexagonal panel aerobrake structural system
NASA Technical Reports Server (NTRS)
Dorsey, John T.; Mikulas, Martin M., Jr.
1990-01-01
This paper introduces an aerobrake structural concept consisting of two primary components: (1) a lightweight erectable tetrahedral support truss, and (2) a heatshield composed of individual sandwich hexagonal panels which, when attached to the truss, function as a continuous aerobraking surface. A general preliminary analysis procedure to design the aerobrake components is developed, and values of the aerobrake design parameters which minimize the mass and packaging volume for a 120-foot-diameter aerobrake are determined. Sensitivity of the aerobrake design to variations in design parameters is also assessed.
Nuclear tetrahedral states and high-spin states studied using quantum number projection method
S. Tagami; M. Shimada; Y. Fujioka; Y. R. Shimizu; J. Dudek
2014-04-21
We have recently developed an efficient method of performing the full quantum number projection from the most general mean-field (HFB type) wave functions including the angular momentum, parity as well as the proton and neutron particle numbers. With this method, we have been investigating several nuclear structure mechanisms. In this report, we discuss the obtained quantum rotational spectra of the tetrahedral nuclear states formulating certain experimentally verifiable criteria, of the high-spin states, focussing on the wobbling- and chiral-bands, and of the drip-line nuclei as illustrative examples.
Dudek, J.; Dubray, N.; Pangon, V. [Institut Pluridisciplinaire Hubert Curien IN2P3-CNRS/Universite Louis Pasteur, F-67037 Strasbourg Cedex 2 (France); Curien, D. [Institut Pluridisciplinaire Hubert Curien IN2P3-CNRS, F-67037 Strasbourg Cedex 2 (France); Dobaczewski, J.; Olbratowski, P. [Institute of Theoretical Physics, Warsaw University, Hoza 69, PL-00681 Warsaw (Poland); Schunck, N. [Departamento de Fisica Teorica, Modulo C-XI, Universidad Autonoma de Madrid, Cantoblanco 28049 Madrid (Spain)
2006-08-18
Calculations using realistic mean-field methods suggest the existence of nuclear shapes with tetrahedral T{sub d} and/or octahedral O{sub h} symmetries sometimes at only a few hundreds of keV above the ground states in some rare earth nuclei around {sup 156}Gd and {sup 160}Yb. The underlying single-particle spectra manifest exotic fourfold rather than Kramers's twofold degeneracies. The associated shell gaps are very strong, leading to a new form of shape coexistence in many rare earth nuclei. We present possible experimental evidence of the new symmetries based on the published experimental results--although an unambiguous confirmation will require dedicated experiments.
R. M. Ferrer; Y. Y. Azmy
2009-05-01
We present a robust arbitrarily high order transport method of the characteristic type for unstructured tetrahedral grids. Previously encountered difficulties have been addressed through the reformulation of the method based on coordinate transformations, evaluation of the moments balance relation as a linear system of equations involving the expansion coefficients of the projected basis, and the asymptotic expansion of the integral kernels in the thin cell limit. The proper choice of basis functions for the high-order spatial expansion of the solution is discussed and its effect on problems involving scattering discussed. Numerical tests are presented to illustrate the beneficial effect of these improvements, and the improved robustness they yield.
Gilkes, K.W. [School of Physics, University of East Anglia, Norwich NR47TJ (United Kingdom)] [School of Physics, University of East Anglia, Norwich NR47TJ (United Kingdom); Sands, H.S.; Batchelder, D.N. [Department of Physics and Astronomy, University of Leeds, Leeds LS29JT (United Kingdom)] [Department of Physics and Astronomy, University of Leeds, Leeds LS29JT (United Kingdom); Robertson, J.; Milne, W.I. [Engineering Department, Cambridge CB21PZ (United Kingdom)] [Engineering Department, Cambridge CB21PZ (United Kingdom)
1997-04-01
The vibrational modes of the sp{sup 3} sites in tetrahedral amorphous carbon ({ital ta}-C) thin films are revealed directly using ultraviolet Raman spectroscopy at 244 nm excitation and are shown to produce a Raman peak centered around 1100 cm{sup {minus}1}. In addition, the main Raman peak associated with sp{sup 2} vibrational modes is shifted upward in frequency by 100 cm{sup {minus}1} relative to its position in spectra excited at 514 nm. The spectra are interpreted in terms of the bonding in {ital ta}-C. {copyright} {ital 1997 American Institute of Physics.}
Instabilities of quadratic band crossing points
NASA Astrophysics Data System (ADS)
Uebelacker, Stefan; Honerkamp, Carsten
2011-11-01
Using a functional renormalization-group approach, we study interaction-driven instabilities in quadratic band crossing point two-orbital models in two dimensions, extending a previous study of Sun [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.046811 103, 046811 (2009)]. The wave-vector dependence of the Bloch eigenvectors of the free Hamiltonian causes interesting instabilities toward spin-nematic, quantum anomalous Hall, and quantum spin Hall states. In contrast with other known examples of interaction-driven topological insulators, in the system studied here, the quantum spin Hall state occurs at arbitrarily small interaction strength and for rather simple intraorbital and interorbital repulsions.
Quadratic dynamical decoupling with nonuniform error suppression
Quiroz, Gregory; Lidar, Daniel A. [Department of Physics and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States); Departments of Electrical Engineering, Chemistry, and Physics, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States)
2011-10-15
We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.
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.
Conversion of Osculating Orbital Elements to Mean Orbital Elements
NASA Technical Reports Server (NTRS)
Der, Gim J.; Danchick, Roy
1996-01-01
Orbit determination and ephemeris generation or prediction over relatively long elapsed times can be accomplished with mean elements. The most simple and efficient method for orbit determination, which is also known as epoch point conversion, performs the conversion of osculating elements to mean elements by iterative procedures. Previous epoch point conversion methods are restricted to shorter elapsed times with linear convergence. The new method presented in this paper calculates an analytic initial guess of the unknown mean elements from a first order theory of secular perturbations and computes a transition matrix with accurate numerical partials. It thereby eliminates the problem of an inaccurate initial guess and an identity transition matrix employed by previous methods. With a good initial guess of the unknown mean elements and an accurate transition matrix, converging osculating elements to mean elements can be accomplished over long elapsed times with quadratic convergence.
Geometric quadratic stochastic operator on countable infinite set
NASA Astrophysics Data System (ADS)
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-02-01
In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.
A New Adaptive Algorithm for Convex Quadratic Multicriteria Optimization
Fliege, JÃ¶rg
the prob- lem of solving one single-criteria convex-quadratic optimization problem by an interior-point method used for this problem. 1 Introduction Multicriteria optimization problems are a class of difficult The Interior-Point Algorithm 2.1 The Problem Let there be given a primal quadratic optimization problem (PQP
The quadratic interior point method solving power system optimization problems
James A. Momoh; S. X. Guo; E. C. Ogbuobiri; R. Adapa
1994-01-01
Karmarkar's interior point method as a computation method for solving linear programming (LP) has attracted interest in the operation research community, due to its efficiency, reliability, and accuracy. This paper presents an extended quadratic interior point (EQIP) method, based on improvement of initial condition for solving both linear and quadratic programming problems, to solve power system optimization problem (PSOP), such
Rational Quadratic Approximation to Real Plane Algebraic Curves
Xiao-shan Gao; Ming Li
2004-01-01
An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of f our steps: topol- ogy determination, curve segmentation, segment approximation and curve tracing. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The final
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…
Design and application of quadratic correlation filters for target detection
ABHIJIT MAHALANOBIS; ROBERT R. MUISE; S. R. Stanfill; A. Van Nevel
2004-01-01
We introduce a method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery. The QCFs are a quadratic classifier that operates 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
Weaving a Parabola Web with the Quadratic Transformer
NSDL National Science Digital Library
2012-07-19
Investigate how the graph of a quadratic function and its symbolic expression relate to each other. Start with a set of four graphs, which we?ll call a Parabola Web. Experiment with manipulating them with transformations such as shifting and reflection. Learn about quadratic equations in vertex and root form, and explore how changing these equations affect the graphs.
Frequency-wavenumber spectrum analysis using quadratic estimators
Michael P. Clark; Louis L. Scharj; Wright-Patterson AFB
1992-01-01
A general representation for all non-negative, modulation invariant estimators of the frequency-wavenumber spectrum shows explicitly how the quadratic estimates are constructed from linear transformations of the array data. The windows associated with these transformations are those normally associated with `classical' spectrum estimators. The authors present closed form representations for the moments of quadratic estimators, and show that variance decreases as
Tangent Lines without Derivatives for Quadratic and Cubic Equations
ERIC Educational Resources Information Center
Carroll, William J.
2009-01-01
In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)
Sketching the General Quadratic Equation Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Stols, G. H.
2005-01-01
This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…
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…
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
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…
THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR DIVERSITY: JOURNAL ARTICLE
NRMRL-ADA- 98217 Jorgensen*, E.E., and Tunnell, S.J. The Effectiveness of Quadrats for Measuring Vascular Diversity. The Texas Journal of Science 53 (4):365-368 (2001). EPA/600/J-02/027. Quadrats are widely used for measuring characterist...
Spinor condensates with a laser-induced quadratic Zeeman effect
L. Santos; M. Fattori; J. Stuhler; T. Pfau
2007-01-01
We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate ²Cr gas, can be used to induce topological defects by controllably quenching across transitions between phases of different
Quadratic maps of the plane: Tutorial and Zeraoulia Elhadj1
Sprott, Julien Clinton
Quadratic maps of the plane: Tutorial and review Zeraoulia Elhadj1 , J. C. Sprott2 1 Department quadratic maps, this paper offers an overview of some important issues related to the general case of these mappings, especially predicting the strange attractors and their properties. PACS numbers: 05.45.-a, 05
On Oppenheim-type conjecture for systems of quadratic forms
Gorodnik, Alexander
On Oppenheim-type conjecture for systems of quadratic forms Alexander Gorodnik Abstract Let Qi, i It was conjectured by Oppenheim that if Q(Â¯x) = i,j aijxixj, Â¯x = (x1, . . . , xd), is a real nondegenerate(Â¯x)| Oppenheim conjecture holds for systems of quadratic forms (see
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,
hal00276700, A Quadratic Loss MultiClass SVM
Paris-Sud XI, Université de
hal00276700, version 1 30 Apr 2008 A Quadratic Loss MultiClass SVM Emmanuel Monfrini --- Yann Guermeur April 30, 2008 #12; #12; A Quadratic Loss Multi-Class SVM Emmanuel Monfrini #3; , Yann Guermeur y recognition SVM have been derived. Among those bounds, the most popular one is probably the radius
Optimal and suboptimal quadratic forms for noncentered Gaussian processes.
Grebenkov, Denis S
2013-09-01
Individual random trajectories of stochastic processes are often analyzed by using quadratic forms such as time averaged (TA) mean square displacement (MSD) or velocity auto-correlation function (VACF). The appropriate quadratic form is expected to have a narrow probability distribution in order to reduce statistical uncertainty of a single measurement. We consider the problem of finding the optimal quadratic form that minimizes a chosen cumulant moment (e.g., the variance) of the probability distribution, under the constraint of fixed mean value. For discrete noncentered Gaussian processes, we construct the optimal quadratic form by using the spectral representation of cumulant moments. Moreover, we obtain a simple explicit formula for the smallest achievable cumulant moment that may serve as a quality benchmark for other quadratic forms. We illustrate the optimality issues by comparing the optimal variance with the variances of the TA MSD and TA VACF of fractional Brownian motion superimposed with a constant drift and independent Gaussian noise. PMID:24125246
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.
Optimal and suboptimal quadratic forms for noncentered Gaussian processes
NASA Astrophysics Data System (ADS)
Grebenkov, Denis S.
2013-09-01
Individual random trajectories of stochastic processes are often analyzed by using quadratic forms such as time averaged (TA) mean square displacement (MSD) or velocity auto-correlation function (VACF). The appropriate quadratic form is expected to have a narrow probability distribution in order to reduce statistical uncertainty of a single measurement. We consider the problem of finding the optimal quadratic form that minimizes a chosen cumulant moment (e.g., the variance) of the probability distribution, under the constraint of fixed mean value. For discrete noncentered Gaussian processes, we construct the optimal quadratic form by using the spectral representation of cumulant moments. Moreover, we obtain a simple explicit formula for the smallest achievable cumulant moment that may serve as a quality benchmark for other quadratic forms. We illustrate the optimality issues by comparing the optimal variance with the variances of the TA MSD and TA VACF of fractional Brownian motion superimposed with a constant drift and independent Gaussian noise.
Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares
NASA Technical Reports Server (NTRS)
Orr, Jeb S.
2012-01-01
A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed
Finite element approximation of free vibration of folded plates
Erwin Hernández; Luis Hervella-Nieto
2009-01-01
In this paper a finite element approximation of the free vibration of folded plates is studied. Naghdi model, including bending, shear and membrane terms for the plate, is considered. Quadrilateral low order MITC (Mixed Interpolation Tensorial Component) elements are used for the bending and shear effect, coupled with standard quadratic elements enriched with a drilling degree of freedom for the
NASA Astrophysics Data System (ADS)
Dudek, J.; Curien, D.; Rouvel, D.; Mazurek, K.; Shimizu, Y. R.; Tagami, S.
2014-05-01
We discuss predictions made by large scale calculations using the realistic realization of phenomenological nuclear mean-field theory. The calculations indicate that certain zirconium nuclei are tetrahedrally symmetric in their ground states. After a short overview of past research into nuclear tetrahedral symmetry we analyse the predictive capacities of the method and focus on the 96Zr nucleus, which is expected to be tetrahedral in its ground state.
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)
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.
Liquid-liquid phase transition in a family of simple models of tetrahedral liquid
NASA Astrophysics Data System (ADS)
Buldyrev, Sergey; Franzese, Giancarlo; Giovambattista, Nicolas
2013-03-01
Liquids with tetrahedral symmetry of the first coordination shell often display anomalous thermodynamic and dynamic behavior. Sometimes, these anomalies are associated with the liquid-liquid phase transition at high pressures and low temperatures. We study a family of simple models with few parameters and investigate the conditions for the existence of the liquid-liquid phase transition. A molecule in these models consists of a hard sphere with a square well and four point particles attached to the center of the hard sphere by directional bonds arranged in tetrahedral geometry. We also impose a condition which does not allow a point particle in one molecule to include in its attractive well more than one point particle belonging to different molecules. We find an optimal range of flexibility of the bonds created by the point particles for which the model displays a clear liquid-liquid critical point in the accessible region of the phase diagram: too flexible bonds weaken the anomalies and destroy the critical point, while too rigid bonds slow down the diffusion and shift the critical point beyond the glass transition. We also investigate how minor changes in the model parameters influence crystallization which might make liquid-liquid unobservable.
A decentralized linear quadratic control design method for flexible structures
NASA Technical Reports Server (NTRS)
Su, Tzu-Jeng; Craig, Roy R., Jr.
1990-01-01
A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties.
Paris-Sud XI, UniversitÃ© de
deficit resulting from cationic substitutions in either the tetrahedral or octahedral sheet is compensated their rheological behavior and its evolution upon dehydration likely contributes to slipping processes.5
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.
NASA Astrophysics Data System (ADS)
Lyapin, A. G.; Brazhkin, V. V.; Bayliss, S. C.; Sapelkin, A. V.; Itié, J. P.; Polian, A.; Clark, S. M.
1996-11-01
The pressure dependence of the average interatomic distances for the first Ga shell in bulk tetrahedral a- GaSb has been studied by Ga K-edge extended x-ray-absorption fine structure. We have found that the microscopic compressibility of the covalent bonds in the disordered network is less than in the crystalline zinc-blende structure. Comparison of the microscopic bond-bulk modulus (Bbond~=105+/-20 GPa) in a-GaSb with the macroscopic bulk modulus (Bcr=35 GPa) and with the bulk modulus of c-GaSb (Bcr=56 GPa) gives unambiguous evidence for a pressure-induced geometrical or topological distortion in the a-GaSb tetrahedral network. Physical reasons for the observed behavior of volume in the amorphous tetrahedral network under pressure, such as a bond-bending distortion mechanism and a nonlinear averaging for a system with heterogeneous compressibility, are discussed.
Use of non-quadratic yield surfaces in design of optimal deep-draw blank geometry
Logan, R.W.
1995-12-01
Planar anisotropy in the deep-drawing of sheet can lead to the formation of ears in cylindrical cups and to undesirable metal flow in the blankholder in the general case. For design analysis purposes in non-linear finite-element codes, this anisotropy is characterized by the use of an appropriate yield surface which is then implemented into codes such as DYNA3D . The quadratic Hill yield surface offers a relatively straightforward implementation and can be formulated to be invariant to the coordinate system. Non-quadratic yield surfaces can provide more realistic strength or strain increment ratios, but they may not provide invariance and thus demand certain approximations. Forms due to Hosford and Badat et al. have been shown to more accurately address the earning phenomenon. in this work, use is made of these non-quadratic yield surfaces in order to determine the optimal blank shape for cups and other shapes using ferrous and other metal blank materials with planar anisotropy. The analyses are compared to previous experimental studies on non-uniform blank motion due to anisotropy and asymmetric geometry.
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.
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.
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
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.
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.
Masanori Koshiba; Shinji Maruyama; Koichi Hirayama
1994-01-01
A vector finite element method with the high-order mixed-interpolation-type triangular elements is described for the analysis of optical waveguiding problems. It is a combination of linear edge elements for transverse components of the electric or magnetic field and quadratic nodal elements for the axial one. The use of mixed-interpolation-type elements provides a direct solution for propagation constants and avoids spurious
sequential quadratic progamming methods for parametric nonlinear ...
2014-07-02
elements to enforce global convergence that can interfere with the potential to ... cause in a conventional SQP method, if the active set has stabilized, the ...... or an accumulation of open sets whose closure represents a non-KKT boundary.
3D Finite Element Meshing from Imaging Data ?
Zhang, Yongjie; Bajaj, Chandrajit; Sohn, Bong-Soo
2009-01-01
This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging 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. The edge contraction and smoothing methods are used to improve the mesh quality. The main contribution is extending the dual contouring method to crack-free interval volume 3D meshing with feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates adaptive and quality 3D meshes without introducing any hanging nodes. The algorithm has been successfully applied to constructing the geometric model of a biomolecule in finite element calculations. PMID:19777144
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.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1988-01-01
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.
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 ...
NASA Astrophysics Data System (ADS)
Aas, M.; Özelci, E.; Jonáš, A.; Kiraz, A.; Liu, H.; Fan, C.; Chen, Q.; Fan, X.
2014-09-01
We demonstrate Förster resonance energy transfer (FRET) lasing from self-assembled tetrahedral DNA complexes labeled with Cy3 and Cy5 dyes and suspended as a gain medium in aqueous microdroplet cavities deposited on a superhydrophobic surface. Threshold fluence and differential efficiency are characterized for DNA complexes containing 1Cy3-3Cy5 and 3Cy3-1Cy5. We demonstrate that at a constant Cy5 concentration, average threshold fluence is reduced 3 to 8 times and average differential efficiency is enhanced 6 to 30 times for 3Cy3-1Cy5 as compared to 1Cy3-3Cy5. Using 3Cy3-1Cy5 nanostructures, FRET lasing is observed at very low concentrations down to ˜ 1 ?M. This work shows that optofluidic microlasers based on droplet resonators can be combined with DNA nanotechnology to explore applications in bio/chemical sensing and novel photonic devices.
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.
NASA Technical Reports Server (NTRS)
Lalvani, Haresh; Collins, Timothy J.
1991-01-01
Morphology (the study of structure and form) of the octahedral-tetrahedral (octet) truss is described. Both the geometry and symmetry of the octet truss are considered. Morphological techniques based on symmetry operations are presented which enable the derivation of reduced-part-count truss configurations from the octet truss by removing struts and nodes. These techniques are unique because their Morphological origination and they allow for the systematic generation and analysis of a large variety of structures. Methods for easily determining the part count and redundancy of infinite truss configurations are presented. Nine examples of truss configurations obtained by applying the derivation techniques are considered. These configurations are structurally stable while at the same time exhibiting significant reductions in part count. Some practical and analytical considerations, such as structural performance, regarding the example reduced-part-count truss geometries are briefly discussed.
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
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
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.
"Crystal-clear" liquid-liquid transition in a tetrahedral fluid.
Starr, Francis W; Sciortino, Francesco
2014-12-21
For a model known to exhibit liquid-liquid transitions, we examine how varying the bond orientational flexibility affects the stability of the liquid-liquid transition relative to that of the crystal phases. For very rigidly oriented bonds, the crystal is favored over all amorphous phase transitions. We find that increasing the bond flexibility decreases both the critical temperature Tc for liquid-liquid phase separation and the melting temperature Tm. The effect of increasing flexibility is much stronger for melting, so that the distance between Tc and Tm progressively reduces and inverts sign. Under these conditions, a "naked" liquid-liquid critical point bulges out in the liquid phase and becomes accessible, without the possibility of crystallization. These results confirm that a crystal-clear, liquid-liquid transition can occur as a genuine, thermodynamically stable phenomenon for tetrahedral coordinated particles with flexible bond orientation, but that such a transition is hidden by crystallization when bonds are highly directional. PMID:25349962
NASA Astrophysics Data System (ADS)
Xu, Shipeng; Li, Xiaowei; Huang, Meidong; Ke, Peiling; Wang, Aiying
2014-04-01
We presented the combined experimental and simulation study on stress evolution as a function of incident angles of carbon ions for the ultrathin tetrahedral amorphous carbon films (ta-C). The residual stress was found about 3.6 ± 0.1 GPa for the incident angle of C ions with range of 0°-30°, while it decreased significantly to 2.8 GPa with the incident angle of 60°. Different with the previous reports, noted that in this case both the sp3 content and mechanical properties of film were not deteriorated. Taking molecular dynamics simulation, it was in particularly concluded that the critical relaxation of distorted C-sp3 bond lengths and bond angles played key role on the unusual stress reduction mechanism. The results provide a route to fabricate the ultrathin ta-C films with low stress and high hardness for the precision wear resistant applications.
NASA Astrophysics Data System (ADS)
Liu, Fanxin; Tang, Chaojun; Zhan, Peng; Chen, Zhuo; Ma, Hongtao; Wang, Zhenlin
2014-03-01
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.
Evaluation of a 3D point cloud tetrahedral tomographic reconstruction method
Pereira, N F; Sitek, A
2011-01-01
Tomographic reconstruction on an irregular grid may be superior to reconstruction on a regular grid. This is achieved through an appropriate choice of the image space model, the selection of an optimal set of points and the use of any available prior information during the reconstruction process. Accordingly, a number of reconstruction-related parameters must be optimized for best performance. In this work, a 3D point cloud tetrahedral mesh reconstruction method is evaluated for quantitative tasks. A linear image model is employed to obtain the reconstruction system matrix and five point generation strategies are studied. The evaluation is performed using the recovery coefficient, as well as voxel- and template-based estimates of bias and variance measures, computed over specific regions in the reconstructed image. A similar analysis is performed for regular grid reconstructions that use voxel basis functions. The maximum likelihood expectation maximization reconstruction algorithm is used. For the tetrahedral reconstructions, of the five point generation methods that are evaluated, three use image priors. For evaluation purposes, an object consisting of overlapping spheres with varying activity is simulated. The exact parallel projection data of this object are obtained analytically using a parallel projector, and multiple Poisson noise realizations of these exact data are generated and reconstructed using the different point generation strategies. The unconstrained nature of point placement in some of the irregular mesh-based reconstruction strategies has superior activity recovery for small, low-contrast image regions. The results show that, with an appropriately generated set of mesh points, the irregular grid reconstruction methods can out-perform reconstructions on a regular grid for mathematical phantoms, in terms of the performance measures evaluated. PMID:20736496
Elements & Compounds Atoms (Elements)
Frey, Terry
#12;Elements & Compounds #12;Atoms (Elements) Molecules (Compounds) Cells Elements & Compounds #12;Nucleus Electrons Cloud of negative charge (2 electrons) Fig. 2.5: Simplified model of a Helium (He) Atom He 4.002602 2 Helium Mass Number (~atomic mass) = number of Neutrons + Protons = 4 for Helium Atomic
Adaptive continuous-time linear quadratic Gaussian control
Duncan, Tyrone E.; Guo, L.; Pasik-Duncan, Bozenna
1999-09-01
The adaptive linear quadratic Gaussian control problem, where the linear transformation of the state A and the linear transformation of the control B are unknown, is solved assuming only that (A, B) is controllable and (A, ...
Constructing Approximations to the Efficient Set of Convex Quadratic ...
quadratic problem with an interior point method, an approach which will be put .... efficient points (i. e. when solving the new optimization problems), we ... of the primal-dual long step algorithm for linear programs by Kojima, Mizuno, and ...
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)
The Quadratic Zeeman Effect in Moderately Strong Magnetic Fields
S. L. Coffey; A. Deprit; B. Miller; C. A. Williams
1987-01-01
Contents: 1. Symmetries. 2. The linear Zeeman effect. 3. The quadratic Zeeman effect. 4. The method of secular perturbations. 5. The phase-space as a sphere. 6. Critical inclinations. 7. The circular orbits. 8. Conclusions.
Beyond symmetric Broyden for updating quadratic models in ...
2011-04-12
without derivatives construct changes to the variables by applying trust region methods to quadratic .... causes substantial relative errors in every xk. Furthermore, the property ..... because of the sparsity structure of ?2F. We employ the usual ...
Semidefinite Relaxations for Non-Convex Quadratic Mixed-Integer ...
2011-11-08
Most algorithms and software tools for quadratic mixed-integer optimization ... cutting planes yields a very fast algorithm for solving the maximum cut prob- .... In our evaluation, we are also interested in the dependance of performance on.
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.
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 ...
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.
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.
Spinor condensates with a laser-induced quadratic Zeeman effect
L. Santos; M. Fattori; J. Stuhler; T. Pfau
2007-01-01
We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate Cr52 gas, can be used to induce topological defects by controllably quenching across transitions between phases of different
Exact solution of the classical mechanical quadratic Zeeman effect
Sambhu N. Datta; Anshu Pandey
2007-01-01
We address the curious problem of quadratic Zeeman effect at the classical mechanical level. The problem has been very well\\u000a understood for decades, but an analytical solution of the equations of motion is still to be found. This state of affairs\\u000a persists because the simultaneous presence of the Coulombic and quadratic terms lowers the dynamical symmetry. Energy and\\u000a orbital angular
Three dimensional modelling of non-local ductile damage: element technology
H. R. Javani; R. H. J. Peerlings; M. G. D. Geers
2009-01-01
This paper presents an engineering scale numerical analysis framework of ductile damage and focusses on the three dimensional\\u000a element technology required for it. A three dimensional low-order tetrahedral element is developed which is free from locking\\u000a and efficient from the calculation time point of view. The element is tested using a well known benchmark problem and the\\u000a results show that
On implementing a primal-dual interior-point method for conic quadratic optimization
Erling D. Andersen; Cornelis Roos; Tamás Terlaky
2003-01-01
Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an ane set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can in
Semiclassical form factor of matrix element fluctuations
Bruno Eckhardt; Joerg Main
1995-08-17
We analyze within a semiclassical approximation the form factor for the fluctuations of quantum matrix elements around their classical average. We find two contributions: one is proportional to the form factor for the density of states, with an amplitude determined by the squared average of the matrix elements. The other is constant and related to the fluctuations of finite time classical trajectory segments around the phase space average. The results are illustrated for an observable in the quadratic Zeeman effect.
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.
Modeling and computation of two phase geometric biomembranes using surface finite elements
Elliott, Charles
M. Elliott, BjÃ¶rn Stinner * Mathematics Institute, Zeeman Building, University of Warwick, Coventry, and we employ triangulated surfaces and H1 conforming quadratic surface finite elements for approximating
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.
NASA Astrophysics Data System (ADS)
Ding, Xue-Hua; Wang, Shi; Li, Yong-Hua; Huang, Wei
2015-01-01
The systematic research has been done into structural variations of supramolecular architectures by the self assembly of two pyridine-based potential anion receptors, 1-(4-pyridyl)piperazine (L1) and 4-pyrrolidinopyridine (L2), and different inorganic acids (HCl, HBr, HI, HNO3, HClO4, HIO4, H2SO4 and H3PO4). The formation of four fascinating salts, i.e. (H2L12+)·(H2PO4-)2 (1), (H2L12+)·(ClO4-)2 (2), (HL2+)·(ClO4-) (3) and (HL2+)·(IO4-) (4), indicates that N-heterocyclic L1 and L2 are prone to cocrystallize with tetrahedral oxyanions and anionic topologies play a crucial role in the crystallization process. Structural analyses reveal that various intermolecular ring motifs have been generated by robust hydrogen-bonding interactions in compounds 1-4. In particular, interesting substructures were observed in H2PO4- from salts 1 due to its polytopic potential hydrogen-bonding donor and acceptor oxygen atoms, including ring motifs, 1D ribbons and 2D supramolecular framework. Much to our surprise, crystal 4 proves to be a member of few supramolecular salts crystallizing with IO4- anion according to the Cambridge Structure Database (CSD).
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.
NASA Astrophysics Data System (ADS)
Zhang, Haijiang; Thurber, Clifford
2005-04-01
We have developed an adaptive mesh seismic tomography method based on tetrahedral and Voronoi diagrams to automatically match the inversion mesh to the data distribution. Two different irregular mesh interpolation methods, linear and natural neighbor, are evaluated. A synthetic test shows that the adaptive mesh seismic tomography method recovers the true synthetic model well in both the linear and natural neighbor interpolation cases. Use of more accurate differential data is helpful in removing artifacts in the model that result from the noisier absolute data. Application of the adaptive mesh scheme to Parkfield, California, results in much more uniform sampling of the model (as measured by the derivative weight sum) on the optimized irregular inversion mesh compared to a regular grid. The across-strike cross sections resulting from using either just the absolute data or both the absolute and differential data show a clear velocity contrast at the San Andreas fault in the linear and natural neighbor interpolation cases. The velocity model obtained using natural neighbor interpolation is smoother than that from linear interpolation. Including the differential data in the inversion yields more clustered event locations and removes a velocity reversal to the southwest of the fault, which is likely caused by noise in the absolute data.
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.
Calculation of internal valence force constants for XY 4 ( Td) tetrahedral molecules
NASA Astrophysics Data System (ADS)
Fernández Gómez, M.; López González, J. J.; Rajamanickam, N.; Martínez-Torres, E.
1992-08-01
Valence force constants have been calculated in terms of simple dependent rectilinear internal coordinates for a series of XY 4 tetrahedral molecules that have been studied from a vibrational point of view. These molecules include the tetrahydrides of carbon, silicon, germanium and tin, and the tetrafluorides of carbon, silicon and germanium. Using the most recent and reliable force constants in symmetry coordinates, the pure vibrational force field has been arrived at by applying Kuczera's treatment. The results show that the seven FR dependent constants are reduced to five F*R independent constants; the same occurs for the F0S independent force constants. The relationships f*r? = - f*'r? and f*'?? = - f*? - 4 f*?? are obtained from the sum rule in Kuczera's treatment. On the basis of Wilson's S vectors and from the interactions between the displacement coordinates, a method is proposed here to obtain the above relationships. This allows individual values to be assigned to the bending, bending—bending and bending—stretching force constants for the above-mentioned molecules, without the need for recourse to any model whatsoever. Likewise, in each case we have attempted to obtain an empirical function to fit the force constant values dependent on the bond lengths. This method allows us to some extent to predict the values of the force constants for some tetrahydride molecules of this group, which has not yet been studied experimentally.
Non-Axial Octupole Deformations and Tetrahedral Symmetry in Heavy Nuclei
Mazurek, Katarzyna [Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow (Poland); Dudek, Jerzy [Institut de Recherches Subatomiques, F-67037 Strasbourg Cedex 2 (France); Universite Louis Pasteur, F-67037 Strasbourg Cedex 2 (France)
2005-11-21
The total energies of about 120 nuclei in the Thorium region have been calculated within the macroscopic-microscopic method in the 5-dimensional space of deformation parameters {alpha}20, {alpha}22, {alpha}30, {alpha}32 and {alpha}40. The macroscopic energy term contains the nuclear surface-curvature dependence as proposed within the LSD approach. The microscopic energies are calculated with the Woods-Saxon single particle potential employing the universal set of parameters.We study a possible presence of the octupole axial and non-axial degrees of freedom all-over in the ({beta}, {gamma})-plane focussing on the ground-states, secondary minima and in the saddle points. In fact, a competition between axial and tri-axial octupole deformation parameters is obtained at the saddle points and in the secondary minima for many isotones with N > 136. The presence of the tetrahedral symmetry minima is predicted in numerous nuclei in the discussed region, although most of the time at relatively high excitation energies.
Output-Adaptive Tetrahedral Cut-Cell Validation for Sonic Boom Prediction
NASA Technical Reports Server (NTRS)
Park, Michael A.; Darmofal, David L.
2008-01-01
A cut-cell approach to Computational Fluid Dynamics (CFD) that utilizes the median dual of a tetrahedral background grid is described. The discrete adjoint is also calculated, which permits adaptation based on improving the calculation of a specified output (off-body pressure signature) in supersonic inviscid flow. These predicted signatures are compared to wind tunnel measurements on and off the configuration centerline 10 body lengths below the model to validate the method for sonic boom prediction. Accurate mid-field sonic boom pressure signatures are calculated with the Euler equations without the use of hybrid grid or signature propagation methods. Highly-refined, shock-aligned anisotropic grids were produced by this method from coarse isotropic grids created without prior knowledge of shock locations. A heuristic reconstruction limiter provided stable flow and adjoint solution schemes while producing similar signatures to Barth-Jespersen and Venkatakrishnan limiters. The use of cut-cells with an output-based adaptive scheme completely automated this accurate prediction capability after a triangular mesh is generated for the cut surface. This automation drastically reduces the manual intervention required by existing methods.
NASA Astrophysics Data System (ADS)
Yeo, Reuben J.; Dwivedi, Neeraj; Tripathy, S.; Bhatia, C. S.
2015-03-01
Developing ultrathin and highly wear-resistant overcoats for magnetic tape heads is one of the current research areas of interest, because of its potential to delay pole tip recession and increase the operational lifetime of high areal density tape drives. Using optimized process conditions and an appropriate overcoat design, we report on the development of a ˜20 nm thick silicon nitride/tetrahedral amorphous carbon (Si/SiNx/ta-C) bilayer overcoat, where the ta-C film was deposited by a filtered cathodic vacuum arc process. The bilayer overcoat deposited on a functional tape head survived 40-50 × 106 m of testing with commercial tape media under standard industrial testing conditions. The excellent wear resistance of the overcoat was attributed to the generation of high (˜72%) sp3 carbon content and the formation of strong interfacial bonds, such as Si-C, C=N, nitrile, and (Al, Ti)N at the interfaces, as confirmed by various spectroscopic techniques. This study demonstrates the pivotal role of high sp3 carbon bonding combined with enhanced interfacial bonding in developing an ultrathin yet durable protective overcoat for magnetic tape heads.
Quadratically consistent nodal integration for second order meshfree Galerkin methods
NASA Astrophysics Data System (ADS)
Duan, Qinglin; Wang, Bingbing; Gao, Xin; Li, Xikui
2014-08-01
Robust and efficient integration of the Galerkin weak form only at the approximation nodes for second order meshfree Galerkin methods is proposed. The starting point of the method is the Hu-Washizu variational principle. The orthogonality condition between stress and strain difference is satisfied by correcting nodal derivatives. The corrected nodal derivatives are essentially linear functions which can exactly reproduce linear strain fields. With the known area moments, the stiffness matrix resulting from these corrected nodal derivatives can be exactly evaluated using only the nodes as quadrature points. The proposed method can exactly pass the quadratic patch test and therefore is named as quadratically consistent nodal integration. In contrast, the stabilized conforming nodal integration (SCNI) which prevails in the nodal integrations for meshfree Galerkin methods fails to pass the quadratic patch test. Better accuracy, convergence, efficiency and stability than SCNI are demonstrated by several elastostatic and elastodynamic examples.
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.
NASA Astrophysics Data System (ADS)
Pothoczki, Szilvia; Temleitner, László; Pusztai, László
2011-01-01
Analyses of the intermolecular structure of molecular liquids containing slightly distorted tetrahedral molecules of the CXY3-type are described. The process is composed of the determination of several different distance-dependent orientational correlation functions, including ones that are introduced here. As a result, a complete structure classification could be provided for CXY3 molecular liquids, namely for liquid chloroform, bromoform, and methyl-iodide. In the present work, the calculations have been conducted on particle configurations resulting from reverse Monte Carlo computer modeling: these particle arrangements have the advantage that they are fully consistent with structure factors from neutron and x-ray diffraction measurements. It has been established that as the separation between neighboring molecules increases, the dominant mutual orientations change from face-to-face to edge-to-edge, via the edge-to-face arrangements. Depending on the actual liquid, these geometrical elements (edges and faces of the distorted tetrahedra) were found to contain different atoms. From the set of liquids studied here, the structure of methyl-iodide was found to be easiest to describe on the basis of pure steric effects (molecular shape, size, and density) and the structure of liquid chloroform seems to be the furthest away from the corresponding "flexible fused hard spheres" like reference system.
Pothoczki, Szilvia; Temleitner, László; Pusztai, László
2011-01-28
Analyses of the intermolecular structure of molecular liquids containing slightly distorted tetrahedral molecules of the CXY(3)-type are described. The process is composed of the determination of several different distance-dependent orientational correlation functions, including ones that are introduced here. As a result, a complete structure classification could be provided for CXY(3) molecular liquids, namely for liquid chloroform, bromoform, and methyl-iodide. In the present work, the calculations have been conducted on particle configurations resulting from reverse Monte Carlo computer modeling: these particle arrangements have the advantage that they are fully consistent with structure factors from neutron and x-ray diffraction measurements. It has been established that as the separation between neighboring molecules increases, the dominant mutual orientations change from face-to-face to edge-to-edge, via the edge-to-face arrangements. Depending on the actual liquid, these geometrical elements (edges and faces of the distorted tetrahedra) were found to contain different atoms. From the set of liquids studied here, the structure of methyl-iodide was found to be easiest to describe on the basis of pure steric effects (molecular shape, size, and density) and the structure of liquid chloroform seems to be the furthest away from the corresponding "flexible fused hard spheres" like reference system. PMID:21280762
Synthesis of tetrahedral quasi-type-II CdSe-CdS core-shell quantum dots
NASA Astrophysics Data System (ADS)
Sugunan, Abhilash; Zhao, Yichen; Mitra, Somak; Dong, Lin; Li, Shanghua; Popov, Sergei; Marcinkevicius, Saulius; Toprak, Muhammet S.; Muhammed, Mamoun
2011-10-01
Synthesis of colloidal nanocrystals of II-VI semiconductor materials has been refined in recent decades and their size dependent optoelectronic properties have been well established. Here we report a facile synthesis of CdSe-CdS core-shell heterostructures using a two-step hot injection process. Red-shifts in absorption and photoluminescence spectra show that the obtained quantum dots have quasi-type-II alignment of energy levels. The obtained nanocrystals have a heterostructure with a large and highly faceted tetrahedral CdS shell grown epitaxially over a spherical CdSe core. The obtained morphology as well as high resolution electron microscopy confirms that the tetrahedral shell have a zinc blende crystal structure. A phenomenological mechanism for the growth and morphology of the nanocrystals is discussed.
Chen, Jun; Zhang, Qing; Zheng, Fa-Kun; Liu, Zhi-Fa; Wang, Shuai-Hua; Wu, A-Qing; Guo, Guo-Cong
2015-02-21
Three air-stable tetrahedral manganese(ii) dihalide complexes [MnX2(DPEPO)] (DPEPO = bis[2-(diphenylphosphino)phenyl]ether oxide; X = Cl, Br and I) were prepared. All of the obtained compounds were structurally characterized by single-crystal X-ray diffraction analyses, which reveal that they crystallize in centrosymmetric space groups and feature an isolated mononuclear structure with Mn(2+) in a tetrahedral environment. Interestingly, these complexes show excellent photoluminescent performance in neat solid form, with the highest total quantum yield (?total) of up to 70% recorded for the dibromide complex. Intense green flashes of light could be observed by the naked eye when rubbing the manganese(ii) complexes. PMID:25597698
Tetrahedral Coordination of Mn(IV) by Oxygen in Manganese Sillenite Bi 12MnO 20
NASA Astrophysics Data System (ADS)
Delicat, U.; Radaev, S. F.; Trömel, M.; Behrens, P.; Kargin, Y. F.; Mar'in, A. A.
1994-05-01
Polycrystalline samples and a single crystal of the Mn sillenite Bi 12MnO 20 have been synthesized and studied. IR spectroscopy, XANES, and XRPD show that manganese atoms are tetravalent and tetrahedrally coordinated by oxygen. The X-ray single-crystal study of Bi 12MnO 20 confirms that this is the first example of a compound containing Mn IV in tetrahedral coordination by oxygen with Mn-O distances of 1.75(2) Å. The crystal is cubic, sp.gr. I23 ( Z = 2); a = 10.206(1) Å. The final agreement factors are w R = 2.83 and R = 3.49% for 625 reflections. Bi 12MnO 20 belongs to the stoichiometric sillenites with tetravalent M atoms of one kind.
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.
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.
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
K. N. Joshipura; Minaxi Vinodkumar; C. G. Limbachiya; B. K. Antony
2004-01-01
Various total cross sections for collisions of electrons in the energy range 10-2000 eV are calculated for the tetrahedral CHâ, SiHâ, GeHâ, CFâ, SiFâ, and CClâ targets and SFâ. Molecular total inelastic cross sections determined in the complex potential formalism are partitioned to account for the ionization and cumulative electronic-excitation channels. The present total cross sections and total ionization cross
K. N. Joshipura; Minaxi Vinodkumar; C. G. Limbachiya; B. K. Antony
2004-01-01
Various total cross sections for collisions of electrons in the energy range 10 2000 eV are calculated for the tetrahedral CH4, SiH4, GeH4, CF4, SiF4, and CCl4 targets and SF6. Molecular total inelastic cross sections determined in the complex potential formalism are partitioned to account for the ionization and cumulative electronic-excitation channels. The present total cross sections and total ionization
Omvir Singh Panwar; Mohd. Alim Khan; Mahesh Kumar; Sonnada Math Shivaprasad; Bukinakere Subbakrihniah Satyanarayana; Prakash Narain Dixit; Raghunath Bhattacharyya
2009-01-01
This paper reports the X-ray photoelectron spectroscopy (XPS), X-ray-induced Auger electron spectroscopy (XAES), and Raman studies of boron- and phosphorous-incorporated tetrahedral amorphous carbon (ta-C) films deposited by the filtered cathodic vacuum arc process. A systematic study of the influence of varying boron (B) and phosphorous (P) content on the properties of the as-grown ta-C films deposited at high negative substrate
O. S. Panwar; B. Deb; B. S. Satyanarayana; Mohd. Alim Khan; R. Bhattacharyya; A. K. Pal
2005-01-01
Reported is a study of the as grown and nitrogen incorporated tetrahedral amorphous carbon (ta-C) films deposited by a pulsed unfiltered cathodic vacuum arc process using Raman scattering, photoluminescence (PL) and Fourier transform infrared (FTIR) spectroscopy. The influence of the substrate bias in as grown ta-C films and the effect of the nitrogen content in nitrogen incorporated ta-C films under
O. S. Panwar; Mohd Alim Khan; B. S. Satyanarayana; Sushil Kumar; Ishpal
2010-01-01
This paper reports the electrical, mechanical, structural and field emission properties of as grown and also boron and phosphorous incorporated tetrahedral amorphous carbon (ta-C) films, deposited using a filtered cathodic vacuum arc process. The effect of varying boron and phosphorous content (up to 2.0at.% in to ta-C) on the conductivity (?D), activation energy (?E1), hardness, microstructure, emission threshold (Eturn-ON) and
O. S. Panwar; Mohd. Alim Khan; Mahesh Kumar; S. M. Shivaprasad; B. S. Satyanarayana; P. N. Dixit; R. Bhattacharyya; M. Y. Khan
2008-01-01
The application of a sufficiently high negative substrate bias, during the growth of tetrahedral amorphous carbon (ta-C), is usually associated with low sp3 bonding configuration and stressed films. However, in an effort to understand and utilize the higher pseudo thermo dynamical conditions during the film growth, at high negative substrate bias (?300 V), reported here is a study on ta-C films
Dongping Liu; Günther Benstetter; Edgar Lodermeier; Johann Vancea
2003-01-01
Tetrahedral amorphous carbon (ta-C) films have been grown on Ar+-beam-cleaned silicon substrates by changing the incident angle of energetic carbon ions produced in the plasma of pulsed cathodic vacuum arc discharge. Their surface roughness, deposition rate, composition, and mechanical and frictional properties as a function of the incident angle of energetic carbon ions were reported. The substrate holder can be
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.
Greenfield, Joshua T; Pak, Chongin; Kamali, Saeed; Lee, Kathleen; Kovnir, Kirill
2015-03-12
The synthesis and structural characterization is reported for [Fe(dien)2][FeSe2]2 and [Fe(tren)][FeSe2]2, two new mixed-valence compounds that contain infinite ?(1)(FeSe2) tetrahedral chains separated by Fe-amine complexes. The inter- and intra-chain magnetic interactions can be controlled by changing the denticity of the amine while preserving the general structural motif. PMID:25482568
NASA Technical Reports Server (NTRS)
Johnson, S. E.; Field, E. I.
1973-01-01
Linear, quadratic, and cubic isoparametric hexahedral solid elements have been added to the element library of NASTRAN. These elements are available for static, dynamic, buckling, and heat-transfer analyses. Because the isoparametric element matrices are generated by direct numerical integration over the volume of the element, variations in material properties, temperatures, and stresses within the elements are represented in the computations. In order to compare the accuracy of the new elements, three similar models of a slender cantilever were developed, one for each element. All elements performed well. As expected, however, the linear element model yielded excellent results only when shear behavior predominated. In contrast, the results obtained from the quadratic and cubic element models were excellent in both shear and bending.
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.
Simple shearing flow of dry soap foams with tetrahedrally close-packed structure
Reinelt, Douglas A. [Department of Mathematics, Southern Methodist University, Dallas, Texas 75275-0156 (United States)] [Department of Mathematics, Southern Methodist University, Dallas, Texas 75275-0156 (United States); Kraynik, Andrew M. [Engineering Sciences Center, Sandia National Laboratories, Albuquerque, New Mexico 87185-0834 (United States)] [Engineering Sciences Center, Sandia National Laboratories, Albuquerque, New Mexico 87185-0834 (United States)
2000-05-01
The microrheology of dry soap foams subjected to quasistatic, simple shearing flow 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 using the Surface Evolver to calculate foam structures that minimize total surface area at each value of strain. 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 structure associated with each stable solution branch results from an avalanche 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. (c) 2000 Society of Rheology.
Yang, Xingyi; Haubold, Lars; DeVivo, Gabriel; Swain, Greg M
2012-07-17
Tetrahedral amorphous carbon (ta-C) consists of a mixture of sp(3)- and sp(2)-bonded carbon ranging from 60 to 40% (sp(3)/sp(3)+sp(2)) depending on the deposition conditions. The physical, chemical, and electrochemical properties depend on the sp(2)/sp(3) bonding ratio as well as the presence of incorporated impurities, such as hydrogen or nitrogen. The ability to grow ta-C at lower temperatures (25-100 °C) on a wider variety of substrates as compared to CVD diamond is an advantage of this material. Herein, we report on the structural and electrochemical properties of nitrogen-incorporated ta-C thin films (ta-C:N). The incorporation of nitrogen into the films decreases the electrical resistivity from 613 ± 60 (0 sccm N(2)) to 1.10 ± 0.07 ?-cm (50 sccm N(2)), presumably by increasing the sp(2)-bonded carbon content and the connectedness of these domains. Similar to boron-doped diamond, these materials are characterized by a low background voltammetric current, a wide working potential window (~ 3 V), and relatively rapid electron-transfer kinetics for aqueous redox systems, including Fe(CN)(6)(-3/-4) and Ru(NH(3))(6)(+3/+2), without conventional pretreatment. Additionally, there is weak molecular adsorption of polar molecules (methylene blue) on the ta-C surface. Overall, the properties of the ta-C and ta-C:N electrodes are such that they could be excellent new choices for electroanalytical measurements. PMID:22715911
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.
An analysis of spectral envelope-reduction via quadratic assignment problems
NASA Technical Reports Server (NTRS)
George, Alan; Pothen, Alex
1994-01-01
A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper, we provide an analysis of the spectral envelope reduction algorithm. We described related 1- and 2-sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work involved in an envelope Cholesky factorization scheme. We formulate the latter two problems as quadratic assignment problems, and then study the 2-sum problem in more detail. We obtain lower bounds on the 2-sum by considering a projected quadratic assignment problem, and then show that finding a permutation matrix closest to an orthogonal matrix attaining one of the lower bounds justifies the spectral envelope reduction algorithm. The lower bound on the 2-sum is seen to be tight for reasonably 'uniform' finite element meshes. We also obtain asymptotically tight lower bounds for the envelope size for certain classes of meshes.
K. Wissing; J. Degen
1998-01-01
A perturbative model for the calculation of electron-phonon coupling constants of tetrahedral transition metal complexes based on the electrostatic ligand field theory is presented. Orbital vibronic coupling constants are expressed in terms of common ligand field parameters, and linear many-electron coupling constants for all d2-d9 strong field states in tetrahedral and octahedral symmetry are reduced to orbital coupling constants, enabling
NASA Astrophysics Data System (ADS)
Boscheri, Walter; Dumbser, Michael
2014-10-01
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with stiff relaxation source terms.
On the Number of Representation of Integers into Quadratic Forms
Nikos Bagis; M. L Glasser
2014-12-18
We give formulas for the number of representations of non negative integers into quadratic forms. We also consider the case cubic and quintic forms. Finally we give a mean value asymptotic formula, for the behavior of the function that counts the number of representations of an integer as sum of two squares, known also as Gauss circle problem.
IMPROVED BOUNDS ON SARKOZY'S THEOREM FOR QUADRATIC POLYNOMIALS
Lyall, Neil
IMPROVED BOUNDS ON SÂ´ARKÂ¨OZY'S THEOREM FOR QUADRATIC POLYNOMIALS MARIAH HAMEL NEIL LYALL ALEX RICE in the late 1970s independently by SÂ´arkÂ¨ozy and Furstenberg. Furstenberg used ergodic theory (see [3]) and obtained a purely qualitative result, proving the conjecture exactly as stated above. SÂ´arkÂ¨ozy, however
IMPROVED BOUNDS ON SARKOZY'S THEOREM FOR QUADRATIC POLYNOMIALS
Lyall, Neil
IMPROVED BOUNDS ON SÂ´ARKÂ¨OZY'S THEOREM FOR QUADRATIC POLYNOMIALS MARIAH HAMEL NEIL LYALL ALEX RICE in the late 1970s independently by SÂ´arkÂ¨ozy and Furstenberg. Furstenberg used ergodic theory in [3] and obtained a purely qualitative result, proving the conjecture exactly as stated above. SÂ´arkÂ¨ozy, however
Iterative Total Variation Regularization with Non-Quadratic Fidelity
Lin He; Martin Burger; Stanley J. Osher
2006-01-01
A generalized iterative regularization procedure based on the total variation penal- ization is introduced for image denoising models with non-quadratic convex fldelity terms. By using a suitable sequence of penalty parameters we solve the issue of solvability of minimization problems arising in each step of the iterative procedure, which has been encountered in a recently developed iterative total variation procedure
Passive harmonic filters design using Fortran Feasible Sequential Quadratic Programming
Mohamed Mamdouh Abdel Aziz; Essam El-Din Abou El-Zahab; Ahmed Faheem Zobaa; Dina Mamdooh Khorshied
2007-01-01
This paper presents an application of Fortran Feasible Sequential Quadratic Programming optimization method for finding the optimum fixed shunt inductive–capacitive compensator for power factor correction of non-linear loads, where source voltage and load current harmonics are considered. Optimization minimizes the transmission line losses, and maximizes the load power factor. The performance of the proposed solution is discussed by means of
Multi-Rank Adaptive Beamforming with Linear and Quadratic Constraints
Pezeshki, Ali
Multi-Rank Adaptive Beamforming with Linear and Quadratic Constraints Henry Cox, Ali Pezeshki the signal is either rank-one of unknown orientation in a subspace or multi-rank. Only signal. The unifying component is the multi-rank MVDR beamformer followed by post processing. Detection statistics
Discriminative learning quadratic discriminant function for handwriting recognition
Cheng-Lin Liu; Hiroshi Sako; Hiromichi Fujisawa
2004-01-01
In character string recognition integrating segmentation and classification, high classification accuracy and resistance to noncharacters are desired to the underlying classifier. In a previous evaluation study, the modified quadratic discriminant function (MQDF) proposed by Kimura et al. was shown to be superior in noncharacter resistance but inferior in classification accuracy to neural networks. This paper proposes a discriminative learning algorithm
Lower Bounds and Exact Algorithms for the Quadratic Minimum ...
2013-12-16
Dec 16, 2013 ... (QMSTP) is a quadratic 0-1 programming problem that consists of finding a .... incidence vector of a spanning tree of G, in an abuse of language, it will ..... Even in the light of Proposition 4, computing Z(F2) by explicitly solving ..... The process stops when the insertion of every edge not in T is evaluated and.
[On skull recognition of quadratic rational Bezier curve fitting].
Zhao, Wenbin; Xie, Xiaowei; Yang, Fuzeng; Zhang, Yanning
2008-04-01
Skull recognition is a new method of biometrics recognition. A skull recognition algorithm is presented in this paper by Quadratic rational Bezier curve fitting which accurately describes the feature of skull edge; the experiment results based on skull x-ray image show the correctness of this method. PMID:18610606
Holomorphic quantum mechanics with a quadratic Hamiltonian constraint
Jorma Louko
1993-01-01
A finite-dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic, and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator algebra. The different representations yield drastically different Hilbert spaces. In particular, all the spaces obtained in the antiholomorphic representation violate classical expectations for the spectra of certain operators, whereas
Interior-point methods for reduced Hessian successive quadratic programming
David J. Ternet; Lorenz T. Biegler
1999-01-01
Typical chemical process optimization problems have a large number of equations, but relatively few degrees of freedom. A reduced Hessian successive quadratic programming (rSQP) algorithm has been shown to be successful in solving these types of models efficiently. While the rSQP algorithm reduces the dimension of the QP subproblem solved at each iteration, the number of inequality constraints could still
LOQO: AN INTERIOR POINT CODE FOR QUADRATIC PROGRAMMING
ROBERT J. VANDERBEI
1998-01-01
This paper describes a software package, called LOQO, which implements a primal- dual interior-point method for general nonlinear programm ing. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programm ing with only brief mention of the extensions to convex and general nonlinear programming, since a detailed paper describing these extensions were published
Further Development on the Interior Algorithm for Convex Quadratic Programming
Ye, Yinyu
Â tion on interior algorithms for quadratic programming (QP) or linear complementarity problem (LCP. This algorithm creates a sequence of primal and dual interior feasible points converging to the optimal solution, which create a sequence of primal and dual interior feasible points converging to the optimal solution
Efficient Color Histogram Indexing for Quadratic Form Distance Functions
James L. Hafner; Harpreet S. Sawhney; William Equitz; Myron Flickner; Wayne Niblack
1995-01-01
In image retrieval based on color, the weighted distance between color histograms of two images, represented as a quadratic form, may be defined as a match measure. However, this distance measure is computationally expensive and it operates on high dimensional features (O(N)). We propose the use of low-dimensional, simple to compute distance measures between the color distributions, and show that
A class of quadratic deformations of Lie superalgebras
NASA Astrophysics Data System (ADS)
Jarvis, P. D.; Rudolph, G.; Yates, L. A.
2011-06-01
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 generalized Jacobi relations in the context of the Koszul property, and give a proof of the Poincaré-Birkhoff-Witt 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 generalization gl2(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. Original title: Finite-dimensional quadratic Lie superalgebras (arXiv:1010.3765v1).
QUADRATIC FORMS AND PFISTER NEIGHBORS IN CHARACTERISTIC 2
DETLEV W. HOFFMANN; AHMED LAGHRIBI
We study Pfister neighbors and their characterization over fields of characteristic 2, where we include the case of singular forms. We give a somewhat simplified proof of a theorem of Fitzgerald which provides a criterion for when a nonsingular quadratic form q is similar to a Pfister form in terms of the hyperbolicity of this form over the function field
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.
Algebraic rules for quadratic regularization of Newton's method
2013-08-06
Aug 6, 2013 ... The use of quadratic regularization dates back to the works of A. N. ... In view of assumption (2), when L is available one can bound the ...... Cholesky factorization fails, the successively more aggressive shifts ... problem name; its dimension (n); the number of performed iterations (#Iter) and function eval-.
ADAPTIVE BEAMPATTERN CONTROL USING QUADRATIC CONSTRAINTS FOR CIRCULAR ARRAY STAP
George Mason University
Space-Time Adaptive Processing (STAP) used in airborne radar systems combines signals from N antenna for adaptive and non-adaptive space- time beampattern synthesis using quadratic beampattern constraints on the weighted mean-square error between the adaptive pattern and a desired beampattern over a set of angle-Doppler
A Survey of the Quadratic Assignment Problem, with Applications
CLAYTON WARREN COMMANDER
2003-01-01
The Quadratic Assignment Problem (QAP) is one of the most inter- esting and most challenging combinatorial optimization problems in exis- tence. This paper will be a survey of the QAP. An introduction discussing the origins of the problem will be provided flrst. Next, formal problem descriptions and mathematical formulations will be given. Issues pertain- ing to the computational complexity of
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
A Linear-Quadratic Game Approach to Estimation and Smoothing
Ravi N. Banavar; Jason L. Speyer
1991-01-01
An estimator and smoother for a linear time varying system, over a finite time interval, are developed from a linear quadratic (LQ) game approach. The exogenous inputs composed of the measurement and process noise, and the initial state, are assumed to be finite energy signals whose statistics are unknown. The measure of performance is in the form of a disturbance
A Model for Quadrat Sampling with “Visibility Bias”
R. Dennis Cook; Frank B. Martin
1974-01-01
In aerial census data “visibility bias” is present because of the failure to observe some animals. A model is presented for quadrat sampling of randomly occurring groups whose size follows a single parameter power series distribution when there is a probability q > 0 of missing single animals. Maximum likelihood estimates of group density, average group size, and the visibility
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
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.
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.
A Factorization Approach to the Linear Regulator Quadratic Cost Problem
NASA Technical Reports Server (NTRS)
Milman, M. H.
1985-01-01
A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.
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 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.
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.
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.
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.
Support set expansion sensitivity analysis in convex quadratic optimization
Kamal Mirnia; Alireza Ghaffari Hadigheh
2007-01-01
In support set expansion sensitivity analysis, one concerns to find the range of parameter variation where the perturbed problem has an optimal solution with the support set that includes the support set of the given optimal solution of the unperturbed problem. In this article, we consider the perturbed convex quadratic optimization problem and present a method to identify the support
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…
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.
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.
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.
The Correlation Between Parity and Quadratic Polynomials Frederic Green
Green, Frederic
The Correlation Between Parity and Quadratic Polynomials Mod 3 Frederic Green Department exponential sums introduced by Cai, Green and Thierauf. The exponential sum and correlation bounds presented of the difficulties are quite formidable (e.g., the natural proof [RR] barrier presented by TC0 ), there are still
Contingency Simulation Using Single Phase Quadratized Power Flow
procedure for power system security assessment, reliability evaluation, and real time operation. Simulation methodology based on a single phase quadratized power flow (SPQPF) model that integrates the compensation assessment, reliability evaluation, and real time operation. It is important that simulation methods solve
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…
Computation of piecewise quadratic Lyapunov functions for hybrid systems
Mikael Johansson; Anders Rantzer
1998-01-01
This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods such as the circle and Popov criteria is explained. Several examples are included to demonstrate the flexibility and power
A Modified Sequence Quadratic Programming Method for Nonlinear Programming
Zhijun Luo; Guohua Chen; Lirong Wang
2011-01-01
Sequence quadratic programming method is one of the most useful methods for solving constrained optimization problem. In this paper, a new modified SQP method is proposed to solve the nonlinear programming. This algorithm starts from an arbitrary initial point and adjusts penalty parameter automatically. A descent direction is obtained by solving only one variant constrained subproblem. In order to avoid
On the spherical quadratic Zeeman problem in hydrogen
Joséreinaldo Silva; Sylvio Canuto
1984-01-01
The factorized wavefunction approach to perturbation theory is applied to the spherical quadratic Zeeman problem in hydrogen. The ground and excited 2p states are considered. The results are in good agreement with other available results and provide a good upper bound to the complete Zeeman energy shifts. Transition strengths are calculated in good agreement with available results and the quantitative
Nodal coordinates for the first-order quadratic Zeeman effect
S. Watanabe; P. F. O'Mahony
1987-01-01
A method due to Pechukas (1972) and De Leon and Heller (1984) is used to construct a curvilinear coordinate system appropriate to the first-order quadratic Zeeman effect. The method is introduced through the example of the classical Coulomb problem. The curvilinear nodal coordinates in momentum space are shown to be the elliptical cylindrical (or conical) coordinates employed by Herrick (1982)
Quadratic Zeeman effect in Rydberg states of NO
M. Raoult; S. Guizard; D. Gauyacq; A. Matzkin
2005-01-01
We analyse a resonant-enhanced multiphoton ionization (REMPI) spectrum of the high n (35-50) members of the Rydberg series of NO molecules recorded in a 1 T external magnetic field. In this range the quadratic Zeeman interaction takes over the Coulomb interaction and gradually scrambles the Coulomb structure of the Rydberg series. A perturbative quantum treatment of the diamagnetic interaction, giving
Number theoretic transforms over the golden section quadratic field
Vassil S. Dimitrov; T. V. Cosklev; B. Bonevsky
1995-01-01
A new number theoretic transform (NTT) over the real quadratic field Q(?5) is suggested and analyzed. Conventional NTTs are used for fast convolution of integer sequences. A new approach for computing number theoretic transforms (NTTs) is proposed, allowing real signals to be processed as well. The method is based on a Diophantine approximation of the input real signal before the
Analytical upstream collocation solution of a quadratically forced
Brill, Stephen H.
", keeping in mind that this is the grid PeÂ´clet number and not the global PeÂ´clet number (the latter of this paper is to present the analytical solution to the Hermite collocation discretization of a quadratically a second-order differential equation (DE) that models physical systems in which a combination of convective
Quadratically gated mixture of experts for incomplete data classification
Xuejun Liao; Hui Li; Lawrence Carin
2007-01-01
We introduce quadratically gated mixture of experts (QGME), a statistical model for multi-class nonlinear classiflcation. The QGME is formulated in the setting of incom- plete data, where the data values are partially observed. We show that the missing val- ues entail joint estimation of the data mani- fold and the classifler, which allows adaptive imputation during classifler learning. The expectation
Parallel Interior Point Solver for Structured Quadratic Programs ...
1910-30-82
Issues of implementation of a library for parallel interior-point methods for quadratic pro- gramming ..... are executed; it needs to access only their results. However ... eral structure exploiting IPM solver, we have tested it in the first instance only on Asset/Liability ... transaction volume (buying, selling) of this asset at this node.
Nash Strategies for Dynamic Noncooperative Linear Quadratic Sequential Games
Sontag, Eduardo
and advertising campaigns strategies of several competing firms in economics. A sequential game was firstNash Strategies for Dynamic Noncooperative Linear Quadratic Sequential Games Dan Shen Member, IEEE strategies, and their existence and uniqueness within the class of state feedback strategies are proved. When
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)
Quadratic interior-point methods in statistical disclosure control
2003-05-09
(they change the cell values) or nonperturbative (no change is performed). The most widely .... Therefore, in principle, that seems to be the best choice. To confirm the ... The second one is similar to the first generator of [11]. Cell values are ..... A thorough study of the behaviour of the spectral radius for quadratic problems is ...
The decimal scale for releves of permanent quadrats
G. Londo
1976-01-01
For vegetation analyses of permanent quadrats the author formerly used a modified scale of Braun-Blanquet with smaller intervals than in the original. For calculations of difference- and change quotients etc., on the basis of coverage, the symbols of this scale have to be converted to values proportional to the real coverage percentages. A conversion in simple terms is not possible;
Confidence set interference with a prior quadratic bound. [in geophysics
NASA Technical Reports Server (NTRS)
Backus, George E.
1989-01-01
Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.
NASA Astrophysics Data System (ADS)
Cabria, I.; López, M. J.; Alonso, J. A.; March, N. H.
2012-04-01
In silica (SiO2) and in most silicates, atomic associations exist with composition SiO4 and a structure with four O atoms in tetrahedral coordination around the Si atom. A similar feature is observed in germania (GeO2) and some solids containing Ge instead of Si, although the number of phases containing GeO4 tetrahedra is smaller. In contrast, and in spite of the fact that C is in the same column of the periodic table as Si and Ge, CO2 is a molecular solid, and crystalline and amorphous phases of CO2 showing CO4 tetrahedra are only obtained under extremely high pressures. We have investigated the relation between free SiO4, GeO4 and CO4 clusters and the tetrahedral associations found in the solids mentioned above. The lowest energy structure of those three free clusters is planar, but they have near-tetrahedral and distorted-tetrahedral isomers. The promotion energy from the planar structure to the distorted tetrahedral is low in SiO4, large in CO4, and intermediate in GeO4. This correlates with the facility to form tetrahedral associations in the solids.
Effect of mesh element type of Finite Element Model (FEM) on unimorph cantilever vibration
NASA Astrophysics Data System (ADS)
Aris, H.; Fitrio, D.; Singh, J.
2013-12-01
This paper discusses mesh refinement methods used to perform Finite Element Analysis (FEA) for vibration based MEMS Energy Harvester. The three types of meshing elements, 1) Linear Hexahedral, 2) Parabolic Hexahedral and 3) Parabolic Tetrahedral, were used in this study. The meshing methods are used to ensure accurate simulation result particularly in stress, and strain analysis obtained, since they are determined by the displacement of each node in the physical structure. The study of the accuracy of an mesh analysis is also known as mesh convergence study which element aspect ratios must be refined consistently. In this paper the dimensions of each elements were also varied in order to investigate the significant of this methods in achieving better ratios of simulation to theoretical results.
Implementation of an Evolving non Quadratic Anisotropic Behaviour for the Closed Packed Materials
Revil-Baudard, Benoit; Massoni, Elisabeth [CEMEF Mines ParisTech, B.P. 207, F-06904 Sophia-Antipolis (France)
2010-06-15
In this paper, the mechanical behaviour of alpha-titanium alloys is modelised for the cold forming processes. The elasto-plastic constitutive law is decomposed in an anisotropic plastic criterion, an isotropic hardening and a kinematic hardening. Non quadratic criteria have been developed by Cazacu et al.[1], to model the plasticity of hexagonal closed packed materials. The implementation of this model in a finite element software switch between two bases, the equilibrium is calculated in a reference basis and the anisotropy axes define a local basis, updated by the deformation gradient. An identification procedure, based on tensile tests, allows defining all the parameters needed to model the elasto-plastic behaviour. Simulations of cold forming processes (bulging and deep drawing) have been done to validate this model. Numerical results are compared with experimental data, obtained from speckles analysis.
Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations
Rainald Loehner; Ken Morgan; Jaime Peraire; Mehdi Vahdati
1987-01-01
A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm.
Haskel, Daniel
and the Center for Microwave Magnetic Materials and Integrated Circuits, Northeastern University, Boston to high permittivity, and low microwave loss for devices that send and receive electromagnetic signals demonstrated the ability to quantify the element-specific cat- ion distribution on tetrahedral and octahedral
Fourteen years of mapped, permanent quadrats in a northern mixed prairie, USA
Technology Transfer Automated Retrieval System (TEKTRAN)
This historical dataset consists of 44 permanent 1-m2 quadrats located on northern mixed prairie in eastern Montana, USA. Individual plants in these quadrats were identified and mapped annually from 1932 through 1945. Quadrats were located in six pastures assigned to cattle grazing treatments with l...
Quadratic forms and quaternion algebras: algorithms and arithmetic John Michael Voight
Voight, John
forms. Jagy and Kaplansky exhibited a table of 68 pairs of positive definite binary quadratic forms of a finite set. In the second part, we investigate a constellation of results concerning algorithms Contents I Quadratic forms 1 1 Primes represented by quadratic forms 2 1.1 Fields of definition
STATIONARY STATES OF QUADRATIC DIFFUSION EQUATIONS WITH LONG-RANGE ATTRACTION
Soatto, Stefano
STATIONARY STATES OF QUADRATIC DIFFUSION EQUATIONS WITH LONG-RANGE ATTRACTION M. BURGER, M. DI to a nonlocal aggregation equation with quadratic diffusion arising in many contexts in population dynamics. The equation is the Wasserstein gradient flow generated by the energy E, which is the sum of a quadratic free
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
SOLVING A QUADRATIC MATRIX EQUATION BY NEWTON'S METHOD WITH EXACT LINE SEARCHES
Higham, Nicholas J.
SOLVING A QUADRATIC MATRIX EQUATION BY NEWTON'S METHOD WITH EXACT LINE SEARCHES NICHOLAS J. HIGHAM for solving the quadratic matrix equation AX2 + BX + C = 0, where A, B and C are square matrices. The line the backward error of an approximate solution. Key words. quadratic matrix equation, solvent, Newton's method
A Hybrid Linear Equation Solver and its Application in Quadratic Placement
Sapatnekar, Sachin
A Hybrid Linear Equation Solver and its Application in Quadratic Placement Haifeng Qian and Sachin-- This paper presents a new hybrid linear equation solver for quadratic placement. The new solver widely used approaches fall into several different paradigms: quadratic placement [6
Algorithms to solve massively under-defined systems of multivariate quadratic equations
Algorithms to solve massively under-defined systems of multivariate quadratic equations Yasufumi chosen multivariate quadratic equations over a finite field is NP-hard. However, when the number quadratic equations; one is for the case of n (about) m2 -2m3/2 +2m and the other is for the case of n m
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 SchrÂ¨odinger equation. This approach is based
Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns
Candes, Emmanuel J.
Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns vector x0 Cn exactly from on the order of n quadratic equations of the form | ai, x0 |2 = bi, i = 1 Introduction Suppose we wish to solve quadratic equations of the form | ai, x0 |2 = bi, i = 1, . . . , m, (1
Optimal Quadratic Spline Collocation Methods for the Shallow Water Equations on the Sphere
Christara, Christina C.
Optimal Quadratic Spline Collocation Methods for the Shallow Water Equations on the Sphere Anita T, for solving the shallow water equations (SWEs) in spherical coÂ ordinates. A quadratic spline collocation formulation, the quadratic spline is computed by making the residual of the differential equations zero
Properties of quadratic equations and their application to power system analysis
Hiskens, Ian A.
Properties of quadratic equations and their application to power system analysis Y.V. Makarova,1 and control can be described by algebraic sets of quadratic equations of the form fx y gx 0 1 where x Rn x as a quadratic equations set with the Jacobian matrix Jx being a linear function of unknown variables. In any
Department of Mathematics 7.1: Quadratic Equations: Completing the Square
Ahmad, Sajjad
UNLV Department of Mathematics Â§7.1: Quadratic Equations: Completing the Square 1. Review) Quadratic Equation: An equation that can be written in the form ax2 + bx + c = 0 where a, b and c are real numbers and a = 0 is called a quadratic equation. (c) To Solve an Equation by Factoring i. Add or subtract
Geodesic diameter of sets defined by few quadratic equations and inequalities
Paris-Sud XI, UniversitÃ© de
Geodesic diameter of sets defined by few quadratic equations and inequalities Michel Coste of the unit ball in Rn described by a fixed number of quadratic equations and inequalities, whichO(k) for the geodesic diameter of (a bounded part of) a semialgebraic subset of Rn defined by k quadratic equations
Invariant nonnegative minimum norm quadratic estimator of variance components and its application
Zhao Ouyang
1992-01-01
Minimum norm quadratic estimators were introduced by C. R. Rao in the 70's to attempt to give an unified approach to variance component estimation. One such estimator, which is called invariant nonnegative minimum norm quadratic, was proposed but not explicitly determined. In this paper, a fnormal solution to the invariant nonnegative minimum norm quadratic estimator is presented and then applied
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
All-optical polarization switch in a quadratic nonlinear photonic quasicrystal
Arie, Ady
-dependent polarization switch based on cascaded three-wave-mixing interactions in a quasiperiodic quadratic nonlinear to the picosecond regime. The switching is obtained by cascad- ing two three-wave-mixing processes in a quadraticAll-optical polarization switch in a quadratic nonlinear photonic quasicrystal Ayelet Ganany
NASA Technical Reports Server (NTRS)
Motiwalla, S. K.
1973-01-01
Using the first and the second derivative of flutter velocity with respect to the parameters, the velocity hypersurface is made quadratic. This greatly simplifies the numerical procedure developed for determining the values of the design parameters such that a specified flutter velocity constraint is satisfied and the total structural mass is near a relative minimum. A search procedure is presented utilizing two gradient search methods and a gradient projection method. The procedure is applied to the design of a box beam, using finite-element representation. The results indicate that the procedure developed yields substantial design improvement satisfying the specified constraint and does converge to near a local optimum.
Pasaja, Nitisak; Sansongsiri, Sakon; Intasiri, Sawate; Vilaithong, Thiraphat; Anders, Andre
2007-01-24
Metal-containing tetrahedral amorphous carbon films wereproduced by dual filtered cathodic vacuum arc plasma sources operatedinsequentially pulsed mode. Negatively pulsed bias was applied to thesubstrate when carbon plasma was generated, whereas it was absentwhen themolybdenum plasma was presented. Film thickness was measured afterdeposition by profilometry. Glass slides with silver padswere used assubstrates for the measurement of the sheet resistance. Themicrostructure and composition of the films were characterizedbyRamanspectroscopy and Rutherford backscattering, respectively. It was foundthat the electrical resistivity decreases with an increaseof the Mocontent, which can be ascribed to an increase of the sp2 content and anincrease of the sp2 cluster size.
Pasaja, Nitisak; Sansongsiri, Sakon; Anders, Andre; Vilaithong,Thiraphat; Intasiri, Sawate
2006-09-10
Metal-containing tetrahedral amorphous carbon films were produced by dual filtered cathodic vacuum arc (FCVA) plasma sources operated in sequential pulsed mode. A negatively pulsed bias was applied to the substrate only when carbon plasma was generated. Films thickness was measured after deposition by profilometry. Glass slides with silver pads were used as substrate for the of the measurement sheet resistance. The microstructure and composition of the films were characterized by Raman spectroscopy and Rutherford backscattering, respectively. It found that the electrical resistivity decreases with an increase of the Mo content, which can be ascribed to an increase of sp2 content and an increase of the sp2 cluster size.
D. X. Li; K. H. Kuo
1985-01-01
Domain boundaries on (001), (111) and (112) planes in the ? phase of a superalloy were found by high resolution electron microscopy. These boundaries consisted of the following tetrahedrally close-packed phases:(001), other stacking variants such as C14, C15, C36, K7Cs6- and Zr4Al3-types;(111), C14, C (V2(Co, Si)3-type); and(112), differently oriented ? W2FeSi-type, M.The intergrowth of these closely related phases with pentagonal
NSDL National Science Digital Library
Ms. Schultz
2007-03-08
To find quick facts on elements The Photographic Periodic Table of Elements-shows a photograhpic representation of most of the elements (remember some are invisible gases) The Element Song Click on the following links to find quick facts about the elements and peridoic table: Periodic Table of Elements: LANL - Originally this resource, the Periodic Table, was created by Robert Husted at Los Alamos National Laboratory during his time ...
Quadratic nonlinear Klein-Gordon equation in one dimension
NASA Astrophysics Data System (ADS)
Hayashi, Nakao; Naumkin, Pavel I.
2012-10-01
We study the initial value problem for the quadratic nonlinear Klein-Gordon equation vtt + v - vxx = ?v2, t ? R, x ? R, with initial conditions v(0, x) = v0(x), vt(0, x) = v1(x), x ? R, where v0 and v1 are real-valued functions, ? ? R. Using the method of normal forms of Shatah ["Normal forms and quadratic nonlinear Klein-Gordon equations," Commun. Pure Appl. Math. 38, 685-696 (1985)], we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data, which was assumed in the previous work of J.-M. Delort ["Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi-linéaire á données petites en dimension 1," Ann. Sci. Ec. Normale Super. 34(4), 1-61 (2001)].
Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials
NASA Astrophysics Data System (ADS)
Aquilanti, V.; Marinelli, D.; Marzuoli, A.
2014-03-01
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger-like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed.
Linear quadratic regulators with eigenvalue placement in a specified region
NASA Technical Reports Server (NTRS)
Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar
1988-01-01
A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at + or - pi/2k (k = 2 or 3) from the negative real axis with a sector angle of pi/2 or less, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. The design method is mainly based on the solution of a linear matrix Liapunov equation, and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.
Spinor condensates with a laser-induced quadratic Zeeman effect
Santos, L. [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstr. 2, D-30167 Hannover (Germany); Fattori, M.; Stuhler, J.; Pfau, T. [5. Physikalisches Institut, Universitaet Stuttgart, Pfaffenwaldring 57 V, D-70550 Stuttgart (Germany)
2007-05-15
We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate {sup 52}Cr gas, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein-de Haas effect for relatively large magnetic fields, and may be employed to create S=1/2 systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exciting new control tool in spinor systems.
In situ aberration measurement technique based on quadratic Zernike model
NASA Astrophysics Data System (ADS)
Yang, Jishuo; Wang, Xiangzhao; Li, Sikun; Duan, Lifeng; Yan, Guanyong; Xu, Dongbo; Bourov, Anatoly Y.; Erdmann, Andreas
2012-12-01
A novel technique (AMAI-Quad) for aberration extraction of lithographic projection based on quadratic relationship model between aerial-image intensity distribution and Zernike coefficients is proposed. Zernike coefficients in this case represent the imaging quality of lithographic projection lens in a semiconductor wafer exposure scanner. The proposed method uses principal component analysis and multivariate linear regression analysis for model generation. This quadratic model is then used to extract Zernike coefficients by nonlinear least-squares. Compared with earlier techniques, based on a linear relationship between Zernike coefficients and aerial images, proposed by Duan, the new method can extend the types of aberrations measured. The application of AMAI-Quad to computed images of lithography simulators PROLITH and Dr.LiTHO for randomly varied wavefront aberrations within a range of 50m? demonstrated an accuracy improvement of 30%.
On solutions analysis of quadratic programming with fuzzy random coefficients and variables
NASA Astrophysics Data System (ADS)
Ammar, E. E.
2005-01-01
In this paper, we study a quadratic programming problem having fuzzy random coefficients matrix in the objective and constraints and the decision vector is a fuzzy pseudorandom variable. The first results show the fact that a fuzzy pseudorandom (random) optimal solution of a fuzzy random quadratic programming may be resolved into a series of pseudorandom (random) optimal solutions of relative random quadratic programming. Also we show that a fuzzy pseudorandom (fuzzy random) optimal solution of relative random quadratic programming is structured by a class of pseudorandom (random) optimal solutions of relative random quadratic programming. Illustrative examples are given.
Multipolar engineering of molecules and materials for quadratic nonlinear optics
Isabelle Ledoux; Joseph Zyss
2002-01-01
The first generation of molecular engineering studies whereby a one-dimensional bipolar donor–acceptor conjugated system had served, since the early 1970s, as a quasi-exclusive template, had failed to take into account the tensorial dimension attached to the ? quadratic hyperpolarizability tensor. We review here the outgoing second generation of molecular design studies based on three-dimensional multipolar charge transfer which reflects on
Metric operators for non-Hermitian quadratic su(2) Hamiltonians
NASA Astrophysics Data System (ADS)
Assis, Paulo E. G.
2011-07-01
A class of non-Hermitian quadratic su(2) Hamiltonians having an anti-linear symmetry is constructed. This is achieved by analysing the possible symmetries of such systems in terms of automorphisms of the algebra. In fact, different realizations for this type of symmetry are obtained, including the natural occurrence of charge conjugation together with parity and time reversal. Once specified, the underlying anti-linear symmetry of the Hamiltonian, the former, if unbroken, leads to a purely real spectrum and the latter can be mapped to a Hermitian counterpart by, amongst other possibilities, a similarity transformation. Here, Lie-algebraic methods which were used to investigate the generalized Swanson Hamiltonian (Assis and Fring 2009 J. Phys. A: Math. Theor. 42 015203) are employed to identify the class of quadratic Hamiltonians that allow for such a mapping to the Hermitian counterpart. Whereas for the linear su(2) system, every Hamiltonian of this type can be mapped to a Hermitian counterpart by a transformation which is itself an exponential of a linear combination of su(2) generators, the situation is more complicated for quadratic Hamiltonians. Therefore, the possibility of more elaborate similarity transformations, including quadratic exponents, is also explored in detail. The existence of finite-dimensional representations for the su(2) Hamiltonian, as opposed to the su(1, 1) studied before, allows for comparison with explicit diagonalization results for finite matrices. Finally, the similarity transformations constructed are compared with the analogue of Swanson's method for exact diagonalization of the problem, establishing a simple relation between both approaches.
Imprints of Quadratic Theories of Gravity on Accreting Matter
NASA Astrophysics Data System (ADS)
Macedo, C. F. B.; Crispino, L. C. B.
2015-01-01
In this work we present an analytical solution of a slowly rotating black hole in a modified theory of gravity in four dimensions, described by the Einstein-Hilbert action plus all quadratic, algebraic curvature invariants, generically coupled to a single scalar field. We explicitly show the frequencies of the innermost stable circular orbits and the light ring in this modified theory of gravity, to first order in the spin parameter.
Ultracold two-level atom in a quadratic potential
F. Soto-Eguibar; A. Zúñiga-Segundo; B. M. Rodríguez-Lara; H. M. Moya-Cessa
2014-12-17
We use a right unitary decomposition to study an ultracold two-level atom interacting with a quantum field. We show that such a right unitary approach simplifies the numerical evolution for arbitrary position-dependent atom-field couplings. In particular, we provide a closed form, analytic time evolution operator for atom-field couplings with quadratic dependence on the position of the atom.
Central Control, Sewers and (0,1) quadratic programming
NASA Astrophysics Data System (ADS)
Kolechkina, Alla; van Nooijen, Ronald
2013-04-01
We consider small sewer systems that combine foul water and storm water sewer functions in flat terrain. These systems are a combination of local gravity flow networks connected by pumps. The pumps are usually fixed speed, so they are on or off. We formulate a (0,1) quadratic programming problem, provide an overview of known solution methods and examine the relative speed of different solution methods.
Hirota quadratic equations for the extended Toda hierarchy
Todor E. Milanov
2007-01-01
The extended Toda hierarchy (ETH) was introduced by E. Getzler [Ge] and independently by Y. Zhang [Z] in order to describe an integrable hierarchy that governs the Gromov-Witten invariants of $\\\\mathbb{C}P^1$ . The Lax-type presentation of the ETH was given in [CDZ]. In this article, we give a description of the ETH in terms of tau functions and Hirota quadratic
A Predictorcorrector algorithm with multiple corrections for convex quadratic programming
Zhongyi Liu; Yue Chen; Wenyu Sun; Zhihui Wei
2012-01-01
Recently an infeasible interior-point algorithm for linear programming (LP) was presented by Liu and Sun. By using similar\\u000a predictor steps, we give a (feasible) predictor-corrector algorithm for convex quadratic programming (QP). We introduce a\\u000a (scaled) proximity measure and a dynamical forcing factor (centering parameter). The latter is used to force the duality gap\\u000a to decrease. The algorithm can decrease the
Quantum integrals of motion for variable quadratic Hamiltonians
Cordero-Soto, Ricardo, E-mail: ricardojavier81@gmail.co [Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States); Suazo, Erwin, E-mail: erwin.suazo@upr.ed [Department of Mathematical Sciences, University of Puerto Rico, Mayaquez, call box 9000, PR 00681-9000 (Puerto Rico); Suslov, Sergei K., E-mail: sks@asu.ed [School of Mathematical and Statistical Sciences and Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States)
2010-09-15
We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
Design of Linear Quadratic Regulators and Kalman Filters
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L.
1986-01-01
AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.
A fixed point approach to stability of a quadratic equation
M. Mirzavaziri; M. S. Moslehian
2006-01-01
. Using the fixed point alternative theorem we establish the orthogonal stability of the quadratic functional equation of Pexider\\u000a type f (x+y)+g(x?y) = h(x)+k(y), where f, g, h, k are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and\\u000a sufficient condition on f.
Observation of spectral drift in engineered quadratic nonlinear media
NASA Astrophysics Data System (ADS)
Marangoni, M.; Sanna, G.; Brida, D.; Conforti, M.; Cirmi, G.; Manzoni, C.; Baronio, F.; Bassi, P.; De Angelis, C.; Cerullo, G.
2008-07-01
Spectral blueshifts of femtosecond pulses induced by quadratic cascaded nonlinearities are experimentally studied in an engineered aperiodically poled stoichiometric lithium tantalate crystal with optimized nonlinear pattern and chirp of the input pump pulses. Starting from nearly Gaussian input pulses centered at 1420nm with 70nm spectral width, spectral shifts as high as 40nm were obtained in combination with an almost unaltered spectral shape and a transform-limited pulse duration.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Quantum integrals of motion for variable quadratic Hamiltonians
NASA Astrophysics Data System (ADS)
Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.
2010-09-01
We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
Dispersion relations for the quadratic Zeeman effect in heliumlike atoms
S. C. Kanavi; S. H. Patil
1981-01-01
The analyticity properties and the asymptotic behavior of the quadratic Zeeman energy shifts deltaE for an atom are analyzed, leading to once-subtracted dispersion relations for the energy shifts. In conjunction with the WKB expression for ImdeltaE in the weak-field limit and perturbation expressions for the susceptibility and the strong-field limit of ImdeltaE, these dispersion relations allow us to obtain (i)
Symmetry of the quadratic Zeeman effect for hydrogen
David R. Herrick
1982-01-01
The O(4) symmetry of the hydrogen-atom degeneracy is exploited to obtain an exact separation of the quadratic Zeeman interaction on the Fock hypersphere in momentum space, and hence a complete classification of levels in the weak-field limit. The separation constant includes a double-minimum potential, and levels below the top of the barrier have an approximate O(2)×O(2) symmetry and vibrational structure.
Symmetry of the quadratic Zeeman effect for hydrogen
David Herrick
1982-01-01
The O(4) symmetry of the hydrogen-atom degeneracy is exploited to obtain an exact separation of the quadratic Zeeman interaction on the Fock hypersphere in momentum space, and hence a complete classification of levels in the weak-field limit. The separation constant includes a double-minimum potential, and levels below the top of the barrier have an approximate O(2) x O(2) symmetry and
Nonperturbative dynamical-group approach to the quadratic Zeeman effect
Christopher C. Gerry; Jeffery Laub
1985-01-01
In this paper we consider the quadratic Zeeman effect from the point of view of scaling variational method based on the SO(4,2) dynamical group of the point Coulomb problem. In this formulation, the tilting angle is treated as a variational parameter. We scale a linear combination of the SO(4,2) basis states, solving numerically for the eigenvalues by diagonalization of the
Quadratic Zeeman Splitting of Highly Excited Relativistic Atomic Hydrogen
D. A. Arbatsky; P. A. Braun
Using the classical mechanical perturbation approach we were able to explain the structure of the quadratic Zeeman effect\\u000a spectrum of the atomic hydrogen Rydberg levels in weak magnetic fields in which the fine structure of the levels cannot be\\u000a neglected. The general structure of the spectrum turns out to be very different from the non-relativistic scheme. In particular\\u000a the division
Core scattering of quadratic Zeeman orbits in barium
Zhan Mingsheng; Liu Hongping; Shen Li; Jean-Patrick Connerade
2007-01-01
We report a method to uncover the peaks due to scattering of quadratic Zeeman orbits by the atomic core of a many-electron atom. The method is experimental, and consists in identifying the supernumerary peaks in the scaled-energy spectra by comparing them with the corresponding hydrogenic calculations using closed-orbit theory. The scaled actions of the observed additional peaks correspond to combining
On the spherical quadratic Zeeman problem in hydrogen
NASA Astrophysics Data System (ADS)
Silva, JoséReinaldo; Canuto, Sylvio
1984-04-01
The factorized wavefunction approach to perturbation theory is applied to the spherical quadratic Zeeman problem in hydrogen. The ground and excited 2p states are considered. The results are in good agreement with other available results and provide a good upper bound to the complete Zeeman energy shifts. Transition strengths are calculated in good agreement with available results and the quantitative role of the residual non-spherical perturbation is briefly analyzed.
Periodic solutions of quadratic Weyl fractional integral equations
NASA Astrophysics Data System (ADS)
Chen, Qian; Wang, JinRong; Chen, Fulai; Zhang, Yuruo
2014-06-01
In this paper, we study periodic solutions of quadratic Weyl fractional integral equations. We derive the convergence, periodicity, continuity and boundedness of Weyl kernel. With the help of these basic properties, we prove the existence of 2?-periodic solutions of the desired equation by using a technique of measure of noncompactness via Schauder fixed point theorem. Moreover, we obtain uniform local attractivity of the 2?-periodic solutions. Finally, an example is given to illustrate the obtained results.
Discrete quadratic solitons with competing second-harmonic components
Setzpfandt, Frank; Pertsch, Thomas [Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, D-07743 Jena (Germany); Sukhorukov, Andrey A. [Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra, 0200 ACT (Australia)
2011-11-15
We describe families of discrete solitons in quadratic waveguide arrays supported by competing cascaded nonlinear interactions between one fundamental and two second-harmonic modes. We characterize the existence, stability, and excitation dynamics of these solitons and show that their features may resemble those of solitons in saturable media. Our results also demonstrate that a power threshold may appear for soliton formation, leading to a suppression of beam self-focusing which explains recent experimental observations.
ON CONTINUITY PROPERTIES OF THE SOLUTION MAP IN QUADRATIC PROGRAMMING
NGUYEN NANG TAM
1999-01-01
We study in detail the lower semicontinuity and the upper semicontinuity properties of the set-valued map (D;A;c;b)7! sol (D;A;c;b), where sol(D;A;c;b) denotes the solution set of the quadratic programming problem Minimize f(x):=cTx+ 1 2x T Dx subject to Ax‚b; x‚0. In particular, a complete characterization for the lower semicontinuity of the map sol(¢) is obtained.
Solving semidefinite-quadratic-linear programs using SDPT3
Reha H. Tütüncü; K. C. Toh; Michael J. Todd
2003-01-01
. ?This paper discusses computational experiments with linear optimization problems involving semidefinite, quadratic, and linear\\u000a cone constraints (SQLPs). Many test problems of this type are solved using a new release of SDPT3, a Matlab implementation\\u000a of infeasible primal-dual path-following algorithms. The software developed by the authors uses Mehrotra-type predictor-corrector\\u000a variants of interior-point methods and two types of search directions: the HKM
Integer roots of quadratic and cubic polynomials with integer coefficients
Konstantine Zelator
2011-10-26
The subject matter of this work is quadratic and cubic polynomial functions with integer coefficients;and all of whose roots are integers. The material of this work is directed primarily at educators,students,and teachers of mathematics,grades K12 to K20.The results of this work are expressed in Theorems3,4,and5. Of these theorems, Theorem3, is the one that most likely, the general reader of this article will have some familiarity with.In Theorem3, precise coefficient conditions are given;in order that a quadratic trinomial(with integer) have two integer roots or zeros.On the other hand, Theorems4 and5 are largely unfamiliar territory. In Theorem4, precise coefficient conditions are stated; for a monic cubic polynomial to have a double(i.e.of multiplicity 2) integer root, and a single integer root(i.e.of multiplicity 1).The entire family of such cubics can be described in terms of four groups or subfamilies; each such group being a two-integer parameter subfamily. In Theorem5, a one-integer parameter family of quadratic trinomials(with integer coefficients) with two integer roots; is described.The parameter can take any odd positive integer values.
Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations
Holger R. Dullin; James D. Meiss
2008-07-04
We study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R^3. This family is the unfolded normal form for a bifurcation of a fixed point with a triple-one multiplier and also is the general form of a quadratic three-dimensional map with a quadratic inverse. Much of the nontrivial dynamics of this map occurs when its two fixed points are saddle-foci with intersecting two-dimensional stable and unstable manifolds that bound a spherical ``vortex-bubble''. We show that this occurs near a saddle-center-Neimark-Sacker (SCNS) bifurcation that also creates, at least in its normal form, an elliptic invariant circle. We develop a simple algorithm to accurately compute these elliptic invariant circles and their longitudinal and transverse rotation numbers and use it to study their bifurcations, classifying them by the resonances between the rotation numbers. In particular, rational values of the longitudinal rotation number are shown to give rise to a string of pearls that creates multiple copies of the original spherical structure for an iterate of the map.
Electroweak vacuum stability and finite quadratic radiative corrections
Isabella Masina; Germano Nardini; Mariano Quiros
2015-02-23
If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale $\\Lambda$ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. These can destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of physical masses. If the UV mass spectrum involves several scales the cutoff is not unique and each sector has its own UV cutoff $\\Lambda_i$. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic correction to the Higgs mass is equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs $\\Lambda_i$, these contributions can cancel even at TeV scales, unlike the case of a unique cutoff where the cancellation occurs at Planckian energies. Gauginos heavier than squarks tend to be favored. From the UV MSSM point of view, the quadratic sensitivity is incorporated into the matching conditions and for instance it provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM.
Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer
NASA Astrophysics Data System (ADS)
Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre
2014-07-01
We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.
NSDL National Science Digital Library
Integrated Teaching and Learning Program,
Students examine the periodic table and the properties of elements. They learn the basic definition of an element and the 18 elements that compose most of the matter in the universe. The periodic table is described as one method of organization for the elements. The concepts of physical and chemical properties are also reviewed.
A Comparison of Gradient-and Hessian-Based Optimization Methods for Tetrahedral Mesh
Shontz, Suzanne M.
Improvement Shankar Prasad Sastry1 and Suzanne M. Shontz1 Department of Computer Science and Engineering differential equations (PDEs). The accuracy of the computed solution to the PDE depends on the degree of using one solver over another in order to smooth a particular unstructured, finite element mesh
S. Ø. Wille
1997-01-01
This paper presents the development of the three- dimensional prolonged adaptive finite element equation solver for the Navier-Stokes equations. The finite element used is the tetrahedron with quadratic approximation of the velocities and linear approximation of the pressure. The equation system is formulated in the basic variables. The grid is adapted to the solution by the element Reynolds number. An
The MITC9 shell element in plate bending: mathematical analysis of a simplified case
Klaus-Jürgen Bathe; Franco Brezzi; L. Donatella Marini
2011-01-01
We consider the 9-node shell element referred to as the MITC9 shell element in plate bending solutions and present a simplified mathematical analysis. The element uses bi-quadratic interpolations of the rotations\\u000a and transverse displacement, and the “rotated Raviart-Thomas” interpolations for the transverse shear stresses. A rigorous\\u000a mathematical analysis of the element is still lacking, even for the simplified case of
Relativistic Stellar Model Admitting a Quadratic Equation of State
NASA Astrophysics Data System (ADS)
Sharma, R.; Ratanpal, B. S.
2013-11-01
A class of solutions describing the interior of a static spherically symmetric compact anisotropic star is reported. The analytic solution has been obtained by utilizing the Finch and Skea [Class. Quantum Grav.6 (1989) 467] ansatz for the metric potential grr which has a clear geometric interpretation for the associated background spacetime. Based on physical grounds, appropriate bounds on the model parameters have been obtained and it has been shown that the model admits an equation of state (EOS) which is quadratic in nature.
A-REI A Linear and Quadratic System
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Consider the linear and quadratic functions appearing in the figure below. What are the coordinates of the point Q? Show step-by-step algebra work. Wha...
Analysis of electroperforated materials using the quadrat counts method
NASA Astrophysics Data System (ADS)
Miranda, E.; Garzón, C.; Martínez-Cisneros, C.; Alonso, J.; García-García, J.
2011-06-01
The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.
Exact cascading nonlinearity in quasi-phase-matched quadratic media.
Conforti, Matteo
2014-04-15
The evolution of light pulses and beams in a quasi-phase-matched (QPM) quadratic medium is usually described by considering only the spatial harmonic of the QPM grating that minimizes the residual phase-mismatch. I show that, for strongly phase-mismatched interactions (the cascading regime), several harmonics need to be accounted for in order to obtain the correct value of the effective cubic nonlinearity, for which I find a simple analytical expression. I discuss the effects of the higher order harmonics of the grating on solitary wave propagation. PMID:24979010
On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations
Sekine, Jun [Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)], E-mail: sekine@kier.kyoto-u.ac.jp
2006-09-15
The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula.
Strange Quark Star Model with Quadratic Equation of State
Malaver, Manuel
2014-01-01
In this paper, we studied the behaviour of compact relativistic objects with anisotropic matter distribution considering quadratic equation of state of Feroze and Siddiqui (2011). We specify the gravitational potential Z(x) in order to integrate the fields equations and there has been calculated the energy density, the radial pressure, the anisotropy and the mass function. The new solutions to the Einstein-Maxwell system of equations are found in term of elementary functions. For n=2, we have obtained the expressions for mass function, energy density, radius and metric functions of the model of Thirukkanesh and Ragel (2012) with polytropic equation of state.
Discrete-time Markovian-jump linear quadratic optimal control
NASA Technical Reports Server (NTRS)
Chizeck, H. J.; Willsky, A. S.; Castanon, D.
1986-01-01
This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.
Strange Quark Star Model with Quadratic Equation of State
Manuel Malaver
2014-07-03
In this paper, we studied the behaviour of compact relativistic objects with anisotropic matter distribution considering quadratic equation of state of Feroze and Siddiqui (2011). We specify the gravitational potential Z(x) in order to integrate the fields equations and there has been calculated the energy density, the radial pressure, the anisotropy and the mass function. The new solutions to the Einstein-Maxwell system of equations are found in term of elementary functions. For n=2, we have obtained the expressions for mass function, energy density, radius and metric functions of the model of Thirukkanesh and Ragel (2012) with polytropic equation of state.