Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.
Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A
2016-03-21
Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. PMID:26900037
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
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.
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.
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.
A suitable low-order, eight-node tetrahedral finite element for solids
Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.
1998-03-01
To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the eight-node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties.
NASA Astrophysics Data System (ADS)
Cheng, Jiahao; Shahba, Ahmad; Ghosh, Somnath
2016-01-01
Image-based CPFE modeling involves computer generation of virtual polycrystalline microstructures from experimental data, followed by discretization into finite element meshes. Discretization is commonly accomplished using three-dimensional four-node tetrahedral or TET4 elements, which conform to the complex geometries. It has been commonly observed that TET4 elements suffer from severe volumetric locking when simulating deformation of incompressible or nearly incompressible materials. This paper develops and examines three locking-free stabilized finite element formulations in the context of crystal plasticity finite element analysis. They include a node-based uniform strain (NUS) element, a locally integrated B-bar (LIB) based element and a F-bar patch (FP) based element. All three formulations are based on the partitioning of TET4 element meshes and integrating over patches to obtain favorable incompressibility constraint ratios without adding large degrees of freedom. The results show that NUS formulation introduces unstable spurious energy modes, while the LIB and FP elements stabilize the solutions and are preferred for reliable CPFE analysis. The FP element is found to be computationally efficient over the LIB element.
Uniform Strain Elements for Three-Node Triangular and Four-Node Tetrahedral Meshes
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.; Witkowski, W.R.
1999-03-02
A family of uniform strain elements is presented for three-node triangular and four-node tetrahedral meshes. The elements use the linear interpolation functions of the original mesh, but each element is associated with a single node. As a result, a favorable constraint ratio for the volumetric response is obtained for problems in solid mechanics. The uniform strain elements do not require the introduction of additional degrees of freedom and their performance is shown to be significantly better than that of three-node triangular or four-node tetrahedral elements. In addition, nodes inside the boundary of the mesh are observed to exhibit superconvergent behavior for a set of example problems.
Tetrahedral Element Shape Optimization via the Jacobian Determinant and Condition Number
FREITAG,LORI A.; KNUPP,PATRICK
1999-09-27
We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. We use this shape measure to formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the tetrahedral mesh; the second aims to improve the worst-quality element in the mesh. Because the element condition number is not defined for tetrahedral with negative volume, these objective functions can be used only when the initial mesh is valid. Therefore, we formulate a third objective function using the determinant of the element Jacobian that is suitable for mesh untangling. We review the optimization techniques used with each objective function and present experimental results that demonstrate the effectiveness of the mesh improvement and untangling methods. We show that a combined optimization approach that uses both condition number objective functions obtains the best-quality meshes.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES
RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT
2013-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called ‘serendipity’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974
NASA Astrophysics Data System (ADS)
Zehner, Björn; Börner, Jana H.; Görz, Ines; Spitzer, Klaus
2015-06-01
Subsurface processing numerical simulations require accurate discretization of the modeling domain such that the geological units are represented correctly. Unstructured tetrahedral grids are particularly flexible in adapting to the shape of geo-bodies and are used in many finite element codes. In order to generate a tetrahedral mesh on a 3D geological model, the tetrahedrons have to belong completely to one geological unit and have to describe geological boundaries by connected facets of tetrahedrons. This is especially complicated at the contact points between several units and for irregular sharp-shaped bodies, especially in case of faulted zones. This study develops, tests and validates three workflows to generate a good tetrahedral mesh from a geological basis model. The tessellation of the model needs (i) to be of good quality to guarantee a stable calculation, (ii) to include certain nodes to apply boundary conditions for the numerical solution, and (iii) support local mesh refinement. As a test case we use the simulation of a transient electromagnetic measurement above a salt diapir. We can show that the suggested workflows lead to a tessellation of the structure on which the simulation can be run robustly. All workflows show advantages and disadvantages with respect to the workload, the control the user has over the resulting mesh and the skills in software handling that are required.
NASA Astrophysics Data System (ADS)
Usui, Yoshiya
2015-08-01
A 3-D magnetotelluric (MT) inversion code using unstructured tetrahedral elements has been developed in order to correct the topographic effect by directly incorporating it into computational grids. The electromagnetic field and response functions get distorted at the observation sites of MT surveys because of the undulating surface topography, and without correcting this distortion, the subsurface structure can be misinterpreted. Of the two methods proposed to correct the topographic effect, the method incorporating topography explicitly in the inversion is applicable to a wider range of surveys. For forward problems, it has been shown that the finite element method using unstructured tetrahedral elements is useful for the incorporation of topography. Therefore, this paper shows the applicability of unstructured tetrahedral elements in MT inversion using the newly developed code. The inversion code is capable of using the impedance tensor, the vertical magnetic transfer function (VMTF), and the phase tensor as observational data, and it estimates the subsurface resistivity values and the distortion tensor of each observation site. The forward part of the code was verified using two test models, one incorporating topographic effect and one without, and the verifications showed that the results were almost the same as those of previous works. The developed inversion code was then applied to synthetic data from a MT survey, and was verified as being able to recover the resistivity structure as well as other inversion codes. Finally, to confirm its applicability to the data affected by topography, inversion was performed using the synthetic data of the model that included two overlapping mountains. In each of the cases using the impedance tensor, the VMTF and the phase tensor, by including the topography in the mesh, the subsurface resistivity was determined more proficiently than in the case using the flat-surface mesh. Although the locations of the anomalies were not accurately estimated by the inversion using distorted impedance tensors due to the slightly undervalued gain, these locations were correctly estimated by using undistorted impedance tensors or adding VMTFs in the data. Therefore, it can be concluded that the inversion using the unstructured tetrahedral element effectively prevents the misinterpretation of subsurface resistivity and recovers subsurface resistivity proficiently by representing the topography in the computational mesh.
Finite-element analysis of earing using non-quadratic yield surfaces
Logan, R.W.
1995-06-18
During deep draw cupping, the phenomenon known as earing may occur as the cup wall is formed, resulting in a periodic variation of cup wall height around the perimeter of the finished cup. This is generally due to planar anisotropy of flow in rolled sheet product. It is generally observed that the anisotropy parameter R will vary in the plane of the sheet when ears are observed in cupping, with a parameter {Delta}R describing the variation of R in the plane of the sheet. For many common textures in face-centered and body-centered materials, the ears form relative to the sheet rolling direction at 0{degrees} and 90{degrees} around the perimeter if {Delta}R>0, and at -45{degrees} and +45{degrees} if {Delta}R<0. There is extensive experimental evidence that ear height shows a linear correlation with {Delta}R/R, but attempts to duplicate this using the finite-element method are highly dependent on both the methodology and yield surface used. It was shown previously that using a coarse mesh and the quadratic Hill yield surface tends to greatly under predict earing. In this study, we have used two different finite-element codes developed at LLNL to examine the predicted earing using both quadratic Hill and alternative non-quadratic yield surfaces. These results are compared to experimental data and conclusions drawn about the most desirable closed-form yield surfaces to duplicate the observed earing phenomena.
Hollaus, K; Magele, C; Merwa, R; Scharfetter, H
2004-02-01
Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed. PMID:15005313
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.
NASA Astrophysics Data System (ADS)
Liu, Yang; Lissenden, Cliff J.; Rose, J. L.
2013-01-01
A comprehensive analysis for guided wave preferred fundamental excitation that satisfies cumulative conditions of second harmonic generation in a weakly nonlinear plate has been carried out and then confirmed by finite element modeling for selected cases. The properties of nonlinear forcing terms and secondary mode shapes are manipulated to determine the cumulative second harmonics. Analysis shows that the synchronism points with higher power flux intensity are the preferred fundamental excitations that are suitable for nonlinear guided wave NDE. Finite element modeling of SH mode and Lamb mode fundamental excitation has been conducted on the excitation points selected by the co-analysis method. A linear increase of qualitative nonlinear parameter over the propagation distance has been observed for both Lamb wave and SH wave fundamental excitations.
Weichert, Frank; Schröder, Andreas; Landes, Constantin; Shamaa, Ali; Awad, Said Kamel; Walczak, Lars; Müller, Heinrich; Wagner, Mathias
2010-06-01
In this article, we present a new method for the generation of surface meshes of biological soft tissue. The method is based on the deformable surface model technique and is extended to histological data sets. It relies on an iterative adjustment towards polygonal segments describing the histological structures of the soft tissue. The generated surface meshes allow for the construction of volumetric meshes through a standard constrained Delaunay approach and, thus, for the application in finite element methods. The geometric properties of volumetric meshes have an immediate influence on the numerical conditioning and, therewith, on the stability of the finite element method and the convergence of iterative solvers. In this article, the influence of the surface meshes on the quality of the volumetric meshes is analysed in terms of the spectral condition number of the stiffness matrices, which are assembled within Newton's method. The non-linear material behavior of biological soft tissue is modeled by the Mooney-Rivlin material law. The subject is motivated by the requirements of virtual surgery. PMID:20411435
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…
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 manyâ€¦
Streaming simplification of tetrahedral meshes.
Vo, Huy T; Callahan, Steven P; Lindstrom, Peter; Pascucci, Valerio; Silva, Cláudio T
2007-01-01
Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish real-time visualization necessary for scientific analysis. We propose a two-step approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/O-efficient format that allows coherent access to the tetrahedral cells. A quadric-based simplification is sequentially performed on small portions of the mesh in-core. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates out-of-core to process meshes too large for main memory. PMID:17093343
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[superscriptâ€¦
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…
Circuit analog of quadratic optomechanics
NASA Astrophysics Data System (ADS)
Kim, Eun-jong; Johansson, J. R.; Nori, Franco
2015-03-01
We propose a superconducting electrical circuit that simulates a quadratic optomechanical system. A capacitor placed between two transmission-line (TL) resonators acts like a semitransparent membrane, and a superconducting quantum interference device (SQUID) that terminates a TL resonator behaves like a movable mirror. Combining these circuit elements, it is possible to simulate a quadratic optomechanical coupling whose coupling strength is determined by the coupling capacitance and the tunable bias flux through the SQUIDs. Estimates using realistic parameters suggest that an improvement in the coupling strength could be realized, to five orders of magnitude from what has been observed in membrane-in-the-middle cavity optomechanical systems. This leads to the possibility of achieving the strong-coupling regime of quadratic optomechanics.
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
Unstructured tetrahedral mesh generation technology
NASA Astrophysics Data System (ADS)
Danilov, A. A.
2010-01-01
We present a robust unstructured tetrahedral mesh generation technology. This technology is a combination of boundary discretization methods, an advancing front technique and a Delaunay-based mesh generation technique. For boundary mesh generation we propose four different approaches using analytical boundary parameterization, interface with CAD systems, surface mesh refinement, and constructive solid geometry. These methods allow us to build a flexible grid generation technology with a user friendly interface.
A tetrahedral entropy for water.
Kumar, Pradeep; Buldyrev, Sergey V; Stanley, H Eugene
2009-12-29
We introduce the space-dependent correlation function C (Q)(r) and time-dependent autocorrelation function C (Q)(t) of the local tetrahedral order parameter Q identical with Q(r,t). By using computer simulations of 512 waterlike particles interacting through the transferable interaction potential with five points (TIP5 potential), we investigate C (Q)(r) in a broad region of the phase diagram. We find that at low temperatures C (Q)(t) exhibits a two-step time-dependent decay similar to the self-intermediate scattering function and that the corresponding correlation time tau(Q) displays a dynamic cross-over from non-Arrhenius behavior for T > T (W) to Arrhenius behavior for T < T (W), where T (W) denotes the Widom temperature where the correlation length has a maximum as T is decreased along a constant-pressure path. We define a tetrahedral entropy S (Q) associated with the local tetrahedral order of water molecules and find that it produces a major contribution to the specific heat maximum at the Widom line. Finally, we show that tau(Q) can be extracted from S (Q) by using an analog of the Adam-Gibbs relation. PMID:20018692
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.
Building Tetrahedral Kites. Grades 6-8.
ERIC Educational Resources Information Center
Rushton, Erik; Ryan, Emily; Swift, Charles
Working in teams of four, students build a tetrahedral kite following a specific set of directions and using specific provided materials. Students use basic processes of manufacturing systems-- cutting, shaping, forming, conditioning, assembling, joining, finishing, and quality control--to manufacture a complete tetrahedral kite within a givenâ€¦
Refitted tetrahedral covalent radii for solids
NASA Astrophysics Data System (ADS)
Pyykkö, Pekka
2012-01-01
The previous systems of molecular single-, double-, and triple-bond self-consistent, additive covalent radii R(AB) = r(A) + r(B) are now completed with a fit for crystals, where both atoms are tetrahedrally coordinated. A self-consistent primary fit is carried out using elements such as Si and binary compounds such as GaAs or ZnS. Further checks involve also ternary compounds such as chalcopyrites, CuInS2, and the quaternary compounds Cu2ZnSnS4 and Cu2ZnSnSe4, the latter two with both kesterite and stannite structures. The input bond lengths R are taken from experimental or theoretical data. For the 30 elements in the primary fit, the mean-square deviation of the predicted R(AB) values is only 0.67 pm for the 48 systems used. The results are compared to earlier radii by Pauling and Huggins [Z. Kristallogr. A 87, 205 (1934)] or by Van Vechten and Phillips [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.2.2160 2, 2160 (1970)], and to the recent molecular covalent radii.
Tetrahedral Hohlraum Visualization and Pointings
NASA Astrophysics Data System (ADS)
Klare, K. A.; Wallace, J. M.; Drake, D.
1997-11-01
In designing experiments for Omega, the tetrahedral hohlraum (a sphere with four holes) can make full use of all 60 beams. There are some complications: the beams must clear the laser entrance hole (LEH), must miss a central capsule, absolutely must not go out the other LEHs, and should distribute in the interior of the hohlraum to maximize the uniformity of irradiation on the capsule while keeping reasonable laser spot sizes. We created a 15-offset coordinate system with which an IDL program computes clearances, writes a file for QuickDraw 3D (QD3D) visualization, and writes input for the viewfactor code RAYNA IV. Visualizing and adjusting the parameters by eye gave more reliable results than computer optimization. QD3D images permitted quick live rotations to determine offsets. The clearances obtained insured safe operation and good physics. The viewfactor code computes the initial irradiation of the hohlraum and capsule or of a uniform hohlraum source with the loss through the four LEHs and shows a high degree of uniformity with both, better for lasers because this deposits more energy near the LEHs to compensate for the holes.
Sequentially deployable maneuverable tetrahedral beam
NASA Technical Reports Server (NTRS)
Mikulas, M. M., Jr.; Crawford, R. F. (inventors)
1985-01-01
A tetrahedral beam that can be compactly stowed, sequentially deployed, and widely manipulated to provide a structurally sound yet highly maneuverable truss structure is comprised of a number of repeating units of tandem tetralhedral sharing common sides. Fixed length battens are jointed into equilateral triangles called batten frames. Apexes of adjacent triangles are interconnected by longerons having a mid-point folding hinge. Joints, comprised of gussets pivotabley connected by links, permit two independent degrees of rotational freedom between joined adjacent batten frames, and provide a stable structure from packaged configuration to complete deployment. The longerons and joints can be actuated in any sequence, independently of one another. The beam is suited to remote actuation. Longerons may be provided with powered mid-point hinges enabling beam erection and packaging under remote control. Providing one or more longerons with powered telescoping segments permits the shape of the beam central axis to be remotely manipulated so that the beam may function as a remote manipulator arm.
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]â€¦
The Mystical "Quadratic Formula."
ERIC Educational Resources Information Center
March, Robert H.
1993-01-01
Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)
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]…
Au40: A Large Tetrahedral Magic Cluster
Jiang, Deen; Walter, Michael
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.
Neutrino Mixing and the Double Tetrahedral Group
NASA Astrophysics Data System (ADS)
Bentov, Yoni; Zee, A.
2013-11-01
In the spirit of a previous study of the tetrahedral group T ?A4, we discuss a minimalist scheme to derive the neutrino mixing matrix using the double tetrahedral group T?, the double cover of T. The new features are three distinct two-dimensional representations and complex Clebsch-Gordan coefficients, which can result in a geometric source of CP violation in the neutrino mass matrix. In an appendix, we derive explicitly the relevant group theory for the tetrahedral group T and its double cover T?.
Details of tetrahedral anisotropic mesh adaptation
NASA Astrophysics Data System (ADS)
Jensen, Kristian Ejlebjerg; Gorman, Gerard
2016-04-01
We have implemented tetrahedral anisotropic mesh adaptation using the local operations of coarsening, swapping, refinement and smoothing in MATLAB without the use of any for- N loops, i.e. the script is fully vectorised. In the process of doing so, we have made three observations related to details of the implementation: 1. restricting refinement to a single edge split per element not only simplifies the code, it also improves mesh quality, 2. face to edge swapping is unnecessary, and 3. optimising for the Vassilevski functional tends to give a little higher value for the mean condition number functional than optimising for the condition number functional directly. These observations have been made for a uniform and a radial shock metric field, both starting from a structured mesh in a cube. Finally, we compare two coarsening techniques and demonstrate the importance of applying smoothing in the mesh adaptation loop. The results pertain to a unit cube geometry, but we also show the effect of corners and edges by applying the implementation in a spherical geometry.
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.
Motion compensation for PET image reconstruction using deformable tetrahedral meshes
NASA Astrophysics Data System (ADS)
Manescu, P.; Ladjal, H.; Azencot, J.; Beuve, M.; Shariat, B.
2015-12-01
Respiratory-induced organ motion is a technical challenge to PET imaging. This motion induces displacements and deformation of the organs tissues, which need to be taken into account when reconstructing the spatial radiation activity. Classical image-based methods that describe motion using deformable image registration (DIR) algorithms cannot fully take into account the non-reproducibility of the respiratory internal organ motion nor the tissue volume variations that occur during breathing. In order to overcome these limitations, various biomechanical models of the respiratory system have been developed in the past decade as an alternative to DIR approaches. In this paper, we describe a new method of correcting motion artefacts in PET image reconstruction adapted to motion estimation models such as those based on the finite element method. In contrast with the DIR-based approaches, the radiation activity was reconstructed on deforming tetrahedral meshes. For this, we have re-formulated the tomographic reconstruction problem by introducing a time-dependent system matrix based calculated using tetrahedral meshes instead of voxelized images. The MLEM algorithm was chosen as the reconstruction method. The simulations performed in this study show that the motion compensated reconstruction based on tetrahedral deformable meshes has the capability to correct motion artefacts. Results demonstrate that, in the case of complex deformations, when large volume variations occur, the developed tetrahedral based method is more appropriate than the classical DIR-based one. This method can be used, together with biomechanical models controlled by external surrogates, to correct motion artefacts in PET images and thus reducing the need for additional internal imaging during the acquisition.
NASA Astrophysics Data System (ADS)
Colin, M.; Di Menza, L.; Saut, J. C.
2016-03-01
In this paper, we investigate the properties of solitonic structures arising in quadratic media. First, we recall the derivation of systems governing the interaction process for waves propagating in such media and we check the local and global well-posedness of the corresponding Cauchy problem. Then, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or non-elliptic systems and we address the problem of orbital stability. Finally, some numerical experiments are carried out in order to compute localized states for several regimes and to study dynamic stability as well as long-time asymptotics.
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.
Tetrahedral boron in naturally occurring tourmaline
Tagg, S.L.; Cho, H.; Dyar, M.D.; Grew, E.S.
1999-09-01
Evidence for boron in both trigonal and tetrahedral coordination has been found in {sup 11}B magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectra of natural, inclusion-free specimens of aluminum-rich lithian tourmaline from granitic pregmatites.
Search for Tetrahedral Symmetry in 70Ge
NASA Astrophysics Data System (ADS)
Le, Khanh; Haring-Kaye, R. A.; Elder, R. M.; Jones, K. D.; Morrow, S. I.; Tabor, S. L.; Tripathi, V.; Bender, P. C.; Allegro, P. R. P.; Medina, N. H.; Oliveira, J. R. B.; Doring, J.
2014-09-01
The even-even Ge isotopes have recently become an active testing ground for a variety of exotic structural characteristics, including the existence of tetrahedral symmetry (pyramid-like shapes). Although theoretical shape calculations predict the onset of tetrahedral symmetry near 72Ge, the experimental signatures (including vanishing quadrupole moments within high-spin bands) remain elusive. This study searched for possible experimental evidence of tetrahedral symmetry in 70Ge. Excited states in 70Ge were populated at Florida State University using the 55Mn(18O,p2n) fusion-evaporation reaction at 50 MeV. Prompt ?- ? coincidences were measured with a Compton-suppressed Ge array consisting of three Clover detectors and seven single-crystal detectors. The existing level scheme was enhanced through the addition of 20 new transitions and the rearrangement of five others based on the measured coincidence relations and relative intensities. Lifetimes of 24 states were measured using the Doppler-shift attenuation method, from which transition quadrupole moments were inferred. These results will be compared with those obtained from cranked Woods-Saxon calculations. The even-even Ge isotopes have recently become an active testing ground for a variety of exotic structural characteristics, including the existence of tetrahedral symmetry (pyramid-like shapes). Although theoretical shape calculations predict the onset of tetrahedral symmetry near 72Ge, the experimental signatures (including vanishing quadrupole moments within high-spin bands) remain elusive. This study searched for possible experimental evidence of tetrahedral symmetry in 70Ge. Excited states in 70Ge were populated at Florida State University using the 55Mn(18O,p2n) fusion-evaporation reaction at 50 MeV. Prompt ?- ? coincidences were measured with a Compton-suppressed Ge array consisting of three Clover detectors and seven single-crystal detectors. The existing level scheme was enhanced through the addition of 20 new transitions and the rearrangement of five others based on the measured coincidence relations and relative intensities. Lifetimes of 24 states were measured using the Doppler-shift attenuation method, from which transition quadrupole moments were inferred. These results will be compared with those obtained from cranked Woods-Saxon calculations. This work was supported by the National Science Foundation and by the Ohio Wesleyan University Summer Science Research Program.
On a combined adaptive tetrahedral tracing and edge diffraction model
NASA Astrophysics Data System (ADS)
Hart, Carl R.
A major challenge in architectural acoustics is the unification of diffraction models and geometric acoustics. For example, geometric acoustics is insufficient to quantify the scattering characteristics of acoustic diffusors. Typically the time-independent boundary element method (BEM) is the method of choice. In contrast, time-domain computations are of interest for characterizing both the spatial and temporal scattering characteristics of acoustic diffusors. Hence, a method is sought that predicts acoustic scattering in the time-domain. A prediction method, which combines an advanced image source method and an edge diffraction model, is investigated for the prediction of time-domain scattering. Adaptive tetrahedral tracing is an advanced image source method that generates image sources through an adaptive process. Propagating tetrahedral beams adapt to ensonified geometry mapping the geometric sound field in space and along boundaries. The edge diffraction model interfaces with the adaptive tetrahedral tracing process by the transfer of edge geometry and visibility information. Scattering is quantified as the contribution of secondary sources along a single or multiple interacting edges. Accounting for a finite number of diffraction permutations approximates the scattered sound field. Superposition of the geometric and scattered sound fields results in a synthesized impulse response between a source and a receiver. Evaluation of the prediction technique involves numerical verification and numerical validation. Numerical verification is based upon a comparison with analytic and numerical (BEM) solutions for scattering geometries. Good agreement is shown for the selected scattering geometries. Numerical validation is based upon experimentally determined scattered impulse responses of acoustic diffusors. Experimental data suggests that the predictive model is appropriate for high-frequency predictions. For the experimental determination of the scattered impulse response the merits of a maximum length sequence (MLS) versus a logarithmic swept-sine (LSS) are compared and contrasted. It is shown that a LSS is an appropriate stimuli for testing acoustic diffusors by comparing against scattered relative levels measured by a MLS signal.
Use of quadratic components for buckling calculations
Dohrmann, C.R.; Segalman, D.J.
1996-12-31
A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.
Kinetically Trapped Tetrahedral Cages via Alkyne Metathesis.
Lee, Semin; Yang, Anna; Moneypenny, Timothy P; Moore, Jeffrey S
2016-02-24
In dynamic covalent synthesis, kinetic traps are perceived as disadvantageous, hindering the system from reaching its thermodynamic equilibrium. Here we present the near-quantitative preparation of tetrahedral cages from simple tritopic precursors using alkyne metathesis. While the cages are the presumed thermodynamic sink, we experimentally demonstrate that the products no longer exchange their vertices once they have formed. The example reported here illustrates that kinetically trapped products may facilitate high yields of complex products from dynamic covalent synthesis. PMID:26854552
Quadratic Generalized Scale Invariance
NASA Astrophysics Data System (ADS)
Lovejoy, S.; Schertzer, D.; Addor, J. B.
Nearly twenty years ago, two of us argued that in order to account for the scaling strat- ification of the atmosphere, that an anisotropic "unified scaling model" of the atmo- sphere was required with elliptical dimension 23/9=2.555... "in between" the standard 3-D (small scale) and 2-D large scale model. This model was based on the formal- ism of generalized scale invariance (GSI). Physically, GSI is justified by arguing that various conserved fluxes (energy, buoyancy force variance etc.) should define the ap- propriate notion of scale. In a recent large scale satellite cloud image analysis, we directly confirmed this model by studying the isotropic (angle averaged) horizontal cloud statistics. Mathematically, GSI is based on a a group of scale changing opera- tors and their generators but to date, both analyses (primarily of cloud images) and nu- merical (multifractal) simulations, have been limited to the special case of linear GSI. This has shown that cloud texture can plausibly be associated with local linearizations. However realistic morphologies involve spatially avarying textures; the full non linear GSI is clearly necessary. In this talk, we first show that the observed angle averaged (multi)scaling statistics only give a realtively weak constraint on the nonlinear gner- ator: that the latter can be expressed by self-similar (isotropic) part, and a deviatoric part described (in two dimensions) by an arbitrary scalar potential which contains all the information about the cloud morphology. We then show (using a theorem due to Poincaré) how to reduce nonlinear GSI to linear GSI plus a nonlinear coordinate trans- formation numerically, using this to take multifractal GSI modelling to the next level of approximation: quadratic GSI. We show many examples of the coresponding simu- lations which include transitions from various morphologies (including cyclones) and we discuss the results in relation to satellite cloud images.
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 80â€‰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
Boundary Recovery For Delaunay Tetrahedral Meshes Using Local Topological Transformations.
Ghadyani, Hamid; Sullivan, John; Wu, Ziji
2010-01-01
Numerous high-quality, volume mesh-generation systems exist. However, no strategy can address all geometry situations without some element qualities being compromised. Many 3D mesh generation algorithms are based on Delaunay tetrahedralization which frequently fails to preserve the input boundary surface topology. For biomedical applications, this surface preservation can be critical as they usually contain multiple material regions of interest coherently connected. In this paper we present an algorithm as a post-processing method that optimizes local regions of compromised element quality and recovers the original boundary surface facets (triangles) regardless of the original mesh generation strategy. The algorithm carves out a small sub-volume in the vicinity of the missing boundary facet or compromised element, creating a cavity. If the task is to recover a surface boundary facet, a natural exit hole in the cavity will be present. This hole is patched with the missing boundary surface face first followed by other patches to seal the cavity. If the task was to improve a compromised region, then the cavity is already sealed. Every triangular facet of the cavity shell is classified as an active face and can be connected to another shell node creating a tetrahedron. In the process the base of the tetrahedron is removed from the active face list and potentially 3 new active faces are created. This methodology is the underpinnings of our last resort method. Each active face can be viewed as the trunk of a tree. An exhaustive breath and depth search will identify all possible tetrahedral combinations to uniquely fill the cavity. We have streamlined this recursive process reducing the time complexity by orders of magnitude. The original surfaces boundaries (internal and external) are fully restored and the quality of compromised regions improved. PMID:20305743
Equivalence of quadratic performance criteria.
NASA Technical Reports Server (NTRS)
Martin, C.
1973-01-01
Necessary and sufficient conditions are derived in terms of system parameters and quadratic weighting matrices for two quadratic cost functionals that are defined to be equivalent if they generate the same optimal control law. The derived conditions lie between the conditions of Tanaka and Asai (1971) and those of Kreindler and Hedrick (1970). Sufficient conditions for a vector valued function to attain an infimum are stated.
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.
Dark Matter from Binary Tetrahedral Flavor Symmetry
NASA Astrophysics Data System (ADS)
Eby, David; Frampton, Paul
2012-03-01
Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.
Shock wave admissibility for quadratic conservation laws
Canic, S.
1992-01-01
This dissertation presents a new approach to analysing admissible shock wave solutions for the systems of quadratic conservation laws, i.e., systems of the form U[sub t] + F(U)[sub x] = 0, x [element of] R, t > 0, U(x,t) [element of] R[sup 2], where the flux function F is a quadratic polynomial in U. The author studies systems that change type from hyperbolic to elliptic. The viscosity admissibility criterion is used to study admissibility of shock waves. This criterion requires for a shock wave to be admissible that its end states are joined by an orbit for an associated dynamical system. The author analyzes the stability of shock waves with respect to the change of the state on the left to the shock wave, and the shock speed. The stability analysis for admissible shock waves reduces to the bifurcation analysis of the three-parameter family of planar, quadratic dynamical systems. The family of all such dynamical systems is parameterized by the fundamental wave manifold W. The region of W comprising admissible shock waves is bounded by the loci of structurally unstable dynamical systems. Explicit formulae are presented for the admissibility boundaries that include the loci associated with saddle-node, Hopf, and straight line heteroclinic connections. Using the Melnikov's integral analysis, the tangent manifold to the homoclinic part of the admissibility boundary is calculated at the Bogdanov-Takens points of W. The heteroclinic loci are explored corresponding to the curved connecting orbits and the true homoclinic locus. The author shows the region of admissible waves for a generic, two-dimensional slice of the fundamental wave manifold, and compares it with the set of shock points that comply with the classical Lax criterion. The subregions are presented where the two criteria are not equivalent.
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.
ADAPTIVE TETRAHEDRAL GRID REFINEMENT AND COARSENING IN MESSAGE-PASSING ENVIRONMENTS
Hallberg, J.; Stagg, A.
2000-10-01
A grid refinement and coarsening scheme has been developed for tetrahedral and triangular grid-based calculations in message-passing environments. The element adaption scheme is based on an edge bisection of elements marked for refinement by an appropriate error indicator. Hash-table/linked-list data structures are used to store nodal and element formation. The grid along inter-processor boundaries is refined and coarsened consistently with the update of these data structures via MPI calls. The parallel adaption scheme has been applied to the solution of a transient, three-dimensional, nonlinear, groundwater flow problem. Timings indicate efficiency of the grid refinement process relative to the flow solver calculations.
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.
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)
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.
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.
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.
Analytical and Photogrammetric Characterization of a Planar Tetrahedral Truss
NASA Technical Reports Server (NTRS)
Wu, K. Chauncey; Adams, Richard R.; Rhodes, Marvin D.
1990-01-01
Future space science missions are likely to require near-optical quality reflectors which are supported by a stiff truss structure. This support truss should conform closely with its intended shape to minimize its contribution to the overall surface error of the reflector. The current investigation was conducted to evaluate the planar surface accuracy of a regular tetrahedral truss structure by comparing the results of predicted and measured node locations. The truss is a 2-ring hexagonal structure composed of 102 equal-length truss members. Each truss member is nominally 2 meters in length between node centers and is comprised of a graphite/epoxy tube with aluminum nodes and joints. The axial stiffness and the length variation of the truss components were determined experimentally and incorporated into a static finite element analysis of the truss. From this analysis, the root mean square (RMS) surface error of the truss was predicted to be 0.11 mm (0004 in). Photogrammetry tests were performed on the assembled truss to measure the normal displacements of the upper surface nodes and to determine if the truss would maintain its intended shape when subjected to repeated assembly. Considering the variation in the truss component lengths, the measures rms error of 0.14 mm (0.006 in) in the assembled truss is relatively small. The test results also indicate that a repeatable truss surface is achievable. Several potential sources of error were identified and discussed.
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.
MMS Spacecraft Transition to Tetrahedral Flying Formation - Duration: 49 seconds.
In the latter half of July 2015, the four satellites of the Magnetosphere Multi-scale (MMS) mission move into their tetrahedral formation flying configuration as part of the checkout for the scienc...
Low-energy tetrahedral polymorphs of carbon, silicon, and germanium
NASA Astrophysics Data System (ADS)
Mujica, Andrés; Pickard, Chris J.; Needs, Richard J.
2015-06-01
Searches for low-energy tetrahedral polymorphs of carbon and silicon have been performed using density functional theory computations and the ab initio random structure searching approach. Several of the hypothetical phases obtained in our searches have enthalpies that are lower or comparable to those of other polymorphs of group 14 elements that have either been experimentally synthesized or recently proposed as the structure of unknown phases obtained in experiments, and should thus be considered as particularly interesting candidates. A structure of P b a m symmetry with 24 atoms in the unit cell was found to be a low-energy, low-density metastable polymorph in carbon, silicon, and germanium. In silicon, P b a m is found to have a direct band gap at the zone center with an estimated value of 1.4 eV, which suggests applications as a photovoltaic material. We have also found a low-energy chiral framework structure of P 41212 symmetry with 20 atoms per cell containing fivefold spirals of atoms, whose projected topology is that of the so-called Cairo-type two-dimensional pentagonal tiling. We suggest that P 41212 is a likely candidate for the structure of the unknown phase XIII of silicon. We discuss P b a m and P 41212 in detail, contrasting their energetics and structures with those of other group 14 elements, particularly the recently proposed P 42/n c m structure, for which we also provide a detailed interpretation as a network of tilted diamondlike tetrahedra.
Inhibitors of angiotensin-converting enzyme containing a tetrahedral arsenic atom.
Galardy, R E; Kortylewicz, Z P
1985-01-01
A series of tetrahedral oxo acids of Group VA and VIA elements and of silicon and boron were examined as inhibitors of angiotensin-converting enzyme. Arsenate is a competitive inhibitor with a Ki of 27 +/- 1 mM, at least 10-fold more potent than phosphate. Dimethylarsinate is a competitive inhibitor with a Ki of 70 +/- 9 mM, 2-fold more potent than dimethylphosphinate. Oxo acids of boron, silicon, antimony, sulphur and selenium are not inhibitors. On the basis of these results and the strong inhibition of this zinc metallopeptidase by substrate analogues containing a tetrahedral phosphorus atom, two substrate analogues containing a tetrahedral arsenic atom were prepared. 2-Arsonoacetyl-L-proline is a competitive inhibitor with a Ki of 18 +/- 7 mM, more than 2000-fold weaker than that of its phosphorus analogue 2-phosphonoacetyl-L-proline. 4-Arsono-2-benzylbutanoic acid is a mixed inhibitor with a Ki of 0.5 +/- 0.2 mM, indistinguishable in potency from its phosphorus analogue 2-benzyl-4-phosphonobutanoic acid. PMID:2986596
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 semiparametric Von Mises calculus
Robins, James; Li, Lingling; Tchetgen, Eric
2009-01-01
We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter. For parameters for which the matching cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n–1/2-rate. In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n–1/2-rate. PMID:23087487
Quadratic fluctuation-dissipation theorem for multilayer plasmas
Golden, K.I.
1999-01-01
The author establishes the dynamical and static quadratic fluctuation-dissipation theorems (QFDTs) for multilayer classical one-component plasmas in the absence of external magnetic fields. Areal densities and spacings between layers need not be equal. The static QFDT is used to derive the lowest-order (in coupling parameter) Mayer cluster expansion for the layer-space matrix elements of the equilibrium three-point correlation function. {copyright} {ital 1999} {ital The American Physical Society}
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
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…
A comparison of tetrahedral mesh improvement techniques
Freitag, L.A.; Ollivier-Gooch, C.
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.
Pejov, Ljupco; Ivanovski, Gjorgji; Petrusevski, Vladimir M
2004-11-01
A theoretical model that enables a quantitative description of latent symmetry effects in the case of matrix isolated tetrahedral species is developed. Several particular cases are considered, that are of special interest from vibrational spectroscopic viewpoint. It is shown that the observed appearances of the IR spectra of various XY4n- anions isomorphously isolated in solid matrices may be systematically explained in terms of the orientation of the effective local crystalline field vector. The model also principally enables calculation of the magnitude of the effective local homogeneous field vector as well as its direction with respect to the symmetry elements of the dopant species, and it can be successively corrected accounting for the field non-homogeneity. Also, a solid theoretical basis is for the first time presented for the significantly smaller site group splitting of the nu4 modes of dopant XY4n- species in comparison to the splitting of nu3 ones, which is often observed in the IR spectra. However, the presented approach has potentially a much wider applicability, as it in facts considers the vibrational states of tetrahedral molecular species in electric fields, which may be of a different origin, for example, electrodes in electrochemical systems, external fields in Stark-type spectroscopies, etc. PMID:15477164
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…
Hinge specification for a square-faceted tetrahedral truss
NASA Technical Reports Server (NTRS)
Adams, L. R.
1984-01-01
A square-faceted tetrahedral truss is geometrically analyzed. Expressions are developed for single degree of freedom hinges which allow packaging of the structure into a configuration in which all members are parallel and closely packed in a square pattern. Deployment is sequential, thus providing control over the structure during deployment.
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.)
Gravitational Energy in Quadratic-Curvature Gravities
NASA Astrophysics Data System (ADS)
Deser, S.; Tekin, Bayram
2002-08-01
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 Î›, and E is the ``cosmological'' Abbott-Deser (AD) expression; instead, E always vanishes in flat, Î›=0, background. For combined Einstein-quadratic curvature systems without explicit Î›-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Î›-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.
Kuprat, A.; George, D.
1998-12-01
When modeling deformation of geometrically complex regions, unstructured tetrahedral meshes provide the flexibility necessary to track interfaces as they change geometrically and topologically. In the class of time-dependent simulations considered in this paper, multimaterial interfaces are represented by sets of triangular facets, and motion of the interfaces is controlled by physical considerations. The motion of interior points in the conforming tetrahedral mesh (i.e., points not on interfaces) is arbitrary and may be chosen to produce good element shapes. In the context of specified boundary motion driven by physical considerations, they have found that a rather large glossary of mesh changes is required to allow the simulation to survive all the transitions of interface geometry and topology that occur during time evolution. This paper will describe mesh changes required to maintain good element quality as the geometry evolves, as well as mesh changes required to capture changes i n topology that occur when material regions collapse or pinch off. This paper will present a detailed description of mesh changes necessary for capturing the aforementioned geometrical and topological changes, as implemented in the code GRAIN3D, and will provide examples from a metallic grain growth simulation in which the normal velocity of the grain boundary is proportional to mean curvature.
On ideal structure in quadratic DDS in R{sup 2}
Kutnjak, Milan
2008-11-13
We consider the dynamics in a special case of two-dimensional quadratic homogeneous discrete dynamical systems. It is well known (c.f. [1, 2]) that homogeneous quadratic maps are in one to one correspondence with two-dimensional commutative (nonassociative) algebras. Algebraic concepts (such as the structure of algebra and existence of special elements like idempotents and nilpotents) help us to study the dynamics of the corresponding discrete homogeneous quadratic maps. It is well-known that such systems can exhibit chaotic behavior [3], In this article we consider the influence of the existence of an algebra ideal on the dynamics of the corresponding discrete homogeneous quadratic system. We also present some examples in the plane.
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.
Coarse-grained theory of a realistic tetrahedral liquid model
NASA Astrophysics Data System (ADS)
Procaccia, I.; Regev, I.
2012-02-01
Tetrahedral liquids such as water and silica-melt show unusual thermodynamic behavior such as a density maximum and an increase in specific heat when cooled to low temperatures. Previous work had shown that Monte Carlo and mean-field solutions of a lattice model can exhibit these anomalous properties with or without a phase transition, depending on the values of the different terms in the Hamiltonian. Here we use a somewhat different approach, where we start from a very popular empirical model of tetrahedral liquids â€”the Stillinger-Weber modelâ€” and construct a coarse-grained theory which directly quantifies the local structure of the liquid as a function of volume and temperature. We compare the theory to molecular-dynamics simulations and show that the theory can rationalize the simulation results and the anomalous behavior.
Tetrahedrally bonded carbonates and aqueous carbonate anions under extreme conditions
NASA Astrophysics Data System (ADS)
Pan, Ding; Galli, Giulia; Deep Carbon Observatory Collaboration
The carbonate ion, CO32- , has a trigonal planar structure composed of carbon bonded with three oxygen atoms. The existence of tetrahedrally bonded carbonate units, CO4, analogous to SiO4 in silicates, has long been under debate. Using a combination of first-principles calculations and in situ infrared spectroscopy measurements, we provided definitive evidence that in magnesite, at pressures above 80 GPa, sp2 bonded CO3 trigonal groups transforms into sp3 bonded CO4 tetrahedral units. These units were found to be asymmetric, with two longer and two shorter C-O bonds. In addition, using first principles molecular dynamics we investigated carbonate anions in water at high temperature and pressure, corresponding to Earth's upper mantle conditions. We found significant quantities of bicarbonate ions dissolved in the liquid. The relevance of our simulation results for geophysical models of hydrous carbonates in the Earth will be discussed. Supported by the Sloan Foundation through the Deep Carbon Observatory.
Tetrahedral gray code for visualization of genome information.
Ichinose, Natsuhiro; Yada, Tetsushi; Gotoh, Osamu
2014-01-01
We propose a tetrahedral Gray code that facilitates visualization of genome information on the surfaces of a tetrahedron, where the relative abundance of each [Formula: see text]-mer in the genomic sequence is represented by a color of the corresponding cell of a triangular lattice. For biological significance, the code is designed such that the [Formula: see text]-mers corresponding to any adjacent pair of cells differ from each other by only one nucleotide. We present a simple procedure to draw such a pattern on the development surfaces of a tetrahedron. The thus constructed tetrahedral Gray code can demonstrate evolutionary conservation and variation of the genome information of many organisms at a glance. We also apply the tetrahedral Gray code to the honey bee (Apis mellifera) genome to analyze its methylation structure. The results indicate that the honey bee genome exhibits CpG overrepresentation in spite of its methylation ability and that two conserved motifs, CTCGAG and CGCGCG, in the unmethylated regions are responsible for the overrepresentation of CpG. PMID:24475080
Tetrahedral Gray Code for Visualization of Genome Information
Ichinose, Natsuhiro; Yada, Tetsushi; Gotoh, Osamu
2014-01-01
We propose a tetrahedral Gray code that facilitates visualization of genome information on the surfaces of a tetrahedron, where the relative abundance of each -mer in the genomic sequence is represented by a color of the corresponding cell of a triangular lattice. For biological significance, the code is designed such that the -mers corresponding to any adjacent pair of cells differ from each other by only one nucleotide. We present a simple procedure to draw such a pattern on the development surfaces of a tetrahedron. The thus constructed tetrahedral Gray code can demonstrate evolutionary conservation and variation of the genome information of many organisms at a glance. We also apply the tetrahedral Gray code to the honey bee (Apis mellifera) genome to analyze its methylation structure. The results indicate that the honey bee genome exhibits CpG overrepresentation in spite of its methylation ability and that two conserved motifs, CTCGAG and CGCGCG, in the unmethylated regions are responsible for the overrepresentation of CpG. PMID:24475080
Binary signaling over channels containing quadratic nonlinearities
NASA Technical Reports Server (NTRS)
Lawless, W. J.; Schwartz, M.
1974-01-01
This paper examines the transmission of binary data signals over channels which contain quadratic nonlinearities and additive Gaussian noise. We consider the case where the channel is nonlinear with memory and where the signal is passed through an input receiver filter and sampled once every signaling interval. The samples are represented by a discrete Volterra series and a special case where the received sample contains a single quadratic distortion term is examined. The optimum (maximum-likelihood) receiver (processor) is derived and upper and lower performance bounds obtained. The performance of a practical, suboptimum receiver is examined by means of computer simulation and is shown to be very close to the lower bound of the optimum receiver. Next we examine the case where the received sample contains two quadratic distortion terms. Again, upper and lower performance bounds are obtained.
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
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
Quadratic ??-corrections to heterotic double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2015-10-01
We investigate ??-corrections of heterotic double field theory up to quadratic order in the language of supersymmetric O (D, D + dim ? G) gauged double field theory. After introducing double-vielbein formalism with a parametrization which reproduces heterotic supergravity, we show that supersymmetry for heterotic double field theory up to leading order ??-correction is obtained from supersymmetric gauged double field theory. We discuss the necessary modifications of the symmetries defined in supersymmetric gauged double field theory. Further, we construct supersymmetric completion at quadratic order in ??.
Guises and disguises of quadratic divergences
Cherchiglia, A.L.; Vieira, A.R.; Hiller, Brigitte; BaÃªta Scarpelli, A.P.; Sampaio, Marcos
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale Î». We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Quintessence with quadratic coupling to dark matter
Boehmer, Christian G.; Chan, Nyein; Caldera-Cabral, Gabriela; Lazkoz, Ruth; Maartens, Roy
2010-04-15
We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.
Guises and disguises of quadratic divergences
NASA Astrophysics Data System (ADS)
Cherchiglia, A. L.; Vieira, A. R.; Hiller, Brigitte; Baêta Scarpelli, A. P.; Sampaio, Marcos
2014-12-01
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale ?. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
On orthogonality preserving quadratic stochastic operators
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Quadratic-Like Dynamics of Cubic Polynomials
NASA Astrophysics Data System (ADS)
Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen
2016-02-01
A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.
An inner-outer nonlinear programming approach for constrained quadratic matrix model updating
NASA Astrophysics Data System (ADS)
Andretta, M.; Birgin, E. G.; Raydan, M.
2016-01-01
The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric second-order finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model. Taking advantage of the special structure of the constraint set, it is first shown that the QFEMUP can be formulated as a suitable constrained nonlinear programming problem. Using this formulation, a method based on successive optimizations is then proposed and analyzed. To avoid that spurious modes (eigenvectors) appear in the frequency range of interest (eigenvalues) after the model has been updated, additional constraints based on a quadratic Rayleigh quotient are dynamically included in the constraint set. A distinct practical feature of the proposed method is that it can be implemented by computing only a few eigenvalues and eigenvectors of the associated quadratic matrix pencil.
NASA Astrophysics Data System (ADS)
Kwack, JaeHyuk; Masud, Arif
2014-04-01
This paper presents a stabilized mixed finite element method for shear-rate dependent fluids. The nonlinear viscosity field is a function of the shear-rate and varies uniformly in space and in time. The stabilized form is developed via application of Variational Multiscale (VMS) framework to the underlying generalized Navier-Stokes equation. Linear and quadratic tetrahedral and hexahedral elements are employed with equal-order interpolations for the velocity and pressure fields. A variety of benchmark problems are solved to assess the stability and accuracy properties of the resulting method. The method is then applied to non-Newtonian shear-rate dependent flows in bifurcating artery geometry, and significant non-Newtonian fluid effects are observed. A comparative study of the proposed method shows that the additional computational costs due to the nonlinear shear-rate dependent viscosity are only ten percent more than the computational cost for a Newtonian model.
Fourier analysis of quadratic phase interferograms
NASA Astrophysics Data System (ADS)
MuÃ±oz-Maciel, JesÃºs; Mora-GonzÃ¡lez, Miguel; Casillas-RodrÃguez, Francisco J.; PeÃ±a-Lecona, Francisco G.
2015-06-01
A phase demodulation method from a single interferogram with a quadratic phase term is developed. The fringe pattern being analysed may contain circular, elliptic or astigmatic fringes. The Fourier transform of such interferograms is seen to be also a sine or a cosine of a second order polynomial in both the real and imaginary parts. In this work we take a discrete Fourier transform of the fringe patterns and then we take separate inverse discrete transforms of the real and imaginary parts of the frequency spectrum. This results in two new interferograms corresponding to the sine and cosine of the quadratic term of the phase modulated by the sine and cosine of the linear term. The linear term of these interferograms may be recovered with similar procedures of fringe analysis from open fringe interferograms. Once the linear term is retrieved the quadratic phase of the interferogram being analysed can also be calculated. The present approach is also being investigated for interferograms with nearly circularly symmetry given that the phase contains some tilt. The described procedure of Fourier analysis from quadratic phase interferograms of nearly symmetric interferograms could be used instead of complex and time consuming algorithms for phase recovery from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.
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…
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.
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.
Tribological and Mechanical Properties of Aluminum Containing Tetrahedral Amorphous Carbon Films
NASA Astrophysics Data System (ADS)
Liu, E.; Gao, J. X.; Tay, B. K.; Shi, X.; Zeng, A.
Tetrahedral amorphous carbon (ta-C) films which contained aluminum element were fabricated by filtered cathodic vacuum arc (FCVA) method. The tribological characteristics of the ta-C films were investigated with ball-on-disk tribometer. The increment of aluminum in the ta-C film leads to an increase of sp2 carbon bonding and a decrease of sp3 fraction in the film. The roughness of the films was measured with atomic force microscope, and the hardness and Young's modulus of the films were measured with nanoindentation. The results showed that the film hardness and Young's modulus dropped with the increase of Al content in the films. The results have been interpreted with respect to the change of sp3 and sp2 fractions in the ta-C:Al films.
Ligands effects on the magnetic anisotropy of tetrahedral cobalt complexes.
Saber, Mohamed R; Dunbar, Kim R
2014-10-21
The effect of ligands with heavy donor atoms on the magnetic anisotropy of the pseudo-tetrahedral cobalt complexes, Co(quinoline)2I2 (1) and Co(EPh3)2I2 (2-3) (E = P, As) has been investigated. The axial zero-field splitting parameter D was found to vary from +9.2 cm(-1) in 1 to -36.9 cm(-1) in 2 and -74.7 cm(-1) in 3. Compounds 2 and 3 exhibit slow relaxation of the magnetization up to 4 K under an applied dc field, indicating SMM behavior. PMID:25183324
Computational studies of polyvinyl alcohol encapsulated tetrahedral cadmium sulphide cluster
NASA Astrophysics Data System (ADS)
Bala, Vaneeta; Tripathi, S. K.; Kumar, Ranjan
2013-06-01
In the present work theoretical encapsulation of tetrahedral cluster of cadmium sulphide within polyvinyl alcohol (PVA) chains has been studied. Density of states, binding energy and optical properties are calculated using density functional theory (DFT) as implemented in SIESTA code with local density approximation (LDA) functionals. We observe that PVA chains strongly interact with [Cd4(SH)10]2- cluster through-OH groups and results in broadening of the band gap. Absorption spectrum of hybrid structure is also computed which is comparable to experimental results.
Platelet adhesion on phosphorus-incorporated tetrahedral amorphous carbon films
NASA Astrophysics Data System (ADS)
Liu, Aiping; Zhu, Jiaqi; Liu, Meng; Dai, Zhifei; Han, Xiao; Han, Jiecai
2008-11-01
The haemocompatibility of phosphorus-incorporated tetrahedral amorphous carbon (ta-C:P) films, synthesized by filtered cathodic vacuum arc technique with PH 3 as the dopant source, was assessed by in vitro platelet adhesion tests. Results based on scanning electron microscopy and contact angle measurements reveal that phosphorus incorporation improves the wettability and blood compatibility of ta-C film. Our studies may provide a novel approach for the design and synthesis of doped ta-C films to repel platelet adhesion and reduce thrombosis risk.
Search for Fingerprints of Tetrahedral Symmetry in ^{156}Gd
Doan, Q. T.; Curien, D.; Stezowski, O.; Dudek, J.; Mazurek, K.; Gozdz, A.; Piot, J.; Duchene, G.; Gall, B.; Molique, H.; Richet, M.; Guinet, D.; Redon, N.; Schmitt, Ch.; Jones, P.; Peura, P.; Ketelhut, S.; Nyman, M.; Jakobsson, U.; Greenlees, P. T.; Julin, R.; Juutinen, S.; Rahkila, P.; Maj, A.; Zuber, K.; Bednarczyk, P.; Schunck, N.; Dobaczewski, J.; Astier, A.; Deloncle, I.; Verney, D.; Gerl, J.
2009-01-01
Theoretical predictions suggest the presence of tetrahedral symmetry as an explanation for the vanishing intra-band E2 transitions at the bottom of the odd-spin negative-parity band in ^{156}Gd. The present study reports on experiment performed to address this phenomenon. It allowed to remove certain ambiguities related to the intra-band E2 transitions in the negative-parity bands to determine the new inter-band transitions and reduced probability ratios B(E2)/B(E1) and, for the first time, to determine the experimental uncertainties related to the latter observable.
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.
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)
New exact solutions of quadratic curvature gravity
NASA Astrophysics Data System (ADS)
Gürses, Metin; ?i?man, Tahsin Ça?r?; Tekin, Bayram
2012-07-01
It is a known fact that the Kerr-Schild type solutions in general relativity satisfy both exact and linearized Einstein field equations. We show that this property remains valid also for a special class of the Kerr-Schild metrics in arbitrary dimensions in generic quadratic curvature theory. In addition to the anti-de Sitter (AdS) wave (or Siklos) metric which represents plane waves in an AdS background, we present here a new exact solution, in this class, to the quadratic gravity in D dimensions which represents a spherical wave in an AdS background. The solution is a special case of the Kundt metrics belonging to spacetimes with constant curvature invariants.
Higgsed Stueckelberg vector and Higgs quadratic divergence
NASA Astrophysics Data System (ADS)
Demir, DurmuÅŸ 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.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-01-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-12-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
Coherent States of Systems with Quadratic Hamiltonians
NASA Astrophysics Data System (ADS)
Bagrov, V. G.; Gitman, D. M.; Pereira, A. S.
2015-06-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to SchrÃ¶dinger 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.
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.
Communications circuit including a linear quadratic estimator
Ferguson, Dennis D.
2015-07-07
A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.
Quadratic Stochastic Euclidean Bipartite Matching Problem
NASA Astrophysics Data System (ADS)
Caracciolo, Sergio; Sicuro, Gabriele
2015-12-01
We propose a new approach for the study of the quadratic stochastic Euclidean bipartite matching problem between two sets of N points each, N ?1 . The points are supposed independently randomly generated on a domain ? ?Rd with a given distribution ? (x ) on ? . In particular, we derive a general expression for the correlation function and for the average optimal cost of the optimal matching. A previous ansatz for the matching problem on the flat hypertorus is obtained as a particular case.
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.
An alternative method on quadratic programming problems
NASA Astrophysics Data System (ADS)
Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.
2015-05-01
In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.
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.
The dines theorem and some other properties of quadratic mappings
NASA Astrophysics Data System (ADS)
Karamzin, D. Yu.
2015-10-01
Real homogeneous quadratic mappings from Rn to R2 are examined. It is known that the image of such a mapping is always convex. A proof of the convexity of the image based on the quadratic extremum principle is given. The following fact is noted: If the quadratic mapping Q is surjective and n > 2 + dimker Q, then there exists a regular zero of Q. A certain criterion of the linear dependence of quadratic forms is also stated.
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 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.
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...
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.
Carabineiro, Sónia A; Silva, Leonel C; Gomes, Pedro T; Pereira, Laura C J; Veiros, Luís F; Pascu, Sofia I; Duarte, M Teresa; Namorado, Sónia; Henriques, Rui T
2007-08-20
A series of 2-iminopyrrole ligand precursors with increasing bulkiness [HNC4H3C(R)=N-2,6-R'2C6H3] (R = R' = H, 1a; R = Me, R'= H, 1b; R = H, R' = Me, 1c; R = R' = Me, 1d; R = H, R' = iPr, 1e; R = Me, R' = iPr, 1f) were synthesized and deprotonated with NaH to give the corresponding iminopyrrolyl sodium salts 2a-f. A set of homoleptic bis-ligand Co(II) complexes of the type [Co(kappa2N,N'-NC4H3C(R)=N-2,6-R'2C6H3)2] (R = R'= H, 3a; R = Me, R'= H, 3b; R = H, R' = Me, 3c; R = R' = Me, 3d; R = H, R' = iPr, 3e; R = Me, R' = iPr, 3f) was prepared by reaction of CoCl2 with the corresponding iminopyrrolyl sodium salts 2a-f. The new complexes were characterized by elemental analysis, magnetic susceptibility measurements, in powder and in solution, UV/vis/NIR, and, in some cases, X-ray crystallography. According to X-ray diffraction and magnetic measurements, the Co complexes 3a-e proved to be tetrahedral, which is the preferred geometry for Co(II) compounds. However, a square planar geometry is observed in the case of 3f, as determined by several characterization techniques. In this case, DFT calculations suggest the square planar geometry is slightly more stable than the tetrahedral one probably due to a combination of steric and electronic reasons. PMID:17658870
Half-solidity of tetrahedral-like Al(55) clusters.
Kang, Joongoo; Kim, Yong-Hyun
2010-02-23
A new dynamic melting state, which has both solid and liquid characteristics, is revealed from first-principles molecular dynamics simulations of Al(55) clusters. In thermal fluctuations near the melting point, the low-energy tetrahedral-like Al(55) survives through rapid, collective surface transformations-such as parity conversions and correlated diffusion of two distant vacancies-without losing its structural orders. The emergence of the collective motions is solely due to efficient thermal excitation of soft phonon modes at nanoscale. A series of spontaneous surface reconfigurations result in a mixture or effective flow of surface atoms as is random color shuffling of a Rubik's cube. This novel flexible solid state (termed as half-solidity) provides useful insights into understanding stability, flexibility, and functionality of nanosystems near or below melting temperatures. PMID:20055435
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.
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…
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 thatâ€¦
Collision-broadened linewidths of tetrahedral molecules. III - Dispersion and induction interactions
NASA Technical Reports Server (NTRS)
Varanasi, P.
1975-01-01
Expressions for the interruption functions S2(b) have been derived for the dispersion interaction between a tetrahedral molecule and a linear molecule, and for the interaction between the octopole moment of a tetrahedral molecule and the octopole-induced dipole moment in a perturbing molecule.
Asymptotically safe inflation from quadratic gravity
NASA Astrophysics Data System (ADS)
Bonanno, Alfio; Platania, Alessia
2015-11-01
Asymptotically Safe theories of gravity have recently received much attention. In this work we discuss a class of inflationary models derived from quantum-gravity modification of quadratic gravity according to the induced scaling around the non-Gaussian fixed point at very high energies. It is argued that the presence of a three dimensional ultraviolet critical surface generates operators of non-integer power of the type R 2 - ? / 2 in the effective Lagrangian, where ? > 0 is a critical exponent. The requirement of a successful inflationary model in agreement with the recent Planck 2015 data puts important constraints on the strength of this new type of couplings.
Holographic entropy increases in quadratic curvature gravity
NASA Astrophysics Data System (ADS)
Bhattacharjee, Srijit; Sarkar, Sudipta; Wall, Aron C.
2015-09-01
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is nonstationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a second law.
Efficient quadratic regularization for expression arrays.
Hastie, Trevor; Tibshirani, Robert
2004-07-01
Gene expression arrays typically have 50 to 100 samples and 1000 to 20,000 variables (genes). There have been many attempts to adapt statistical models for regression and classification to these data, and in many cases these attempts have challenged the computational resources. In this article we expose a class of techniques based on quadratic regularization of linear models, including regularized (ridge) regression, logistic and multinomial regression, linear and mixture discriminant analysis, the Cox model and neural networks. For all of these models, we show that dramatic computational savings are possible over naive implementations, using standard transformations in numerical linear algebra. PMID:15208198
Bianchi I Solutions of Effective Quadratic Gravity
NASA Astrophysics Data System (ADS)
Müller, Daniel; de Deus, Juliano A.
2012-04-01
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model E3 for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for nondiagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi I spaces.
NASA Astrophysics Data System (ADS)
Mazzia, Annamaria; Putti, Mario
2005-09-01
Two-dimensional Godunov mixed methods have been shown to be effective for the numerical solution of density-dependent flow and transport problems in groundwater even when concentration gradients are high and the process is dominated by density effects. This class of discretization approaches solves the flow equation by means of the mixed finite element method, thus guaranteeing mass conserving velocity fields, and discretizes the transport equation by mixed finite element and finite volumes techniques combined together via appropriate time splitting. In this paper, we extend this approach to three dimensions employing tetrahedral meshes and introduce a spatially variable time stepping procedure that improves computational efficiency while preserving accuracy by adapting the time step size according to the local Courant-Friedrichs-Lewy (CFL) constraint. Careful attention is devoted to the choice of a truly three-dimensional limiter for the advection equation in the time-splitting technique, so that to preserve second order accuracy in space (in the sense that linear functions are exactly interpolated). The three-dimensional Elder problem and the saltpool problem, recently introduced as a new benchmark for testing three-dimensional density models, provide assessments with respect to accuracy and reliability of this numerical approach.
Contact symmetries of constrained quadratic Lagrangians
NASA Astrophysics Data System (ADS)
Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.
2016-01-01
The conditions for the existence of (polynomial in the velocities) contact symmetries of constrained systems that are described by quadratic Lagrangians is presented. These Lagrangians mainly appear in mini-superspace reductions of gravitational plus matter actions. In the literature, one usually adopts a gauge condition (mostly for the lapse N) prior to searching for symmetries. This, however, is an unnecessary restriction which may lead to a loss of symmetries and consequently to the respective integrals of motion. A generalization of the usual procedure rests in the identification of the lapse function N as an equivalent degree of freedom and the according extension of the infinitesimal generator. As a result, conformal Killing tensors (with appropriate conformal factors) can define integrals of motion (instead of just Killing tensors used in the regular gauge fixed case). Additionally, rheonomic integrals of motion - whose existence is unique in this type of singular systems - of various orders in the momenta can be constructed. An example of a relativistic particle in a pp-wave space-time and under the influence of a quadratic potential is illustrated.
An hp-adaptive discontinuous Galerkin finite-element method for 3-D elastic wave modelling
NASA Astrophysics Data System (ADS)
Etienne, V.; Chaljub, E.; Virieux, J.; Glinsky, N.
2010-11-01
We present a discontinuous Galerkin finite-element method (DG-FEM) formulation with Convolutional Perfectly Matched Layer (CPML) absorbing boundary condition for 3-D elastic seismic wave modelling. This method makes use of unstructured tetrahedral meshes locally refined according to the medium properties (h-adaptivity), and of approximation orders that can change from one element to another according to an adequate criterion (p-adaptivity). These two features allow us to significantly reduce the computational cost of the simulations. Moreover, we have designed an efficient CPML absorbing boundary condition, both in terms of absorption and computational cost, by combining approximation orders in the numerical domain. A quadratic interpolation is typically used in the medium to obtain the required accuracy, while lower approximation orders are used in the CPMLs to reduce the total computational cost and to obtain a well-balanced workload over the processors. While the efficiency of DG-FEMs have been largely demonstrated for high approximation orders, we favour the use of low approximation orders as they are more appropriate to the applications we are interested in. In particular, we address the issues of seismic modelling and seismic imaging in cases of complex geological structures that require a fine discretization of the medium. We illustrate the efficiency of our approach within the framework of the EUROSEISTEST verification and validation project, which is designed to compare high-frequency (up to 4 Hz) numerical predictions of ground motion in the Volvi basin (Greece). Through the tetrahedral meshing, we have achieved fine discretization of the basin, which appears to be a sine qua non condition for accurate computation of surface waves diffracted at the basin edges. We compare our results with predictions computed with the spectral element method (SEM), and demonstrate that our method yields the same level of accuracy with computation times of the same order of magnitude.
Multi-Criterion Preliminary Design of a Tetrahedral Truss Platform
NASA Technical Reports Server (NTRS)
Wu, K. Chauncey
1995-01-01
An efficient method is presented for multi-criterion preliminary design and demonstrated for a tetrahedral truss platform. The present method requires minimal analysis effort and permits rapid estimation of optimized truss behavior for preliminary design. A 14-m-diameter, 3-ring truss platform represents a candidate reflector support structure for space-based science spacecraft. The truss members are divided into 9 groups by truss ring and position. Design variables are the cross-sectional area of all members in a group, and are either 1, 3 or 5 times the minimum member area. Non-structural mass represents the node and joint hardware used to assemble the truss structure. Taguchi methods are used to efficiently identify key points in the set of Pareto-optimal truss designs. Key points identified using Taguchi methods are the maximum frequency, minimum mass, and maximum frequency-to-mass ratio truss designs. Low-order polynomial curve fits through these points are used to approximate the behavior of the full set of Pareto-optimal designs. The resulting Pareto-optimal design curve is used to predict frequency and mass for optimized trusses. Performance improvements are plotted in frequency-mass (criterion) space and compared to results for uniform trusses. Application of constraints to frequency and mass and sensitivity to constraint variation are demonstrated.
Polyamorphism in tetrahedral substances: similarities between silicon and ice
NASA Astrophysics Data System (ADS)
Antonelli, Alex; Garcez, Karl
2015-03-01
Tetrahedral substances, such as silicon, water, germanium, and silica, share several thermodynamical anomalies. Among them, the so-called polyamorphism, i.e., the existence of more than one amorphous state, is, perhaps, the most studied one. In this work, we study the transformations between amorphs of silicon using Monte Carlo simulations. The simulations indicate that by compressing the low density amorphous state (LDA), which is obtained by quenching the liquid at high temperature, a new denser amorph is found. The transformation between these two forms of amorphous silicon displays clear hysteresis, similar to the experiment reported by McMillan et al.. However, analogously to the case of ice, our simulations indicate that upon annealing the unannealed high density amorphous silicon (uHDA) evolves to more stable forms. The annealing of uHDA at pressures on the order of 20 GPa gives rise to an even denser form, the very high density amorphous silicon (VHDA), while at much lower pressures, about 5 GPa, the uHDA transforms into a lower density form, the expanded high density amorphous silicon (eHDA). Work supported by FAPESP, CNPq, CAPES, and FAEPEX/UNICAMP.
TET peptidases: A family of tetrahedral complexes conserved in prokaryotes.
Appolaire, Alexandre; Colombo, Matteo; Basbous, Hind; Gabel, Frank; Girard, E; Franzetti, Bruno
2016-03-01
The TET peptidases are large polypeptide destruction machines present among prokaryotes. They form 12-subunits hollow tetrahedral particles, and belong to the family of M42 metallo-peptidases. Structural characterization of various archaeal and bacterial complexes has revealed a unique mechanism of internal compartmentalization and peptide trafficking that distinguishes them from the other oligomeric peptidases. Different versions of the TET complex often co-exist in the cytosol of microorganisms. In depth enzymatic studies have revealed that they are non-processive cobalt-activated aminopeptidases and display contrasting substrate specificities based on the properties of the catalytic chambers. Recent studies have shed light on the assembly mechanism of homo and hetero-dodecameric TET complexes and shown that the activity of TET aminopeptidase towards polypeptides is coupled with its assembly process. These findings suggested a functional regulation based on oligomerization control inÂ vivo. This review describes a current knowledge on M42 TET peptidases biochemistry and discuss their possible physiological roles. This article is a part of the Special Issue entitled: Â«A potpourri of proteases and inhibitors: from molecular toolboxes to signalling scissorsÂ». PMID:26546839
Theoretical Studies of Routes to Synthesis of Tetrahedral N4
NASA Technical Reports Server (NTRS)
Lee, Timothy J.; Dateo, Christopher E.
2007-01-01
A paper [Chem. Phys. Lett. 345, 295 (2001)] describes theoretical studies of excited electronic states of nitrogen molecules, with a view toward utilizing those states in synthesizing tetrahedral N4, or Td N4 a metastable substance under consideration as a high-energy-density rocket fuel. Several ab initio theoretical approaches were followed in these studies, including complete active space self-consistent field (CASSCF), state-averaged CASSCF (SA-CASSCF), singles configuration interaction (CIS), CIS with second-order and third-order correlation corrections [CIS(D) and CIS(3)], and linear response singles and doubles coupled-cluster (LRCCSD). Standard double zeta polarized and triple zeta double polarized one-particle basis sets were used. The CASSCF calculations overestimated the excitation energies, while SACASSCF calculations partly corrected these overestimates. The accuracy of the CIS calculations varied, depending on the particular state, while the CIS(D), CIS(3), and LRCCSD results were in generally good agreement. The energies of the lowest six excited singlet states of Td N4 as calculated by the LRCCSD were compared with the energies of possible excited states of N2 + N2 fragments, leading to the conclusion that the most likely route for synthesis of Td N4 would involve a combination of two bound quintet states of N2.
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.
Steller Structure Treatment of Quadratic Gravity
NASA Astrophysics Data System (ADS)
Chen, Y.; Shao, C.; Chen, X.
2001-07-01
A scheme for considering stellar structure by taking advantage of the quadratic theory of gravitation in four-dimensions is proposed, citing the fact that the possible deviation of gravity in astrophysical systems from the Newtonian inverse square law can be explained through the use of this theory. A modified Lane-Emden equation is derived by making use of the linearized static field equation of quadratic gravity and the polytropic equation of state for a fluid. The influence on stellar structure of the additional force included in quadratic gravity is investigated. It is shown that the additional force can be treated as a perturbation of a bound system by solutions of the modified Lane-Emden equation and an order-of-magnitude analysis. %ZY. Fujii, Nature (London) 234 (1971), 5; Phys. Rev. D9 (1974), 874. D. R. Long, Phys. Rev. D 9 (1974), 850. J. O'Hanlon, Phys. Rev. Lett. 29 (1972), 137. D. R. Mikkelson and M. J. Newman, Phys. Rev. D 16 (1977), 919. R. V. Wagoner, Phys. Rev. D 1 (1970), 3209. J. Z. Xu and Y. H. Chen, Gen. Relat. Gravit. J. 23 (1991), 169. K. S. Stelle, Gen. Relat. Gravit. J. 8 (1978), 631. C. Xu and G. F. R. Ellis, Class. Quant. Grav. 8 (1991), 1747. A. Eddington, The Mathematical Theory of Relativity, 2nd ed. (Cambridge University Press, Cambridge, 1924). W. Pauli, Theory of Relativity (Pergamon Press, New York, 1921). H. A. Buchdahl, Proc. Edinburgh Math. Soc. 8 (1948), 89. J. D. Barrow and A. C. Ottewill, J. of Phys. A 16 (1983), 2757. M. B. Mijic, M. S. Morris and W. M. Suen, Phys. Rev. D 34 (1986), 2934. A. L. Berkin, Phys. Rev. D 42 (1990), 1017. N. D. Birrell and P. C. W. Davies, Quantum Field in Curved Space (Cambridge University Press, 1982). E. T. Tomboulis, Quantum Theory of Gravity, ed. S. M. Christensen (Bristol: Adam Hilger 1984). H. J. Treder, Ann. der Phys. 32 (1975), 383. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York 1972). E. N. Glass and G. Szamosi, Phys. Rev. D 35 (1987), 1205.
A quadratic pulse height analyzer for space applications.
NASA Technical Reports Server (NTRS)
Burtis, D. W.; Aalami, D.; Evelyn-Veere, R. H.; Sarkady, A. A.
1972-01-01
A flight-worthy pulse height analyzer that has a quadratic transfer function is described. This quadratic function permits optimum usage of the entire PHA dynamic range due to the quadratic nature of the gamma ray spectrometer's resolution vs energy. After the theoretical design discussion, the implementation of the design is examined and test results described. The analyzer is part of the University of New Hampshire gamma ray monitor for OSO-H.
Quasimultipartite entanglement measure based on quadratic functions
NASA Astrophysics Data System (ADS)
Zhang, Jing; Li, Chun-Wen; Wu, Jian-Wu; Wu, Re-Bing; Tarn, Tzyh-Jong
2006-02-01
We develop an entanglement measure by extending Jaeger’s Minkowskian norm entanglement measure. This measure can be applied to a much wider class of multipartite mixed states, although still “quasi” in the sense that it is still incapable of dividing precisely the sets of all separable and entangled states. As a quadratic scalar function of the system density matrix, the quasimeasure can be easily expressed in terms of the so-called coherence vector of the system density matrix, by which we show the basic properties of the quasimeasure including (1) zero entanglement for all separable states, (2) invariance under local unitary operations, and (3) nonincreasing under local positive operator-valued measure measurements. These results open up perspectives in further studies of dynamical problems in open systems, especially the dynamic evolution of entanglement, and the entanglement preservation against the environment-induced decoherence effects.
Quadratic dynamical decoupling with nonuniform error suppression
Quiroz, Gregory; Lidar, Daniel A.
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}.
NASA Astrophysics Data System (ADS)
Noakes, Lyle
2004-11-01
Interpolation problems in the space SO(3) of rotations of Euclidean 3-space E3 are reviewed in Secs. I s2 as background and motivation to a study of curves in E3 called Lie quadratics. Except for a special class called null, Lie quadratics have resisted analysis until now. The rest of the present paper is devoted to new results showing non-null Lie quadratics have rich analytical, geometrical, and asymptotic structures: rates of growth are studied using differential equations and inequalities, Lie quadratics are proved to be extendible over the whole of R, and existence of axes is proved under fairly general conditions. Examples show sharpness of many results.
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.
Optimum structural design using MSC/NASTRAN and sequential quadratic programming
NASA Astrophysics Data System (ADS)
Mahmoud, K. G.; Engl, H. W.; Holzleitner, L.
1994-08-01
A methodology is described for structural optimization using the commercial finite element package MSC/NASTRAN for structural analysis, a quasi-analytical method for design sensitivity analysis, and sequential quadratic programming with an active set strategy for optimization. The optimization and sensitivity analysis modules are efficiently coupled with MSC/NASTRAN using DMAP (direct matrix abstraction program) statements. To demonstrate the feasibility of the proposed methodology, the design optimization of a unit injector rocker arm is presented as an example.
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.
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; Charest, Marc R.; Canfield, Thomas R.; Wohlbier, John G.
2015-02-24
We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmoreÂ Â» the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Rungeâ€“Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.Â«Â less
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; Charest, Marc R.; Canfield, Thomas R.; Wohlbier, John G.
2015-02-24
We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Rungeâ€“Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
NASA Astrophysics Data System (ADS)
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; Charest, Marc R.; Canfield, Thomas R.; Wohlbier, John G.
2015-06-01
We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge-Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.
Lu Yongming; Lan Yaqian; Xu Yanhong; Su Zhongmin; Li Shunli; Zang Hongying; Xu Guangjuan
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.
Geometric quadratic stochastic operator on countable infinite set
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-02-03
In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.
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…
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...
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.)
Quadratic algebras for three-dimensional superintegrable systems
Daskaloyannis, C. Tanoudis, Y.
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.
Characterizing the regularity of tetrahedral packing motifs in protein tertiary structure
Day, Ryan; Lennox, Kristin P.; Dahl, David B.; Vannucci, Marina; Tsai, Jerry W.
2010-01-01
Motivation: While protein secondary structure is well understood, representing the repetitive nature of tertiary packing in proteins remains difficult. We have developed a construct called the relative packing group (RPG) that applies the clique concept from graph theory as a natural basis for defining the packing motifs in proteins. An RPG is defined as a clique of residues, where every member contacts all others as determined by the Delaunay tessellation. Geometrically similar RPGs define a regular element of tertiary structure or tertiary motif (TerMo). This intuitive construct provides a simple approach to characterize general repetitive elements of tertiary structure. Results: A dataset of over 4 million tetrahedral RPGs was clustered using different criteria to characterize the various aspects of regular tertiary structure in TerMos. Grouping this data within the SCOP classification levels of Family, Superfamily, Fold, Class and PDB showed that similar packing is shared across different folds. Classification of RPGs based on residue sequence locality reveals topological preferences according to protein sizes and secondary structure. We find that larger proteins favor RPGs with three local residues packed against a non-local residue. Classifying by secondary structure, helices prefer mostly local residues, sheets favor at least two local residues, while turns and coil populate with more local residues. To depict these TerMos, we have developed 2 complementary and intuitive representations: (i) Dirichlet process mixture density estimation of the torsion angle distributions and (ii) kernel density estimation of the Cartesian coordinate distribution. The TerMo library and representations software are available upon request. Contact: jtsai@pacific.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:21047817
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.
Quadratic optical nonlinearity of gold nanoparticles
NASA Astrophysics Data System (ADS)
Bergmann, E.; BruyÃ¨re, A.; Riporto, J.; Benichou, E.; Jonin, Ch.; Brevet, P. F.
2015-08-01
We investigate the quadratic nonlinear optical response from metallic gold nanoparticles homogeneously dispersed in a medium or deposited on glass substrates. The nanoparticles are prepared by the wet chemistry method in solution used afterwards. The diameter of the gold nanoparticle is 80 nm. In a homogeneous medium, hyper Rayleigh scattering, effectively incoherent second harmonic generation is used to determine the origin of the response. It is shown that for 80 nm diameter gold nanoparticles, the overall response stems from the deviation of the shape of the nanoparticle from that of a perfect sphere and from retardation effects with a similar weight. The latter retardation effects occur because the diameter of the nanoparticle is no longer vanishing before the wavelength of the incoming electromagnetic field. For deposited nanoparticles, the sample is illuminated through the transparent glass slide and the light at the harmonic frequency, produced through the second harmonic generation phenomenon, is observed in the retro-reflection. From the collected SHG images, it can be unambiguously concluded that the origin of the nonlinearity in 80 nm diameter gold nanoparticles stems from the substrate influence normal to the interface. It can also be concluded that the gold nanoparticles can be used to map out the electromagnetic field in the focal volume.
Extremal Optimization for Quadratic Unconstrained Binary Problems
NASA Astrophysics Data System (ADS)
Boettcher, S.
We present an implementation of ?-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.
Object-oriented software for quadratic programming.
Gertz, M.; Wright, S.; Mathematics and Computer Science; Northwestern Univ.; Univ. of Wisconsin-Madison
2003-01-01
The object-oriented software package OOQP for solving convex quadratic programming problems (QP) is described. The primal-dual interior point algorithms supplied by OOQP are implemented in a way that is largely independent of the problem structure. Users may exploit problem structure by supplying linear algebra, problem data, and variable classes that are customized to their particular applications. The OOQP distribution contains default implementations that solve several important QP problem types, including general sparse and dense QPs, bound-constrained QPs, and QPs arising from support vector machines and Huber regression. The implementations supplied with the OOQP distribution are based on such well known linear algebra packages as MA27/57, LAPACK, and PETSc. OOQP demonstrates the usefulness of object-oriented design in optimization software development, and establishes standards that can be followed in the design of software packages for other classes of optimization problems. A number of the classes in OOQP may also be reusable directly in other codes.
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
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.
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.
Degenerate nonlinear programming with a quadratic growth condition.
Anitescu, M.; Mathematics and Computer Science
2000-01-01
We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.
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.
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; Guerses, Metin
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.
Reordering between tetrahedral and octahedral sites in ultrathin magnetite films grown on MgO(001)
Bertram, F.; Deiter, C.; Schemme, T.; Jentsch, S.; Wollschlaeger, J.
2013-05-14
Magnetite ultrathin films were grown using different deposition rates and substrate temperatures. The structure of these films was studied using (grazing incidence) x-ray diffraction, while their surface structure was characterized by low energy electron diffraction. In addition to that, we performed x-ray photoelectron spectroscopy and magneto optic Kerr effect measurements to probe the stoichiometry of the films as well as their magnetic properties. The diffraction peaks of the inverse spinel structure, which originate exclusively from Fe ions on tetrahedral sites are strongly affected by the preparation conditions, while the octahedral sites remain almost unchanged. With both decreasing deposition rate as well as decreasing substrate temperature, the integrated intensity of the diffraction peaks originating exclusively from Fe on tetrahedral sites is decreasing. We propose that the ions usually occupying tetrahedral sites in magnetite are relocated to octahedral vacancies. Ferrimagnetic behaviour is only observed for well ordered magnetite films.
Observation of all-in type tetrahedral displacements in nonmagnetic pyrochlore niobates
NASA Astrophysics Data System (ADS)
Torigoe, S.; Ishimoto, Y.; Aoishi, Y.; Murakawa, H.; Matsumura, D.; Yoshii, K.; Yoneda, Y.; Nishihata, Y.; Kodama, K.; Tomiyasu, K.; Ikeda, K.; Nakao, H.; Nogami, Y.; Ikeda, N.; Otomo, T.; Hanasaki, N.
2016-02-01
We observed all-in type Nb tetrahedral displacement in nonmagnetic pyrochlore niobates A2Nb2O7 (A =Nd0.5Ca0.5 and Y0.5Ca0.5 ) through the analysis of the neutron pair distribution function and the extended x-ray absorption function spectroscopy. The all-in type Nb tetrahedral displacement, which has the character of a charge singlet state, is driven by the formation of the bonding orbital. The diffuse scattering in the x-ray diffraction, which has the resonant component in the Nb L3 edge, indicates that the all-in type Nb tetrahedral displacement has the periodicity with its short-range correlation.
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.
Ita, B. I.
2014-11-12
By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.
NASA Astrophysics Data System (ADS)
Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.
2014-11-01
By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.
Transformational part-count in layered octahedral-tetrahedral truss configurations
NASA Technical Reports Server (NTRS)
Lalvani, Haresh
1990-01-01
The number of component part (nodes, struts and panels) termed part count, is an important factor in the design, manufacture, and assembly of modular space structures. Part count expressions are presented for a variety of profiles derived from the layered octahedral-tetrahedral truss configuration. Referred to as the tetrahedral truss in the NASA projects, this specific geometry has been used in several missions. The general expressions presented here transforms to others as one profile changes to another. Such transformational part count relations provide a measure of flexibility and generality, and may be useful when dealing with a wider range of geometric configurations.
Implementation of mixed formulation elements in PC/NASTRAN
NASA Astrophysics Data System (ADS)
Schaeffer, Harry G.
1993-09-01
The purpose of this paper is to describe the implementation and use of a consistent family of two and three dimensional elements in NASTRAN. The elements which are based on a mixed formulation include a replacement of the original NASTRAN shear element and the addition of triangular quadrilateral shell elements and tetrahedral, pentahedral and hexahedral solid elements. These elements support all static loads including temperature gradient and pressure load. The mass matrix is also generated to support all dynamic rigid formats.
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.
Distinct thermal behavior of GeO2 glass in tetrahedral, intermediate, and octahedral forms.
Shen, Guoyin; Liermann, Hanns-Peter; Sinogeikin, Stanislav; Yang, Wenge; Hong, Xinguo; Yoo, Choong-Shik; Cynn, Hyunchae
2007-09-11
One fascinating high-pressure behavior of tetrahedral glasses and melts is the local coordination change with increasing pressure, which provides a structural basis for understanding numerous anomalies in their high-pressure properties. Because the coordination change is often not retained upon decompression, studies must be conducted in situ. Previous in situ studies have revealed that the short-range order of tetrahedrally structured glasses and melts changes above a threshold pressure and gradually transforms to an octahedral form with further pressure increase. Here, we report a thermal effect associated with the coordination change at given pressures and show distinct thermal behaviors of GeO(2) glass in tetrahedral, octahedral, and their intermediate forms. An unusual thermally induced densification, as large as 16%, was observed on a GeO(2) glass at a pressure of 5.5 gigapascal (GPa), based on in situ density and x-ray diffraction measurements at simultaneously high pressures and high temperatures. The large thermal densification at high pressure was found to be associated with the 4- to 6-fold coordination increase. Experiments at other pressures show that the tetrahedral GeO(2) glass displayed small thermal densification at 3.3 GPa arising from the relaxation of intermediate range structure, whereas the octahedral glass at 12.3 GPa did not display any detectable thermal effects. PMID:17804799
Automated Tetrahedral Mesh Generation for CFD Analysis of Aircraft in Conceptual Design
NASA Technical Reports Server (NTRS)
Ordaz, Irian; Li, Wu; Campbell, Richard L.
2014-01-01
The paper introduces an automation process of generating a tetrahedral mesh for computational fluid dynamics (CFD) analysis of aircraft configurations in early conceptual design. The method was developed for CFD-based sonic boom analysis of supersonic configurations, but can be applied to aerodynamic analysis of aircraft configurations in any flight regime.
Fostering Teacher Development to a Tetrahedral Orientation in the Teaching of Chemistry
ERIC Educational Resources Information Center
Lewthwaite, Brian; Wiebe, Rick
2011-01-01
This paper reports on the initial outcomes from the end of the fourth year of a 5 year research and professional development project to improve chemistry teaching among three cohorts of chemistry teachers in Manitoba, Canada. The project responds to a new curriculum introduction advocating a tetrahedral orientation (Mahaffy, "Journal of Chemical…
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 Chemicalâ€¦
Frequency comb generation in quadratic nonlinear media
NASA Astrophysics Data System (ADS)
Ricciardi, Iolanda; Mosca, Simona; Parisi, Maria; Maddaloni, Pasquale; Santamaria, Luigi; De Natale, Paolo; De Rosa, Maurizio
2015-06-01
We experimentally demonstrate and theoretically explain the onset of optical frequency combs in a simple cavity-enhanced second-harmonic-generation system, exploiting second-order nonlinear interactions. Two combs are simultaneously generated around the fundamental pump frequency, with a spectral bandwidth up to about 10 nm, and its second harmonic. We observe different regimes of generation, depending on the phase-matching condition for second-harmonic generation. Moreover, we develop an elemental model which provides a deep physical insight into the observed dynamics. Despite the different underlying physical mechanism, the proposed model is remarkably similar to the description of third-order effects in microresonators, revealing a potential variety of new effects to be explored and laying the groundwork for a novel class of highly efficient and versatile frequency comb synthesizers based on second-order nonlinear materials.
Tormos, Jose R.; Wiley, Kenneth L.; Wang, Yi; Fournier, Didier; Masson, Patrick; Nachon, Florian; Quinn, Daniel M.
2010-01-01
In a previous communication, kinetic ?-deuterium secondary isotope effects were reported that support a mechanism for substrate-activated turnover of acetylthiocholine by human butyrylcholinesterase (BuChE) wherein the accumulating reactant state is a tetrahedral intermediate (Tormos, J. R., et al. (2005) JACS 127, 14538–14539). In this paper additional isotope effect experiments are described with acetyl-labeled acetylthiocholines (CL3COSCH2CH2N+Me3; L = H or D) that also support accumulation of the tetrahedral intermediate in Drosophila melanogaster acetylcholinesterase (DmAChE) catalysis. In contrast to the aforementioned BuChE-catalyzed reaction, for this reaction the dependence of initial rates on substrate concentration is marked by pronounced substrate inhibition at high substrate concentrations. Moreover, kinetic ? -deuterium secondary isotope effects for turnover of acetylthiocholine depended on substrate concentration, and gave the following: D3kcat/Km = 0.95 ± 0.03, D3kcat = 1.12 ± 0.02 and D3 ? kcat = 0.97 ± 0.04. The inverse isotope effect on kcat/Km is consistent with conversion of the sp2 hybridized substrate carbonyl in the E + A reactant state into a quasi-tetrahedral transition state in the acylation stage of catalysis, whereas the markedly normal isotope effect on kcat is consistent with hybridization change from sp3 toward sp2 as the reactant state for deacylation is converted into the subsequent transition state. Transition states for Drosophila melanogaster AChE-catalyzed hydrolysis of acetylthiocholine were further characterized by measuring solvent isotope effects and determining proton inventories. These experiments indicated that the transition state for rate-determining decomposition of the tetrahedral intermediate is stabilized by multiple protonic interactions. Finally, a simple model is proposed for the contribution that tetrahedral intermediate stabilization provides to the catalytic power of acetylcholinesterase. PMID:21105647
Parametric localized modes in quadratic nonlinear photonic structures.
Sukhorukov, A A; Kivshar, Y S; Bang, O; Soukoulis, C M
2001-01-01
We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi(2)) nonlinear interfaces embedded in a linear layered structure--a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi(2) equations) and find, numerically and analytically, the spatially localized solutions--discrete gap solitons. For a single nonlinear interface in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media. PMID:11304386
On Volterra quadratic stochastic operators with continual state space
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-05-15
Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is Ïƒ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (VÎ»)(A)â€‰=â€‰âˆ«{sub X}âˆ«{sub X}P(x,y,A)dÎ»(x)dÎ»(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A âˆˆ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub nâ†’âˆ}â€‰V{sup nâ€‰}(Î») is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel Ïƒ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.
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.
A Projection Neural Network for Constrained Quadratic Minimax Optimization.
Liu, Qingshan; Wang, Jun
2015-11-01
This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network. PMID:25966485
Nikitin, A. V.; Rey, M.; Tyuterev, Vl. G.
2015-03-07
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 AB{sub 4} 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){sup ?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 CH{sub 4} molecule is demonstrated.
Warsa, James S.; Wareing, Todd A.; Morel, Jim E.
2002-07-15
We recently presented a method for efficiently solving linear discontinuous discretizations of the two-dimensional P{sub 1} equations on rectangular meshes. The linear system was efficiently solved with Krylov iterative methods and a novel two-level preconditioner based on a linear continuous finite element discretization of the diffusion equation. Here, we extend the preconditioned solution method to three-dimensional, unstructured tetrahedral meshes. Solution of the P{sub 1} equations forms the basis of a diffusion synthetic acceleration (DSA) scheme for three-dimensional S{sub N} transport calculations with isotropic scattering. The P{sub 1} equations and the transport equation are both discretized with isoparametric linear discontinuous finite elements so that the DSA method is fully consistent. Fourier analysis in three dimensions and computational results show that this DSA scheme is stable and very effective. The fully consistent method is compared to other 'partially consistent' DSA schemes. Results show that the effectiveness of the partially consistent schemes can degrade for skewed or optically thick mesh cells. In fact, one such scheme can degrade to the extent of being unstable even though it is both unconditionally stable and effective on rectangular grids. Results for a model application show that our fully consistent DSA method can outperform the partially consistent DSA schemes under certain circumstances.
Kannan, Chellapandian; Sundaram, Thiravium; Palvannan, Thayumanavan
2008-08-30
The conventional adsorbents like activated carbon, agricultural wastes, molecular sieves, etc., used for dye adsorption are unstable in the environment for long time, and hence the adsorbed dyes again gets liberated and pollute the environment. To avoid this problem, environmentally stable adsorbent of silica and alumina should be employed for malachite green adsorption. The adsorbents were characterized by Fourier transformed infrared spectroscopy (FT-IR) to confirm the tetrahedral framework of silica and non-tetrahedral framework of alumina. The adsorption equilibrium of dye on alumina and silica were 4 and 5h, respectively, this less adsorption time on alumina might be due to the less activation energy on alumina (63.46 kJ mol(-1)) than silica (69.93 kJ mol(-1)). Adsorption increased with increase of temperature on silica, in alumina, adsorption increased up to 60 degrees C, and further increase of temperature decreased the adsorption due to the structural change of non-tetrahedral alumina in water. The optimum pH for dye adsorption on alumina was 5 and silica was 6. The dye adsorptions on both adsorbents followed pseudo-second-order kinetics. The adsorption well matched with Langmuir and Freundlich adsorption isotherms and found that adsorption capacity on alumina was more than silica. The thermodynamic studies proved that the adsorption was endothermic and chemisorptions (DeltaH degrees >40 kJ mol(-1)) on alumina and silica. Recovery of dye on alumina and silica were studied from 30 to 90 degrees C and observed that 52% of dye was recovered from alumina and only 3.5% from silica. The less recovery on silica proved the strong adsorption of dye on silica than alumina. PMID:18289784
Dephasing in Quantum Dots: Quadratic Coupling to Acoustic Phonons
NASA Astrophysics Data System (ADS)
Muljarov, E. A.; Zimmermann, R.
2004-11-01
A microscopic theory of optical transitions in quantum dots with a carrier-phonon interaction is developed. Virtual transitions into higher confined states with acoustic phonon assistance add a quadratic phonon coupling to the standard linear one, thus extending the independent boson model. Summing infinitely many diagrams in the cumulant, a numerically exact solution for the interband polarization is found. Its full time dependence and the absorption line shape of the quantum dot are calculated. It is the quadratic interaction which gives rise to a temperature-dependent broadening of the zero-phonon line, calculated here for the first time in a consistent scheme.
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.
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.
Gorodylova, Nataliia; KosinovÃ¡, Veronika; Å ulcovÃ¡, Petra; BÄ›lina, Petr; VlÄek, Milan
2014-11-01
All the known chromium(III) NASICON-related phosphates are considered to be solid solutions. In these compounds chromium atoms share their position in the basic framework of the crystal lattice with other structure forming elements such as zirconium. In our study, we have hypothesised a completely new way of structural organisation of the chromium(III) zirconium(IV) NASICON framework, consisting in the distribution of chromium over the charge-compensating atom sites with tetrahedral oxygen coordination. The possibility of formation of the corresponding phosphate, Cr(1/3)Zr2P3O12, was studied using a classical ceramic route and a sol-gel method. Structural affiliation of the obtained pure phase product was studied using XRD analysis. The results confirmed that the Cr(1/3)Zr2P3O12 phosphate belongs to monoclinic SW-subtype of the NASICON family. In this structure, chromium atoms occupy charge-compensating sites with a strongly distorted tetrahedral oxygen environment. To the best of our knowledge, it is the first example of tetrahedral coordination of chromium(III) in phosphates. Along with the unusual crystallographic characteristics of chromium, special attention in this paper is devoted to the thermal stability of this phosphate and to its performance as an inorganic pigment. The sample was characterised by heating microscopy and DTA study, particle size distribution analysis, and IR- and VIS-spectroscopy. The stability of the obtained powder in a glaze environment, its colouring performance and lightfastness are discussed as well. PMID:25189199
Solving the Quadratic Capacitated Facilities Location Problem by Computer.
ERIC Educational Resources Information Center
Cote, Leon C.; Smith, Wayland P.
Several computer programs were developed to solve various versions of the quadratic capacitated facilities location problem. Matrices, which represent various business costs, are defined for the factors of sites, facilities, customers, commodities, and production units. The objective of the program is to find an optimization matrix for the lowestâ€¦
Quadratic versus Linear Rules in Predictive Discriminant Analysis.
ERIC Educational Resources Information Center
Young, Brian
Either linear or quadratic rules may be used to derive classification equations in discriminant analysis for the purpose of predicting group membership. Generally, the decision about which rule to use is governed by the degree to which the separate group covariance matrices are unequal. An example is presented that supports the superior internalâ€¦
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…
Tuning a fuzzy controller using quadratic response surfaces
NASA Technical Reports Server (NTRS)
Schott, Brian; Whalen, Thomas
1992-01-01
Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.
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 areâ€¦
Canonical realization of Bondi-Metzner-Sachs symmetry: Quadratic Casimir
NASA Astrophysics Data System (ADS)
Gomis, Joaquim; Longhi, Giorgio
2016-01-01
We study the canonical realization of Bondi-Metzner-Sacks symmetry for a massive scalar field introduced by Longhi and Materassi [J. Math. Phys. 40, 480 (1999)]. We construct an invariant scalar product for the generalized momenta. As a consequence we introduce a quadratic Casimir with the supertranslations.
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)
A Model for Quadratic Outliers in Linear Regression.
ERIC Educational Resources Information Center
Elashoff, Janet Dixon; Elashoff, Robert M.
This paper introduces a model for describing outliers (observations which are extreme in some sense or violate the apparent pattern of other observations) in linear regression which can be viewed as a mixture of a quadratic and a linear regression. The maximum likelihood estimators of the parameters in the model are derived and their asymptoticâ€¦
Unravelling Student Challenges with Quadratics: A Cognitive Approach
ERIC Educational Resources Information Center
Kotsopoulos, Donna
2007-01-01
The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…
[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
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.
NASA Astrophysics Data System (ADS)
Tagami, Shingo; Shimizu, Yoshifumi R.; Dudek, Jerzy
2014-09-01
Possible existence of the tetrahedrally symmetric nuclei was suggested from mean-field calculations such as the Skyrme (SIII) Hartree-Fock-Bogoliubov (HFB) and the Woods-Saxon Strutinsky methods. Because of large energy gaps of the single particle levels, the tetrahedrally deformed nuclei become stable for the particular particle numbers, i.e., the tetrahedral magic numbers. We have recently performed Gogny (D1S) HFB calculations and obtained the tetrahedrally deformed states for nuclei with such magic numbers. The resultant spectra calculated by the quantum number projection nicely follow the predicted spin-parity combinations by the group theory. One of the important findings is that the tetrahedral energy gain by the projection from the spherical configuration is very large, e.g., about 10 MeV for the cases of 80 , 96 , 110Zr nuclei, in contrast to the fact that the HFB energy curve is rather shallow. However, the tetrahedral deformation is one of the octupole deformations; new calculations under investigation suggest that the energy gains for the other octupole deformations are of the similar amount for Zr isotopes. We would like to discuss these multiple softness of octupole shape including the tetrahedral deformation.
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.
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme
Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; Nguyen, Manh Cuong; Wang, Cai -Zhuang; Lin, Zijing; Zhu, Zi -Zhong; Ho, Kai -Ming
2015-10-26
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A_{2}MSiO_{4} with A = Li or Na and M = Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. In addition, these structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs.
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme.
Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; Nguyen, Manh Cuong; Wang, Cai-Zhuang; Lin, Zijing; Zhu, Zi-Zhong; Ho, Kai-Ming
2015-01-01
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A2MSiO4 with A?=?Li or Na and M?=?Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. These structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs. PMID:26497381
Fostering Teacher Development to a Tetrahedral Orientation in the Teaching of Chemistry
NASA Astrophysics Data System (ADS)
Lewthwaite, Brian; Wiebe, Rick
2011-11-01
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 Education 83(1), 49-55, 2006) to the teaching of chemistry. The project in its entirety is based upon several theoretical models in fostering chemistry teacher development (in particular Bronfenbrenner's bio-ecological model). These models are described, as is the progress made by teachers based upon the use of a Chemistry Teacher Inventory and associated teacher responses. Overall, statistical analysis of perceptions of their own teaching and comments made by teachers suggests they are showing limited development towards a tetrahedral orientation, albeit in a manner consistent with the curriculum. Ongoing research-based activities in this project are also described.
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme
NASA Astrophysics Data System (ADS)
Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; Nguyen, Manh Cuong; Wang, Cai-Zhuang; Lin, Zijing; Zhu, Zi-Zhong; Ho, Kai-Ming
2015-10-01
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A2MSiO4 with A?=?Li or Na and M?=?Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. These structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs.
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme
Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; Nguyen, Manh Cuong; Wang, Cai-Zhuang; Lin, Zijing; Zhu, Zi-Zhong; Ho, Kai-Ming
2015-01-01
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A2MSiO4 with Aâ€‰=â€‰Li or Na and Mâ€‰=â€‰Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. These structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs. PMID:26497381
Jalarvo, Niina H; Gourdon, Olivier; Bi, Zhonghe; Gout, Delphine J; Ohl, Michael E; Paranthaman, Mariappan Parans
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.
Halide-Amine Co-Passivated Indium Phosphide Colloidal Quantum Dots in Tetrahedral Shape.
Kim, Kyungnam; Yoo, Dongsuk; Choi, Hyekyoung; Tamang, Sudarsan; Ko, Jae-Hyeon; Kim, Sungwoo; Kim, Yong-Hyun; Jeong, Sohee
2016-03-01
Wet chemical synthesis of covalent III-V colloidal quantum dots (CQDs) has been challenging because of uncontrolled surfaces and a poor understanding of surface-ligand interactions. We report a simple acid-free approach to synthesize highly crystalline indium phosphide CQDs in the unique tetrahedral shape by using tris(dimethylamino) phosphine and indium trichloride as the phosphorus and indium precursors, dissolved in oleylamine. Our chemical analyses indicate that both the oleylamine and chloride ligands participate in the stabilization of tetrahedral-shaped InP CQDs covered with cation-rich (111) facets. Based on density functional theory calculations, we propose that fractional dangling electrons of the In-rich (111) surface could be completely passivated by three halide and one primary amine ligands per the (2Ã—2) surface unit, satisfying the 8-electron rule. This halide-amine co-passivation strategy will benefit the synthesis of stable III-V CQDs with controlled surfaces. PMID:26849683
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme
Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; Nguyen, Manh Cuong; Wang, Cai -Zhuang; Lin, Zijing; Zhu, Zi -Zhong; Ho, Kai -Ming
2015-10-26
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A2MSiO4 with A = Li or Na and M = Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. In addition, these structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been muchmoreÂ Â» less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs.Â«Â less
Flexibility of C3h -Symmetrical Linkers in Tris-oligonucleotide-Based Tetrahedral Scaffolds.
Panagiotidis, Christos; Kath-Schorr, Stephanie; von Kiedrowski, GÃ¼nter
2016-02-01
Flexibility of tris-oligonucleotides is determined by the length of their connecting hydrocarbon chains. Tris-oligonucleotides are branched DNA building blocks with three oligonucleotide arms attached to a C3h -symmetrical linker core at these chains. Four tris-oligonucleotides hybridise into a tetrahedral nanocage by sequence-determined self-assembly. The influence of methylene, ethylene and propylene chains was studied by synthesising sets of tris-oligonucleotides and analysing the relative stability of the hybridisation products against digestion by mung bean nuclease by using gel electrophoresis. Linkers with ethylene chains showed sufficient flexibility, whereas methylene-chain linkers were too rigid. Tris-oligonucleotides based on the latter still formed tetrahedral scaffolds in intermixing experiments with linkers of higher flexibility. Thus, a new generation of versatile isocyanurate-based linkers was established. PMID:26593127
Theory of Andreev reflection spectroscopy for tetrahedral and non-unitary superconductors.
Bohloul, S; Curnoe, S H
2016-02-01
A general formula for point contact conductance from a normal metal tip into a superconductor is derived using the Blonder-Tinkham-Klapwijk theory of Andreev reflection, with special emphasis on non-unitary superconductors. The results of a comprehensive set of conductance spectrum calculations are presented: all symmetry-allowed gap functions for superconductors with tetrahedral symmetry, such as PrOs4Sb12, are considered, including several non-unitary cases. PMID:26750247
A study of pH-dependence of shrink and stretch of tetrahedral DNA nanostructures
NASA Astrophysics Data System (ADS)
Wang, Ping; Xia, Zhiwei; Yan, Juan; Liu, Xunwei; Yao, Guangbao; Pei, Hao; Zuo, Xiaolei; Sun, Gang; He, Dannong
2015-04-01
We monitored the shrink and stretch of the tetrahedral DNA nanostructure (TDN) and the i-motif connected TDN structure at pH 8.5 and pH 4.5, and we found that not only the i-motif can change its structure when the pH changes, but also the TDN and the DNA double helix change their structures when the pH changes.
Theory of Andreev reflection spectroscopy for tetrahedral and non-unitary superconductors
NASA Astrophysics Data System (ADS)
Bohloul, S.; Curnoe, S. H.
2016-02-01
A general formula for point contact conductance from a normal metal tip into a superconductor is derived using the Blonder–Tinkham–Klapwijk theory of Andreev reflection, with special emphasis on non-unitary superconductors. The results of a comprehensive set of conductance spectrum calculations are presented: all symmetry-allowed gap functions for superconductors with tetrahedral symmetry, such as PrOs4Sb12, are considered, including several non-unitary cases.
A 3-D time-dependent unstructured tetrahedral-mesh SP{sub N} method
Morel, J.E.; McGhee, J.M.; Larsen, E.W.
1994-10-01
We have developed a 3-D time-dependent multigroup SP{sub n} method for unstructured tetrahedral meshes. The SP{sub n} equations are expressed in a canonical form which allows them to be solved using standard diffusion solution techniques in conjunction with source iteration, diffusion-synthetic acceleration, and fission-source acceleration. A computational comparison of our SP{sub n} method with an even-parity S{sub n} method is given.
De novo structure-based design of bisurea hosts for tetrahedral oxyanion guests
Bryantsev, Vyacheslav; Hay, Benjamin P.
2006-02-15
This paper presents a computational approach to the deliberate design of improved host architectures. De novo molecule building software, HostDesigner, is interfaced with molecular mechanics software, GMMX, providing a tool for generating and screening millions of potential structures. The efficacy of this computer-aided design methodology is illustrated with a search for bis-urea podands that are structurally organized for complexation with tetrahedral oxyanions.
Ultrahigh-Resolution {gamma}-Ray Spectroscopy of {sup 156}Gd: A Test of Tetrahedral Symmetry
Jentschel, M.; Krempel, J.; Urban, W.; Tonev, D.; Petkov, P.; Dudek, J.; Curien, D.; Lauss, B.; Angelis, G. de
2010-06-04
Tetrahedral symmetry in strongly interacting systems would establish a new class of quantum effects at subatomic scale. Excited states in {sup 156}Gd that could carry the information about the tetrahedral symmetry were populated in the {sup 155}Gd(n,{gamma}){sup 156}Gd reaction and studied using the GAMS4/5 Bragg spectrometers at the Institut Laue-Langevin. We have identified the 5{sub 1}{sup -{yields}}3{sub 1}{sup -} transition of 131.983(12) keV in {sup 156}Gd and determined its intensity to be 1.9(3)x10{sup -6} per neutron capture. The lifetime {tau}=220{sub -30}{sup +180}fs of the 5{sub 1}{sup -} state in {sup 156}Gd has been measured using the GRID technique. The resulting B(E2)=293{sub -134}{sup +61}Weisskopf unit rate of the 131.983 keV transition provides the intrinsic quadrupole moment of the 5{sub 1}{sup -} state in {sup 156}Gd to be Q{sub 0}=7.1{sub -1.6}{sup +0.7} b. This large value, comparable to the quadrupole moment of the ground state in {sup 156}Gd, gives strong evidence against tetrahedral symmetry in the lowest odd-spin, negative-parity band of {sup 156}Gd.
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.
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
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.
A novel ultrasensitive electrochemical DNA sensor based on double tetrahedral nanostructures.
Zeng, Dongdong; Zhang, Huan; Zhu, Dan; Li, Jiang; San, Lili; Wang, Zehua; Wang, Chenguang; Wang, Yunsheng; Wang, Lihua; Zuo, Xiaolei; Mi, Xianqiang
2015-09-15
Electrochemical DNA (E-DNA) sensor is an important tool for detecting DNA biomarker. In this work, we have demonstrated a novel strategy of E-DNA sensor based on DNA tetrahedral nanostructures for the sensitive detection of target DNA. In our design, thiol and biotin modified DNA tetrahedral nanostructures were used as capture and report probes respectively. The biotin-tagged three dimensional DNA tetrahedral nanostructures were employed for efficient signal amplification by capturing multiple catalytic enzymes. Such improved E-DNA sensor can sensitively detect DNA target as low as 1 fM with excellent differentiation ability for even single mismatch. And a mean recovery rate of 90.57% in DNA solution extracted from human serum was obtained. We have also compared this new method of attaching catalytic enzymes with the other two typical methods: One is through biotinylated single-stranded DNA (SSDNA) and the other is through gold nanoparticles (GNPs). Results indicated that the RTSPs-based enzyme amplification system showed much better performance than the other two systems. PMID:25950940
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.
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.
Zhang, X. M.; Xu, G. Z.; Liu, E. K.; Wang, W. H. Wu, G. H.; Liu, Z. Y.
2015-01-28
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 Î“ point of the Brillouin zone.
FIBER OPTIC POINT QUADRAT SYSTEM FOR IMPROVED ACCURACY IN VEGETATION SAMPLING
An automated, fiber optic point quadrat system for vegetation sampling is described. Because the effective point diameter of the system never exceeds 25um it minimizes the substantial errors which can arise with conventional point quadrats. Automatic contact detection eliminates ...
Invariant Approach to Existence Problem of Chaos in 3D Autonomous Quadratic Dynamical Systems
NASA Astrophysics Data System (ADS)
Belozyorov, Vasiliy Ye.
New existence conditions of chaos for a wide class of 3D autonomous quadratic dynamical systems are suggested. These conditions are based on the construction and study of properties of algebraic invariants for some 2D quadratic system differential equations.
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.
Method for amplitude response estimation in quadratic channels
NASA Astrophysics Data System (ADS)
Keskinoz, Mehmet; Vijaya Kumar, Bhagavatula
2002-01-01
Like other coherent optical storage channels, a volume holographic storage channel is a quadratic channel since its output is a function of the magnitude-square of the light incident on the photo-detector array. Because of such intensity detection, the sign/phase information at the output is destroyed which makes the estimation of the amplitude response difficult. In this paper, we present a new method called modified least mean squares (MLMS) method to estimate the amplitude channel response of a volume holographic storage channel in the presence of quadratic non-linearity. Numerical simulations show that MLMS is very effective in estimating the amplitude response of such channels under even severe loss of sign information.
Single-molecule orientation measurements with a quadrated pupil
NASA Astrophysics Data System (ADS)
Backer, Adam S.; Backlund, Mikael P.; Lew, Matthew D.; Diezmann, Alexander R.; Sahl, Steffen J.; Moerner, W. E.
2014-03-01
We present a means of measuring the dipole orientation of a fluorescent, rotationally fixed single molecule (SM), using a specially designed phase mask, termed a "quadrated pupil," conjugate to the back focal plane of a conventional widefield microscope. In comparison to image-fitting techniques that infer orientation by matching simulations to defocused or excessively magnified images, the quadrated pupil approach is more robust to minor modeling discrepancies, defocus, and optical aberrations. Precision on the order of 1°-5° is achieved in proofof- concept experiments for both azimuthal (?) and polar (?) angles. Since the phase mask is implemented on a liquid-crystal spatial light modulator (SLM) that may be deactivated without any mechanical perturbation of the sample or imaging system, the technique may be readily integrated into conventional imaging studies.
No Bel-Robinson tensor for quadratic curvature theories
NASA Astrophysics Data System (ADS)
Deser, S.; Franklin, J.
2011-12-01
We attempt to generalize the familiar covariantly conserved Bel-Robinson tensor B???? ˜ RR of GR and its recent topologically massive third derivative order counterpart B ˜ R?DR to quadratic curvature actions. Two very different models of current interest are examined: fourth-order D = 3 ‘new massive gravity’ and second-order D > 4 Lanczos-Lovelock. On dimensional grounds, the candidates here become B ˜ DRDR + RRR. For the D = 3 model, there indeed exist conserved B ˜ ?R?R in the linearized limit. However, despite a plethora of available cubic terms, B cannot be extended to the full theory. The D > 4 models are not even linearizable about flat space, since their field equations are quadratic in curvature; they also have no viable B, a fact that persists even if one includes cosmological or Einstein terms to allow linearization about the resulting dS vacua. These results are an unexpected, if hardly unique, example of linearization instability.
Bianchi V I I A solutions of effective quadratic gravity
NASA Astrophysics Data System (ADS)
de Deus, Juliano A.; Müller, Daniel
2012-06-01
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model H 3 for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain way. It is found solutions which asymptote de Sitter space, Riemann flat space and a singularity. The question of isotropisation of an initially anisotropic Universe is of great importance in the context of cosmology. Although isotropisation is not directly discussed in this present work, we show that sufficiently small anisotropies, do not increase indefinitely according to particular quadratic gravity theories. It can be understood as weak isotropisation, and we stress that this result is strongly dependent on initial conditions.
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)].
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.
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.
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.
On the Dynamics of n-Dimensional Quadratic Endomorphisms
NASA Astrophysics Data System (ADS)
Romero, N.; Rovella, A.; Vilamajó, F.
Considering a convex endomorphism F (its n coordinates are convex functions) and the one parameter family F?=F-??, where ? is any vector of n, we find sufficient conditions in order that for large values of the parameter, the dynamical behavior of F? is completely described: either the nonwandering set ?(F?) is empty or F? restricted to ?(F?) is an expanding map. These conditions are shown to be generic in the space of quadratic endomorphisms.
Quadratic performance index generation for optimal regular design.
NASA Technical Reports Server (NTRS)
Bullock, T. E.; Elder, J. M.
1971-01-01
Application of optimal control theory to practical problems has been limited by the difficulty of prescribing a performance index which accurately reflects design requirements. The task of deriving equivalent performance indices is considered in the present paper for a plant that is a completely controllable, scalar linear system with state feedback. A quadratic index is developed which leads to an optimal design performance satisfying some of the classical performance criteria.
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.
Quantum integrals of motion for variable quadratic Hamiltonians
Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.
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.
Revisiting the naturalness problem: Who is afraid of quadratic divergences?
NASA Astrophysics Data System (ADS)
Aoki, Hajime; Iso, Satoshi
2012-07-01
It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergencesâ€”which can always be absorbed into a position of the critical surfaceâ€”should be simply subtracted in model constructions. Such a picture gives another justification to the argument [W. A. Bardeen, Report No. FERMILAB-CONF-95-391-T] that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.
Quadratic canonical transformation theory and higher order density matrices.
Neuscamman, Eric; Yanai, Takeshi; Chan, Garnet Kin-Lic
2009-03-28
Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H(2)O and N(2) binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories. PMID:19334803
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.
Measurement of quadratic electrogyration effect in castor oil
NASA Astrophysics Data System (ADS)
Izdebski, Marek; Ledzion, Rafa?; Górski, Piotr
2015-07-01
This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient ?13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.
General quadratic gauge theory: constraint structure, symmetries and physical functions
NASA Astrophysics Data System (ADS)
Gitman, D. M.; Tyutin, I. V.
2005-06-01
How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation to specific features of the theory in the Lagrangian formulation, especially relate the constraint structure to the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether we can identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfil such a programme, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.
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
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.
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...
Primal-Dual Interior Methods for Quadratic Programming
NASA Astrophysics Data System (ADS)
Shustrova, Anna
Interior methods are a class of computational methods for solving a con- strained optimization problem. Interior methods follow a continuous path to the solution that passes through the interior of the feasible region (i.e., the set of points that satisfy the constraints). Interior-point methods may also be viewed as methods that replace the constrained problem by a sequence of unconstrained problems in which the objective function is augmented by a weighted "barrier" term that is infinite at the boundary of the feasible region. Convergence to a solution of the constrained problem is achieved by solving a sequence of unconstrained problems in which the weight on the barrier term is steadily reduced to zero. This thesis concerns the formulation and analysis of interior methods for the solution of a quadratic programming (QP) problem, which is an optimization problem with a quadratic objective function and linear constraints. The linear constraints may include an arbitrary mixture of equality and inequality constraints, where the inequality constraints may be subject to lower and/or upper bounds. QP problems arise in a wide variety of applications. An important application is in sequential quadratic programming methods for nonlinear optimization, which involve minimizing a sequence of QP subproblems based on a quadratic approximation of the nonlinear objective function and a set of linearized nonlinear constraints. Two new interior methods for QP are proposed. Each is based on the properties of a barrier function defined in terms of both the primal and dual variables. The first method is suitable for a QP with all inequality constraints. At each iteration, the Newton equations for minimizing a quadratic model of the primal-dual barrier function are reformulated in terms of a symmetric indefinite system of equations that is solved using an inertia controlling factorization. This factorization provides an effective method for the detection and convexification of nonconvex problems. The second method is intended for problems with a mixture of equality and inequality constraints. In this case, the QP constraints are converted to so- called standard form and a primal-dual augmented Lagrangian is used to ensure the feasibility of the equality constraints in the limit.
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
Tanaka, Masashi; Zhang, Shuai; Inumaru, Kei; Yamanaka, Shoji
2013-05-20
The Zintl compound CaAl2Si2 peritectically decomposes to a new ternary cubic Laves phase Ca(Al,Si)2 and an Al-Si eutectic at temperatures above 750 °C under a pressure of 13 GPa. The ternary Laves phase compound can also be prepared as solid solutions Ca(Al(1-x)Si(x))2 (0.35 ? x ? 0.75) directly from the ternary mixtures under high-pressure and high-temperature conditions. The cubic Laves phase structure can be regarded as a type of clathrate compound composed of face-sharing truncated tetrahedral cages with Ca atoms at the center, Ca@(Al,Si)12. The compound with a stoichiometric composition CaAlSi exhibits superconductivity with a transition temperature of 2.6 K. This is the first superconducting Laves phase compound composed solely of commonly found elements. PMID:23654286
Pak, Chongin; Kamali, Saeed; Pham, Joyce; Lee, Kathleen; Greenfield, Joshua T.; Kovnir, Kirill
2014-01-01
Fragments of the superconducting FeSe layer, FeSe2 tetrahedral chains, were stabilized in the crystal structure of a new mixed-valent compound Fe3Se4(en)2 (en = ethylenediamine) synthesized from elemental Fe and Se. The FeSe2 chains are separated from each other by means of Fe(en)2 linkers. Mössbauer spectroscopy and magnetometry reveal strong magnetic interactions within the FeSe2 chains which result in antiferromagnetic ordering below 170 K. According to DFT calculations, anisotropic transport and magnetic properties are expected for Fe3Se4(en)2. This compound offers a unique way to manipulate the properties of the Fe-Se infinite fragments by varying the topology and charge of the Fe-amino linkers. PMID:24299423
NASA Astrophysics Data System (ADS)
Gálisová, Lucia; Stre?ka, Jozef
2015-10-01
Magnetocaloric effect in a double-tetrahedral chain, in which nodal lattice sites occupied by the localized Ising spins regularly alternate with three equivalent lattice sites available for mobile electrons, is exactly investigated by considering the one-third electron filling and the ferromagnetic Ising exchange interaction between the mobile electrons and their nearest Ising neighbours. The entropy and the magnetic Grüneisen parameter, which closely relate to the magnetocaloric effect, are exactly calculated in order to investigate the relation between the ground-state degeneracy and the cooling efficiency of the hybrid spin-electron system during the adiabatic demagnetization.
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.
Fang, Wei-Hui; Zhang, Lei; Zhang, Jian; Yang, Guo-Yu
2016-02-01
Compared with metal organic frameworks (MOFs), the proton conductivity of cluster organic frameworks has been less studied. Herein, two supertetrahedral cluster organic frameworks (SCOFs) have been made that show two-fold interpenetrated networks built by trivalent lanthanide tetrahedral clusters and monovalent cuprous T3 -supertetrahedral clusters. The structure analysis, second harmonic generation signals, and solid-state circular dichroism spectroscopy consistently reveal the chirality of these SCOFs. Remarkably, the water-stable SCOFs show a high proton conductivity value of 1.4×10(-3) ?S?cm(-1) at 80?°C and 95?% RH (relative humidity). PMID:26710922
A synthetic strategy for switching the single ion anisotropy in tetrahedral Co(II) complexes.
Vaidya, Shefali; Upadhyay, Apoorva; Singh, Saurabh Kumar; Gupta, Tulika; Tewary, Subrata; Langley, Stuart K; Walsh, James P S; Murray, Keith S; Rajaraman, Gopalan; Shanmugam, Maheswaran
2015-03-01
Four novel mononuclear tetrahedral cobalt(II) complexes containing exocyclic mesoionic ligands of molecular formulae [Co(II)(L1)(X)2(MeCN)] X = Cl (1) or Br (2) and [Co(II)(L2)(X)2(MeCN)], X = Cl (3) or Br (4) have been reported. It is found that simple substitution of L1 (O donor in 1 and 2) by L2 (S donor in 3 and 4) results in switching of the single ion magnetic anisotropy parameter (D) from positive to negative, with a significant change in magnitude. PMID:25370832
Dudek, J.; Dubray, N.; Pangon, V.; Dobaczewski, J.; Olbratowski, P.; Schunck, N.
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.
Synthesis of highly tetrahedral amorphous carbon by mixed-mode HiPIMS sputtering
NASA Astrophysics Data System (ADS)
Ganesan, R.; McCulloch, D. G.; Marks, N. A.; Tucker, M. D.; Partridge, J. G.; Bilek, M. M. M.; McKenzie, D. R.
2015-11-01
Tetrahedral amorphous carbon films with an sp 3 content of 80% have been produced by high power impulse magnetron sputtering (HiPIMS) operating in a mixed sputtering/arc mode. In this mode, short-lived cathode spots form in the magnetic racetrack and produce large numbers of carbon ions. The spots move rapidly, inhibiting the formation of macroparticles. An argon pressure below 2.5 mTorr was critical for obtaining films with high sp 3 content, high stress, large Tauc gap and symmetrical Raman spectra, and all four quantities were strongly correlated.
Zhu, Hai; Chi, Quan; Zhao, Yanxi; Li, Chunya; Tang, Heqing; Li, Jinlin; Huang, Tao; Liu, Hanfan; Institute of Chemistry, Chinese Academy of Science, Beijing 100080
2012-11-15
Graphical abstract: By using CO as a reducing agent, uniform and well-defined concave tetrahedral Pd nanocrystals were successfully synthesized. CO flow rate was the most essential for the formation of the concave tetrahedral nanostructures. The morphologies and sizes of the final products can be well controlled by adjusting the flow rate of CO. Highlights: â–º By using CO as a reducing agent, concave tetrahedral Pd nanocrystals were obtained. â–º CO flow rate is critical to the formation of concave tetrahedral Pd nanocrystals. â–º The selective adsorption of CO on (1 1 0) facets is essential to concave Pd tetrahedra. -- Abstract: CO reducing strategy to control the morphologies of palladium nanocrystals was investigated. By using CO as a reducing agent, uniform and well-defined concave tetrahedral Pd nanocrystals with a mean size of about 55 Â± 2 nm were readily synthesized with Pd(acac){sub 2} as a precursor and PVP as a stabilizer. The structures of the as-prepared Pd nanocrystals were characterized by transmission electron microscopy (TEM), X-ray powder diffraction (XRD), ultravioletâ€“visible (UVâ€“vis) absorption spectroscopy and electrochemical measurements. The results demonstrated that CO was the most essential for the formation of the concave tetrahedral Pd nanostructures. The morphologies and sizes of the final products can be well controlled by adjusting the flow rate of CO. The most appropriate CO flow rate, temperature and time for the formation of the ideal concave tetrahedral Pd nanocrystals was 0.033 mL s{sup âˆ’1}, 100 Â°C and 3 h, respectively.
Creepers: Real quadratic orders with large class number
NASA Astrophysics Data System (ADS)
Patterson, Roger
2007-03-01
Shanks's sequence of quadratic fields Q(sqrt{S_{n}}) where S_{n}=(2^n+1)^2 + 2^{n+2} instances a class of quadratic fields for which the class number is large and, therefore, the continued fraction period is relatively short. Indeed, that period length increases linearly with n, that is: in arithmetic progression. The fields have regulator O(n^2). In the late nineties, these matters intrigued Irving Kaplansky, and led him to compute period length of the square root of sequences a^2x^{2n}+bx^{n}+c for integers a, b, c, and x. In brief, Kap found unsurprisingly that, generically, triples (a,b,c) are `leapers': they yield sequences with period length increasing at exponential rate. But there are triples yielding sequences with constant period length, Kap's `sleepers'. Finally, there are triples, as exemplified by the Shanks's sequence, for which the period lengths increase in arithmetic progression. Felicitously, Kaplansky called these `creepers'. It seems that the sleepers and creepers are precisely those for which one is able to detail the explicit continued fraction expansion for all n. Inter alia, this thesis noticeably extends the known classes of creepers and finds that not all are `kreepers' (of the shape identified by Kaplansky) and therefore not of the shape of examples studied by earlier authors looking for families of quadratic number fields with explicitly computable unit and of relatively large regulator. The work of this thesis includes the discovery of old and new families of hyperelliptic curves of increasing genus g and torsion divisor of order O(g^2). It follows that the apparent trichotomy leaper/sleeper/creeper coincides with the folk belief that the just-mentioned torsion is maximum possible.
Restart-Based Genetic Algorithm for the Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Misevicius, Alfonsas
The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.
Ultraviolet fixed points in conformal gravity and general quadratic theories
NASA Astrophysics Data System (ADS)
Ohta, Nobuyoshi; Percacci, Roberto
2016-02-01
We study the beta functions for four-dimensional conformal gravity using two different parametrizations of metric fluctuation, linear split and exponential parametrization. We find that after imposing the traceless conditions, the beta functions are the same in four dimensions though the dependence on the dimensions are quite different. This indicates the universality of these results. We also examine the beta functions in general quadratic theory with the Einstein and cosmological terms for exponential parametrization, and find that it leads to results for beta functions of dimensionful couplings different from linear split, though the fact that there exists a nontrivial fixed point remains the same and the fixed points also remain the same.
Reaction Wheel Control Design Using Linear Quadratic Controller
NASA Astrophysics Data System (ADS)
Nubli Muhamad, Nur; Susanto, Erwin; Syihabuddin, Budi; Prasetya Dwi Wibawa, Ig.
2016-01-01
This paper studies the design of active attitude control system of a nanosatellite in a single axis. In this paper, we consider dc motor based reaction wheel as an actuator, because of its pointing accuracy. However, the power consumption of the dc motor is often relatively large and needed to be optimized. Linear quadratic controller is supposed to have an ability to minimize power consumption and able to enhance the system performance. To show the advantage of this method, simulation result of attitude response, state trajectory, and trajectory of DC motor voltage are presented.
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.
Recent Progress on Nonlinear Schrödinger Systems with Quadratic Interactions
Li, Chunhua; Hayashi, Nakao
2014-01-01
The study of nonlinear Schrödinger systems with quadratic interactions has attracted much attention in the recent years. In this paper, we summarize time decay estimates of small solutions to the systems under the mass resonance condition in 2-dimensional space. We show the existence of wave operators and modified wave operators of the systems under some mass conditions in n-dimensional space, where n ? 2. The existence of scattering operators and finite time blow-up of the solutions for the systems in higher space dimensions is also shown. PMID:25143965
Cyclicity of a fake saddle inside the quadratic vector fields
NASA Astrophysics Data System (ADS)
De Maesschalck, P.; Rebollo-Perdomo, S.; Torregrosa, J.
2015-01-01
This paper concerns the study of small-amplitude limit cycles that appear in the phase portrait near an unfolded fake saddle singularity. This degenerate singularity is also known as an impassable grain. The canonical form of the unperturbed vector field is like a degenerate flow box. Near the singularity, the phase portrait consists of parallel fibers, all but one of which have no singular points, and at the singular fiber, there is one node. We demonstrate different techniques in order to show that the cyclicity is bigger than or equal to two when the canonical form is quadratic.
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.
Quadratic Interaction Functional for General Systems of Conservation Laws
NASA Astrophysics Data System (ADS)
Bianchini, Stefano; Modena, Stefano
2015-09-01
For the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;
Hong Luo; Yidong Xia; Robert Nourgaliev; Chunpei Cai
2011-06-01
A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.
Verification of the three-dimensional tetrahedral grid S{sub N} code THOR
Schunert, S.; Ferrer, R.; Azmy, Y.
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)
Direct observation by X-ray analysis of the tetrahedral "intermediate" of aspartic proteinases.
Veerapandian, B; Cooper, J B; Sali, A; Blundell, T L; Rosati, R L; Dominy, B W; Damon, D B; Hoover, D J
1992-03-01
We report the X-ray analysis at 2.0 A resolution for crystals of the aspartic proteinase endothiapepsin (EC 3.4.23.6) complexed with a potent difluorostatone-containing tripeptide renin inhibitor (CP-81,282). The scissile bond surrogate, an electrophilic ketone, is hydrated in the complex. The pro-(R) (statine-like) hydroxyl of the tetrahedral carbonyl hydrate is hydrogen-bonded to both active-site aspartates 32 and 215 in the position occupied by a water in the native enzyme. The second hydroxyl oxygen of the hydrate is hydrogen-bonded only to the outer oxygen of Asp 32. These experimental data provide a basis for a model of the tetrahedral intermediate in aspartic proteinase-mediated cleavage of the amide bond. This indicates a mechanism in which Asp 32 is the proton donor and Asp 215 carboxylate polarizes a bound water for nucleophilic attack. The mechanism involves a carboxylate (Asp 32) that is stabilized by extensive hydrogen bonding, rather than an oxyanion derivative of the peptide as in serine proteinase catalysis. PMID:1304340
Accelerated expansion from a modified-quadratic gravity
NASA Astrophysics Data System (ADS)
Ahmad Rami, El-Nabulsi
2011-04-01
We investigate the late-time dynamics of a four-dimensional universe based on modified scalar field gravity in which the standard Einstein-Hilbert action R is replaced by f( ?) R+ f( R) where f( ?)= ? 2 and f( R)= AR 2+ BR ?? R ??,( A, B)??. We discussed two independent cases: in the first model, the scalar field potential is quartic and for this special form it was shown that the universe is dominated by dark energy with equation of state parameter w?-0.2 and is accelerated in time with a scale factor evolving like a( t)? t 5/3 and B+3 A?0.036. When, B+3 A?? which corresponds for the purely quadratic theory, the scale factor evolves like a( t)? t 1/2 whereas when B+3 A?0 which corresponds for the purely scalar tensor theory we found when a( t)? t 1.98. In the second model, we choose an exponential potential and we conjecture that the scalar curvature and the Hubble parameter vary respectively like R=? Hdot{?}/?,?inmathbb{R} and H=?dot{?}^{?},(?,?)inmathbb{R}. It was shown that for some special values of ?, the universe is free from the initial singularity, accelerated in time, dominated by dark or phantom energy whereas the model is independent of the quadratic gravity corrections. Additional consequences are discussed.
Accelerated expansion from a modified-quadratic gravity
NASA Astrophysics Data System (ADS)
El-Nabulsi, Ahmad Rami
2011-04-01
We investigate the late-time dynamics of a four-dimensional universe based on modified scalar field gravity in which the standard Einstein-Hilbert action R is replaced by f( ?) R+ f( R) where f( ?)= ? 2 and f( R)= AR 2+ BR ?? R ??,( A, B)??. We discussed two independent cases: in the first model, the scalar field potential is quartic and for this special form it was shown that the universe is dominated by dark energy with equation of state parameter w?-0.2 and is accelerated in time with a scale factor evolving like a( t)? t 5/3 and B+3 A?0.036. When, B+3 A?? which corresponds for the purely quadratic theory, the scale factor evolves like a( t)? t 1/2 whereas when B+3 A?0 which corresponds for the purely scalar tensor theory we found when a( t)? t 1.98. In the second model, we choose an exponential potential and we conjecture that the scalar curvature and the Hubble parameter vary respectively like R=? Hdot{?}/?,?in{R} and H=?dot{?}^{?},(?,?)in{R}. It was shown that for some special values of ?, the universe is free from the initial singularity, accelerated in time, dominated by dark or phantom energy whereas the model is independent of the quadratic gravity corrections. Additional consequences are discussed.
Confidence set inference with a prior quadratic bound
NASA Technical Reports Server (NTRS)
Backus, George E.
1989-01-01
In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.
Hidden and Nonstandard Bifurcation Diagram of an Alternate Quadratic System
NASA Astrophysics Data System (ADS)
Pastor, G.; Romera, M.; Danca, M.-F.; Martin, A.; Orue, A. B.; Montoya, F.; Encinas, L. HernÃ¡ndez
Alternate quadratic systems A : xn+1 = 1 â€‘ axn2,ifÂ nÂ isÂ even 1 â€‘ aâˆ—xn2,ifÂ nÂ isÂ odd andB : xn+1 = 1 â€‘ aâˆ—xn2,ifÂ nÂ isÂ even 1 â€‘ axn2, ifÂ nÂ isÂ odd, where a and aâˆ— are different parameters, seem to be interval maps in a range of the parameter values. However, after a careful graphical analysis of their bifurcation diagrams we conclude that this is true only for system B, but not for system A. In system A we find a hidden and nonstandard bifurcation diagram (â€œhiddenâ€ because it is not visible at normal resolution and â€œnonstandardâ€ because the bifurcation diagram is empty for some ranges of the parameter values). The different behavior of the underlying critical polynomial in the range of parameter values in both alternate quadratic systems explains why the hidden and nonstandard bifurcation diagram is present in system A and not in system B. The analysis of the Lyapunov exponent also shows both the existence and the different behavior of the hidden bifurcation diagram of system A.
Space Time Clustering and the Permutation Moments of Quadratic Form.
Zhou, Yi-Hui; Mayhew, Gregory; Sun, Zhibin; Xu, Xiaolin; Zou, Fei; Wright, Fred A
2013-01-01
The Mantel and Knox space-time clustering statistics are popular tools to establish transmissibility of a disease and detect outbreaks. The most commonly used null distributional approximations may provide poor fits, and researchers often resort to direct sampling from the permutation distribution. However, the exact first four moments for these statistics are available, and Pearson distributional approximations are often effective. Thus, our first goal is to clarify the literature and to make these tools more widely available. In addition, by rewriting terms in the statistics we obtain the exact first four permutation moments for the most commonly used quadratic form statistics, which need not be positive definite. The extension of this work to quadratic forms greatly expands the utility of density approximations for these problems, including for high-dimensional applications, where the statistics must be extreme in order to exceed stringent testing thresholds. We demonstrate the methods using examples from the investigation of disease transmission in cattle, the association of a gene expression pathway with breast cancer survival, regional genetic association with cystic fibrosis lung disease, and hypothesis testing for smoothed local linear regression. PMID:25210205
Single-molecule orientation measurements with a quadrated pupil
Backer, Adam S.; Backlund, Mikael P.; Lew, Matthew D.; Moerner, W. E.
2014-01-01
This Letter presents a means of measuring the dipole orientation of a fluorescent, orientationally fixed single molecule, which uses a specially designed phase mask, termed a “quadrated pupil,” conjugate to the back focal plane of a conventional wide-field microscope. The method leverages the spatial anisotropy of the far-field emission pattern of a dipole emitter and makes this anisotropy amenable to quantitative analysis at the image plane. In comparison to older image-fitting techniques that infer orientation by matching simulations to defocused or excessively magnified images, the quadrated pupil approach is more robust to minor modeling discrepancies and optical aberrations. Precision of 1°–5° is achieved in proof-of-concept experiments for both azimuthal (?) and polar (?) angles without defocusing. Since the phase mask is implemented on a liquid-crystal spatial light modulator that may be deactivated without any mechanical perturbation of the sample or imaging system, the technique may be readily integrated into clear aperture imaging studies. PMID:23632538
Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing
NASA Technical Reports Server (NTRS)
Choi, Benjamin B.
2002-01-01
Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.
Quadratic Reciprocity and the Group Orders of Particle States
DAI,YANG; BORISOV,ALEXEY B.; LONGWORTH,JAMES W.; BOYER,KEITH; RHODES,CHARLES K.
2001-06-01
The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.
NASA Astrophysics Data System (ADS)
Massa, F.; Lallemand, B.; Tison, T.
2015-02-01
Complex eigenvalue analysis is widely used to investigate the stability of a dynamical system with frictional contact. For finite element models, iterative solvers are needed to precisely calculate complex modes and eigenvalues. However, in cases such as reanalysis studies, optimization or uncertainty propagation processes, computational cost can quickly become too time consuming. For multiple samplings, two methods combining homotopy perturbation and projection techniques are proposed for the reanalysis of quadratic eigenvalue problems. To highlight the efficiency of the proposed methods, a complete numerical application including nominal and perturbed solution calculations, coalescence graph and parametric analysis, is performed. The precision of results and computational time are compared with those obtained using commercial software.
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.
A unified multigrid solver for the Navier-Stokes equations on mixed element meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.
NASA Astrophysics Data System (ADS)
Jeschke, Anja; Behrens, Jörn
2015-04-01
In tsunami modeling, two different systems of dispersive long wave equations are common: The nonhydrostatic pressure correction for the shallow water equations derived out of the depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of Boussinesq-type equations obtained by an expansion in the nondimensional parameters for nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a linear vertical interpolation of the nonhydrostatic pressure, whereas the second system's derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure. In this case the analytical dispersion relations do not coincide. We show that the nonhydrostatic correction with a quadratic vertical interpolation yields an equation set equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case of a horizontal bottom. Now, both systems yield the same analytical dispersion relation according up to the first order with the reference dispersion relation of the linear wave theory. The adjusted model is also compared to other Boussinesq-type equations. The numerical model with the nonhydrostatic correction for the shallow water equations uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element space discretization. The numerical dispersion relations are computed and compared by employing a testcase of a standing wave in a closed basin. All numerical values match their theoretical expectations. This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support given by Geir K. Petersen from the University of Oslo.
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.
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.
Advances in 3D electromagnetic finite element modeling
Nelson, E.M.
1997-08-01
Numerous advances in electromagnetic finite element analysis (FEA) have been made in recent years. The maturity of frequency domain and eigenmode calculations, and the growth of time domain applications is briefly reviewed. A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will also be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis is also discussed.
Integrability of Quadratic Non-autonomous Quantum Linear Systems
NASA Astrophysics Data System (ADS)
Lopez, Raquel
The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is constructed. Probability distributions of the particle linear position and momentum, are emphasized with Mathematica animations. The eigenfunctions qualitatively differ from the traditional standing waves of the one-dimensional Schrodinger equation. The physical relevance of these dynamic states is still questionable, and in order to investigate their physical meaning, animations could also be created for the squeezed coherent states. This will be addressed in future work.
Quadratic correction to the linear wave spectrum of two-dimensional random waves
NASA Astrophysics Data System (ADS)
Song, Jin-Bao; Tian, Ji-Wei; Lou, Shun-Li
1998-06-01
A perturbation expansion method's first three order solutions of two-dimensional random gravity waves in finite uniform depth were used as bases to derive the quadratic correction to the linear wave spectrum (i.e., the quadratic spectrum). For infinite water depth, the expression of the quadratic spectrum given in this paper is much simpler than that of Sclavounos (1992) and Olemz and Milgram (1995).
On nuclear spin statistics in rotational transition intensities in tetrahedral AB4 molecules
NASA Technical Reports Server (NTRS)
Rosenberg, A.; Susskind, J.
1979-01-01
A general expression is derived for the integrated intensity of rotational transitions in the vibronic ground state of tetrahedral molecules, taking into account the nuclear spin statistics. It is shown that the ratio of this expression to previously published spin-free integrated intensities depends only on the tensor character N of the operator driving the transition, the appropriate rotational quantum numbers J and J', and the nuclear spin of the identical nuclei. Tables are given for N = 3, 4 and J no more than 50, which enable the calculation of integrated intensities for octopole and hexadecapole collision-induced dipole-moment transitions, centrifugal-distortion-induced dipole-moment transitions, and centrifugal-distortion-induced anisotropic-polarizability-tensor Raman transitions.
Single walled carbon nanotube networkâ€”Tetrahedral amorphous carbon composite film
Iyer, Ajai Liu, Xuwen; Koskinen, Jari; Kaskela, Antti; Kauppinen, Esko I.; Johansson, Leena-Sisko
2015-06-14
Single walled carbon nanotube network (SWCNTN) was coated by tetrahedral amorphous carbon (ta-C) using a pulsed Filtered Cathodic Vacuum Arc system to form a SWCNTNâ€”ta-C composite film. The effects of SWCNTN areal coverage density and ta-C coating thickness on the composite film properties were investigated. X-Ray photoelectron spectroscopy measurements prove the presence of high quality sp{sup 3} bonded ta-C coating on the SWCNTN. Raman spectroscopy suggests that the single wall carbon nanotubes (SWCNTs) forming the network survived encapsulation in the ta-C coating. Nano-mechanical testing suggests that the ta-C coated SWCNTN has superior wear performance compared to uncoated SWCNTN.
Single walled carbon nanotube network—Tetrahedral amorphous carbon composite film
NASA Astrophysics Data System (ADS)
Iyer, Ajai; Kaskela, Antti; Johansson, Leena-Sisko; Liu, Xuwen; Kauppinen, Esko I.; Koskinen, Jari
2015-06-01
Single walled carbon nanotube network (SWCNTN) was coated by tetrahedral amorphous carbon (ta-C) using a pulsed Filtered Cathodic Vacuum Arc system to form a SWCNTN—ta-C composite film. The effects of SWCNTN areal coverage density and ta-C coating thickness on the composite film properties were investigated. X-Ray photoelectron spectroscopy measurements prove the presence of high quality sp3 bonded ta-C coating on the SWCNTN. Raman spectroscopy suggests that the single wall carbon nanotubes (SWCNTs) forming the network survived encapsulation in the ta-C coating. Nano-mechanical testing suggests that the ta-C coated SWCNTN has superior wear performance compared to uncoated SWCNTN.
Electric dipole moments in {sup 230,232}U and implications for tetrahedral shapes
Ntshangase, S. S.; Bark, R. A.; Datta, P.; Lawrie, E. A.; Lawrie, J. J.; Lieder, R. M.; Mullins, S. M.; Aschman, D. G.; Mohammed, H.; Stankiewicz, M. A.; Bvumbi, S.; Masiteng, P. L.; Shirinda, O.; Davidson, P. M.; Nieminen, P.; Wilson, A. N.; Dinoko, T. S.; Sharpey-Shafer, J. F.; Elbasher, M. E. A.; Juhasz, K.
2010-10-15
The nuclei {sup 230}U and {sup 232}U were populated in the compound nucleus reactions {sup 232}Th({alpha},6n) and {sup 232}Th({alpha},4n), respectively. Gamma rays from these nuclei were observed in coincidence with a recoil detector. A comprehensive set of in-band E2 transitions were observed in the lowest lying negative-parity band of {sup 232}U while one E2 transition was also observed for {sup 230}U. These allowed B(E1;I{sup -{yields}}I{sup +}-1)/B(E2;I{sup -{yields}}I{sup -}-2) ratios to be extracted and compared with systematics. The values are similar to those of their Th and Ra isotones. The possibility of a tetrahedral shape for the negative-parity U bands appears difficult to reconcile with the measured Q{sub 2} values for the isotone {sup 226}Ra.
Tetrahedral Iron in the Active Center of Plant Ferredoxins and Beef Adrenodoxin*
Eaton, William A.; Palmer, Graham; Fee, James A.; Kimura, Tokuji; Lovenberg, Walter
1971-01-01
The coordination structure of the iron-sulfur complex in spinach ferredoxin and adrenodoxin is investigated by optical spectroscopy. The circular-dichroism and absorption spectra of these two-iron iron-sulfur proteins reveal weak electronic transitions in the near-infrared wavelength range, 0.8-2.5 ?m (12,500-4000 cm-1). On the basis of the low absorption intensities and large anisotropy factors, d ? d transitions of the iron can be identified in the reduced proteins at about 4000 cm-1 and 6000 cm-1. The low energy of these one-center ligand-field transitions, together with the similarity to the ligand-field spectrum of the one-iron protein rubredoxin, leads to the conclusion that the reduced two-iron iron-sulfur proteins also contain a high-spin ferrous ion in a distorted tetrahedral site. PMID:4332004
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
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.
On the stability of tetrahedral relative equilibria in the positively curved 4-body problem
NASA Astrophysics Data System (ADS)
Diacu, Florin; MartÃnez, Regina; PÃ©rez-Chavela, Ernesto; SimÃ³, Carles
2013-08-01
We consider the motion of point masses given by a natural extension of Newtonian gravitation to spaces of constant positive curvature, in which the gravitational attraction between the bodies acts along geodesics. We aim to explore the spectral stability of tetrahedral orbits of the corresponding 4-body problem in the 2-dimensional case, a situation that can be reduced to studying the motion of the bodies on the unit sphere. We first perform some extensive and highly precise numerical experiments to find the likely regions of stability and instability, relative to the values of the masses and to the latitude of the position of the three equal masses. Then we support the numerical evidence with rigorous analytic proofs in the vicinity of some limit cases in which certain masses are either very large or negligible, or the latitude is close to zero.
Martinez-Miranda, L.J.; Sullivan, J.P.; Friedmann, T.A.; Siegal, M.P.; DiNardo, N.J. |
1997-12-01
The authors present the results of a post-deposition annealing structural study on amorphous tetrahedrally-coordinated carbon (a-tC) films on Si(100) prepared by pulsed-laser deposition. Films as-deposited and post-annealed at 200, 300, 400, 500 and 600 C, respectively, are studied using combined X-ray reflectivity and low-angle scattering measurements. The scans are fit to the Fresnel equations to obtain values for average film density, film and interface thickness, and film and interface roughness. They observe a correlation between the evolution of film density, roughness and the spacing of quasi-periodic structures in the films as a function of annealing temperature. They relate the evolution of these structural features with previous measurements of the resistivity and the observed stress release in these films.
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.
X-ray topography of a natural twinned diamond of unusual pseudo-tetrahedral morphology
NASA Astrophysics Data System (ADS)
Fritsch, Emmanuel; Moore, Moreton; Rondeau, Benjamin; Waggett, Richard G.
2005-06-01
The internal morphology of a natural twinned diamond was investigated using X-ray section topography. The diamond consisted of two crystals joined along a {1 1 1} plane whose remote ends were triangular {1 1 1} faces with sizes approximately 4 mm on the edge. A coating of fibrous growth obscured the morphology of the good quality diamond inside. Although the coat displayed re-entrant surfaces near the twin plane along three edges of the crystal, X-ray topography showed the inner crystal to protrude outwards along these same edges. The good quality inner core displayed the classical "spinel law" twinned octahedral morphology whereas the fibrous rim showed a typical sphalerite-like twinned tetrahedral morphology. A possible growth mechanism which could account for this is discussed.
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.
NASA Astrophysics Data System (ADS)
Chen, Xinchun; Peng, Zhijian; Yu, Xiang; Fu, Zhiqiang; Yue, Wen; Wang, Chengbiao
2011-02-01
In order to smooth the rough surface and further improve the wear-resistance of coarse chemical vapor deposition diamond films, diamond/tetrahedral amorphous carbon composite films were synthesized by a two-step preparation technique including hot-filament chemical vapor deposition for polycrystalline diamond (PCD) and subsequent filtered cathodic vacuum arc growth for tetrahedral amorphous carbon (ta-C). The microstructure and tribological performance of the composite films were investigated by means of various characterization techniques. The results indicated that the composite films consisted of a thick well-grained diamond base layer with a thickness up to 150 ?m and a thin covering ta-C layer with a thickness of about 0.3 ?m, and sp3-C fraction up to 73.93%. Deposition of a smooth ta-C film on coarse polycrystalline diamond films was proved to be an effective tool to lower the surface roughness of the polycrystalline diamond film. The wear-resistance of the diamond film was also enhanced by the self-lubricating effect of the covering ta-C film due to graphitic phase transformation. Under dry pin-on-disk wear test against Si3N4 ball, the friction coefficients of the composite films were much lower than that of the single PCD film. An extremely low friction coefficient (?0.05) was achieved for the PCD/ta-C composite film. Moreover, the addition of Ti interlayer between the ta-C and the PCD layers can further reduce the surface roughness of the composite film. The main wear mechanism of the composite films was abrasive wear.
Quantifying tetrahedral adduct formation and stabilization in the cysteine and the serine proteases.
Cleary, Jennifer A; Doherty, William; Evans, Paul; Malthouse, J Paul G
2015-10-01
Two new papain inhibitors have been synthesized where the terminal ?-carboxyl groups of Z-Phe-Ala-COOH and Ac-Phe-Gly-COOH have been replaced by a proton to give Z-Phe-Ala-H and Ac-Phe-Gly-H. We show that for papain, replacing the terminal carboxylate group of a peptide inhibitor with a hydrogen atom decreases binding 3-4 fold while replacing an aldehyde or glyoxal group with a hydrogen atom decreases binding by 300,000-1,000,000 fold. Thiohemiacetal formation by papain with aldehyde or glyoxal inhibitors is shown to be ~10,000 times more effective than hemiacetal or hemiketal formation with chymotrypsin. It is shown using effective molarities, that for papain, thiohemiacetal stabilization is more effective with aldehyde inhibitors than with glyoxal inhibitors. The effective molarity obtained when papain is inhibited by an aldehyde inhibitor is similar to the effective molarity obtained when chymotrypsin is inhibited by glyoxal inhibitors showing that both enzymes can stabilize tetrahedral adducts by similar amounts. Therefore the greater potency of aldehyde and glyoxal inhibitors with papain is not due to greater thiohemiacetal stabilization by papain compared to the hemiketal and hemiacetal stabilization by chymotrypsin, instead it reflects the greater intrinsic reactivity of the catalytic thiol group of papain compared to the catalytic hydroxyl group of chymotrypsin. It is argued that while the hemiacetals and thiohemiacetals formed with the serine and cysteine proteases respectively can mimic the catalytic tetrahedral intermediate they are also analogues of the productive and non-productive acyl intermediates that can be formed with the cysteine and serine proteases. PMID:26169698
Growth and band gap of the filled tetrahedral semiconductor Li 3AlP 2
NASA Astrophysics Data System (ADS)
Kuriyama, K.; Anzawa, J.; Kushida, K.
2008-04-01
AlP-like Li 3AlP 2 crystallizes in an orthorhombic structure in contrast to cubic nitride semiconductors such as Li 3AlN 2 and Li 3GaN 2. Li 3AlP 2 can be viewed as the zincblende-like (Li 0.5Al 0.5P) - lattice filled with He-like Li + ions at the empty tetrahedral sites. Li 3AlP 2 is grown by direct reaction of Li, Al, and P in an evacuated quartz ampoule. A typical reaction temperature is 1073 K and the temperature is maintained for 100 h. As-grown crystals, which are yellow in color, are confirmed to be a single phase of Li 3AlP 2 (space group: Ibca) with a=11.43 Å, b=11.93 Å, and c=12.03 Å by a powder X-ray diffraction method. Twelve Raman peaks are observed, which are consistent with 12 Raman active modes (3A g+3B 1g+3B 2g+3B 3g) evaluated by a factor group analysis for Li 3AlP 2. The band gap of as-grown Li 3AlP 2 evaluated using photoacoustic spectroscopy is ˜2.75 eV. The gap value is slightly larger than that of AlP ( Eg=2.43 eV), suggesting that the band gap of Li 3AlP 2 is essentially attributed to the six ionic Li-P bonds in the {1}/{8}-sublattice as well as the Li-N bonds in the filled tetrahedral semiconductors Li 3AlN 2 and Li 3GaN 2.
Deterministic macroscopic quantum superpositions of motion by quadratic optomechanical coupling
NASA Astrophysics Data System (ADS)
Tan, Huatang; Bariani, Francesco; Li, Gaoxiang; Meystre, Pierre
2013-05-01
We propose a scheme to prepare macroscopic quantum superpositions of motion of nanomechanical oscillators coupled quadratically to a driven cavity field. These superpositions result from the fact that the nonlinear optomechanical coupling can lead to an effective degenerate three-wave mixing of the mechanical and cavity modes. We show analytically and confirm numerically that different kinds of quantum superpositions can be realized deterministically, depending on the initial mechanical state. The effect of mechanical damping is also quantified by the negativity of the Wigner function. Besides various optomechanical systems, the present scheme could also be applied to other physical systems in which degenerate three-wave mixing can be engineered. Visiting Researcher from Huazhong Normal University.
Quadratic wavelets with short support on the interval
NASA Astrophysics Data System (ADS)
?erná, Dana; Fin?k, Václav
2012-11-01
It is well-known that a B-spline of order m has the shortest support among all compactly supported spline functions with respect to a given smoothness. And recently, B. Han and Z. Shen constructed a Riesz wavelet bases of the space L2(R) with the shortest support and with m vanishing moments based on B-spline of order m. Such wavelets are important for example in signal processing and in numerical solution of differential equations because of their excellent approximation properties and fast algorithms which provide. In our contribution, we present an adaptation of quadratic wavelets to the interval [0,1] which preserves vanishing moments. The proposed adaptation is a modification of the approach proposed by D. ?erná et al. and leads to a better conditioned basis.
Nonlinear equality constraints in feasible sequential quadratic programming
Lawrence, C.; Tits, A.
1994-12-31
In this talk we show that convergence of a feasible sequential quadratic programming algorithm modified to handle smooth nonlinear equality constraints. The modification of the algorithm to incorporate equality constraints is based on a scheme proposed by Mayne and Polak and is implemented in fsqp/cfsqp, an optimization package that generates feasible iterates. Nonlinear equality constraints are treated as {open_quotes}{<=}-type constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function which penalizes negative values. For example, the problem minimize f(x) s.t. h(x) = 0, with h(x) a scalar, is replaced by minimize f(x) - ch(x) s.t. h(x) {<=} 0. The modified problem is equivalent to the original problem when c is large enough (but finite). Such a value is determined automatically via iterative adjustments.
Thermodynamics of charged Lifshitz black holes with quadratic corrections
NASA Astrophysics Data System (ADS)
Bravo-Gaete, MoisÃ©s; HassaÃ¯ne, Mokhtar
2015-03-01
In arbitrary dimension, we consider the Einstein-Maxwell Lagrangian supplemented by the more general quadratic-curvature corrections. For this model, we derive four classes of charged Lifshitz black hole solutions for which the metric function is shown to depend on a unique integration constant. The masses of these solutions are computed using the quasilocal formalism based on the relation established between the off-shell Abbott-Deser-Tekin and Noether potentials. Among these four solutions, three of them are interpreted as extremal in the sense that their masses vanish identically. For the last family of solutions, both the quasilocal mass and the electric charge are shown to depend on the integration constant. Finally, we verify that the first law of thermodynamics holds for each solution and a Smarr formula is also established for the four solutions.
Impact of a global quadratic potential on galactic rotation curves.
Mannheim, Philip D; O'Brien, James G
2011-03-25
We present a conformal gravity fit to the 20 largest of a sample of 110 spiral galaxies. We identify the presence of a universal quadratic potential V(?)(r)=-?c²r²/2 with ?=9.54×10??? cm?² induced by cosmic inhomogeneities. When V(?)(r) is taken in conjunction with both a universal linear potential V(??)(r)=??c²r/2 with ??=3.06×10?³? cm?¹ generated by the homogeneous cosmic background and the contribution generated by the local luminous matter in galaxies, the theory then accounts for the rotation curve systematics observed in the entire 110 galaxies, without the need for any dark matter whatsoever. Our study suggests that using dark matter may be nothing more than an attempt to describe global effects in purely local galactic terms. With V(?)(r) being negative, galaxies can only support bound orbits up to distances of order ??/?=100kpc, with global physics imposing a limit on the size of galaxies. PMID:21517292
A Fixed-Point Iteration Method with Quadratic Convergence
Walker, Kevin P.; Sham, Sam
2012-01-01
The fixed-point iteration algorithm is turned into a quadratically convergent scheme for a system of nonlinear equations. Most of the usual methods for obtaining the roots of a system of nonlinear equations rely on expanding the equation system about the roots in a Taylor series, and neglecting the higher order terms. Rearrangement of the resulting truncated system then results in the usual Newton-Raphson and Halley type approximations. In this paper the introduction of unit root functions avoids the direct expansion of the nonlinear system about the root, and relies, instead, on approximations which enable the unit root functions to considerably widen the radius of convergence of the iteration method. Methods for obtaining higher order rates of convergence and larger radii of convergence are discussed.
Wind turbine power tracking using an improved multimodel quadratic approach.
Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier
2010-07-01
In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. PMID:20434153
Developed Adomian method for quadratic Kaluza-Klein relativity
NASA Astrophysics Data System (ADS)
Azreg-Aïnou, Mustapha
2010-01-01
We develop and modify the Adomian decomposition method (ADecM) to work for a new type of nonlinear matrix differential equations (MDE's) which arise in general relativity (GR) and possibly in other applications. The approach consists in modifying both the ADecM linear operator with highest order derivative and ADecM polynomials. We specialize in the case of a 4 × 4 nonlinear MDE along with a scalar one describing stationary cylindrically symmetric metrics in quadratic five-dimensional GR, derive some of their properties using ADecM and construct the most general unique power series solutions. However, because of the constraint imposed on the MDE by the scalar one, the series solutions terminate in closed forms exhausting all possible solutions.
Qualitative analysis of certain generalized classes of quadratic oscillator systems
NASA Astrophysics Data System (ADS)
Bagchi, Bijan; Ghosh, Samiran; Pal, Barnali; Poria, Swarup
2016-02-01
We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56, 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength Î», the other points to a centre for Î» < 0 but a saddle Î» > 0. On the other hand, the second potential reveals only a center for both the signs of Î» from a linear stability analysis. We carry out our study by extending Quesne's scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term fcosÏ‰t.
Dissipative quadratic solitons supported by a localized gain
NASA Astrophysics Data System (ADS)
Lobanov, Valery E.; Borovkova, Olga V.; Malomed, Boris A.
2014-11-01
We propose two models for the creation of stable dissipative solitons in optical media with the Ï‡(2 ) (quadratic) nonlinearity. To compensate spatially uniform loss in both the fundamental-frequency (FF) and second-harmonic (SH) components of the system, a strongly localized "hot spot" carrying the linear gain is added, acting either on the FF or on the SH component. In both systems, we use numerical methods to find families of dissipative Ï‡(2 ) solitons pinned to the "hot spot". The shape of the existence and stability domains may be rather complex. An existence boundary for the solitons, which corresponds to the guided mode in the linearized version of the systems, is obtained in an analytical form. The solitons demonstrate noteworthy features, such as spontaneous symmetry breaking (of spatially symmetric solitons) and bistability.
Kaluza-Klein reduction of a quadratic curvature model
NASA Astrophysics Data System (ADS)
Ba?kal, Sibel; Kuyrukcu, Halil
2013-02-01
Palatini variational principle is implemented on a five dimensional quadratic curvature gravity model, rendering two sets of equations, which can be interpreted as the field equations and the stress-energy tensor. Unification of gravity with electromagnetism and the scalar dilaton field is achieved through the Kaluza-Klein dimensional reduction mechanism. The reduced curvature invariant, field equations and the stress-energy tensor are obtained in the actual four dimensional spacetime. The structure of the interactions among the constituent fields is exhibited in detail. It is shown that the Lorentz force density naturally emerges from the reduced field equations and the equations of the standard Kaluza-Klein theory are demonstrated to be intrinsically contained in this model.
Quadratic substrate energy term and harmonics in the Halperin-Nelson model
NASA Astrophysics Data System (ADS)
Tönsing, Detlev L.
1991-01-01
The influence of the quadratic term in the Taylor expansion for the substrate potential, which is neglected in the Halperin-Nelson model, is investigated. The quadratic term is found to yield a harmonic series for the equilibrium displacement and a quadratic potential term in the energy of deviations from this displacement. Criteria for convergence of the series and negligibility of the quadratic potential term are derived. The criteria require the misfit vernier period and length scale of deviations not to be large compared with the Van der Merwe discommensuration width.
Confidence set inference with a prior quadratic bound
NASA Technical Reports Server (NTRS)
Backus, George E.
1988-01-01
In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.
Sensitivity Analysis of Parameters in Linear-Quadratic Radiobiologic Modeling
Fowler, Jack F.
2009-04-01
Purpose: Radiobiologic modeling is increasingly used to estimate the effects of altered treatment plans, especially for dose escalation. The present article shows how much the linear-quadratic (LQ) (calculated biologically equivalent dose [BED] varies when individual parameters of the LQ formula are varied by {+-}20% and by 1%. Methods: Equivalent total doses (EQD2 = normalized total doses (NTD) in 2-Gy fractions for tumor control, acute mucosal reactions, and late complications were calculated using the linear- quadratic formula with overall time: BED = nd (1 + d/ [{alpha}/{beta}]) - log{sub e}2 (T - Tk) / {alpha}Tp, where BED is BED = total dose x relative effectiveness (RE = nd (1 + d/ [{alpha}/{beta}]). Each of the five biologic parameters in turn was altered by {+-}10%, and the altered EQD2s tabulated; the difference was finally divided by 20. EQD2 or NTD is obtained by dividing BED by the RE for 2-Gy fractions, using the appropriate {alpha}/{beta} ratio. Results: Variations in tumor and acute mucosal EQD ranged from 0.1% to 0.45% per 1% change in each parameter for conventional schedules, the largest variation being caused by overall time. Variations in 'late' EQD were 0.4% to 0.6% per 1% change in the only biologic parameter, the {alpha}/{beta} ratio. For stereotactic body radiotherapy schedules, variations were larger, up to 0.6 to 0.9 for tumor and 1.6% to 1.9% for late, per 1% change in parameter. Conclusions: Robustness occurs similar to that of equivalent uniform dose (EUD), for the same reasons. Total dose, dose per fraction, and dose-rate cause their major effects, as well known.
Blind deconvolution estimation of fluorescence measurements through quadratic programming
NASA Astrophysics Data System (ADS)
Campos-Delgado, Daniel U.; Gutierrez-Navarro, Omar; Arce-Santana, Edgar R.; Skala, Melissa C.; Walsh, Alex J.; Jo, Javier A.
2015-07-01
Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.
Ren, Dong-Hong; Qiu, Dan; Pang, Chun-Yan; Li, Zaijun; Gu, Zhi-Guo
2015-01-14
A new class of chiral tetrahedral iron(II) cages were prepared from subcomponent self-assembly with high diastereoselectivity. The cages can be interconverted through imine exchange. The chiral cages displayed a spin transition close to room temperature, and the transition temperatures were affected by the substituent and uncoordinated solvents. PMID:25426503
ERIC Educational Resources Information Center
Filgueiras, Carlos A. L.; Carazza, Fernando
1980-01-01
Discusses procedures, theoretical considerations, and results of an experiment involving the preparation of a tetrahedral nickel(II) complex and its transformation into an octahedral species. Suggests that fundamental aspects of coordination chemistry can be demonstrated by simple experiments performed in introductory level courses. (Author/JN)
Li, G.; Dimitrijevic, N. M.; Chen, L.; Nichols, J. M.; Rajh, T.; Gray, K. A.; Northwestern Univ.
2008-04-23
Highly photoactive, tetrahedral Ti{sup 4+} sites can be created, other than in zeolite cavities and on silica substrate, in mixed-phase TiO{sub 2} nanocomposites. The tetrahedral Ti{sup 4+} species was shown to be an intermediate formed during the thermally driven phase transformation from anatase to rutile.
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2012-01-01
In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…
ERIC Educational Resources Information Center
Ellis, Amy B.; Grinstead, Paul
2008-01-01
This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…
Geometrical Solutions of Some Quadratic Equations with Non-Real Roots
ERIC Educational Resources Information Center
Pathak, H. K.; Grewal, A. S.
2002-01-01
This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2012-01-01
In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linearâ€¦
ERIC Educational Resources Information Center
Strickland, Tricia K.; Maccini, Paula
2013-01-01
The current study focuses on the effects of incorporating multiple visual representations on students' conceptual understanding of quadratic expressions embedded within area word problems and students' procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the…
EVA assembly of large space structure element
NASA Technical Reports Server (NTRS)
Bement, L. J.; Bush, H. G.; Heard, W. L., Jr.; Stokes, J. W., Jr.
1981-01-01
The results of a test program to assess the potential of manned extravehicular activity (EVA) assembly of erectable space trusses are described. Seventeen tests were conducted in which six "space-weight" columns were assembled into a regular tetrahedral cell by a team of two "space"-suited test subjects. This cell represents the fundamental "element" of a tetrahedral truss structure. The tests were conducted under simulated zero-gravity conditions. Both manual and simulated remote manipulator system modes were evaluated. Articulation limits of the pressure suit and zero gravity could be accommodated by work stations with foot restraints. The results of this study have confirmed that astronaut EVA assembly of large, erectable space structures is well within man's capabilities.
Quadratic isothermal amplification for the detection of microRNA.
Duan, Ruixue; Zuo, Xiaolei; Wang, Shutao; Quan, Xiyun; Chen, Dongliang; Chen, Zhifei; Jiang, Lei; Fan, Chunhai; Xia, Fan
2014-03-01
This protocol describes an isothermal amplification approach for ultrasensitive detection of specific microRNAs (miRNAs). It achieves this level of sensitivity through quadratic amplification of the target oligonucleotide by using a Bst DNA polymerase-induced strand-displacement reaction and a lambda exonuclease-aided recycling reaction. First, the target miRNA binds to a specifically designed molecular beacon, causing it to become a fluorescence emitter. A primer then binds to the activated beacon, and Bst polymerase initiates the synthesis of a double-stranded DNA segment templated on the molecular beacon. This causes the concomitant release of the target miRNA from the beacon--the first round of 'recycling'. Second, the duplex beacon thus produced is a suitable substrate for a nicking enzyme present in solution. After the duplex beacon is nicked, the lambda exonuclease digests the beacon and releases the DNA single strand just synthesized, which is complementary to the molecular beacon, inducing the second round of recycling. The miRNA detection limit of this protocol is 10 fmol at 37 °C and 1 amol at 4 °C. This approach also affords high selectivity when applied to miRNA extracted from MCF-7 and PC3 cell lines and even from breast cancer tissue samples. Upon isolation of miRNA, the detection process can be completed in ?2 h. PMID:24525753
Quadratic Fermi node in a 3D strongly correlated semimetal
NASA Astrophysics Data System (ADS)
Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.
2015-12-01
Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.
Profile-Following Entry Guidance Using Linear Quadratic Regulator Theory
NASA Technical Reports Server (NTRS)
Dukeman, Greg A.; Fogle, Frank (Technical Monitor)
2002-01-01
This paper describes one of the entry guidance concepts that is currently being tested as part of Marshall Space Flight Center's Advance Guidance and Control Project. The algorithm is of the reference profile tracking type. The reference profile consists of the reference states, range-to-go, altitude, and flight path angle, and reference controls, bank angle and angle of attack, versus energy. A linear control law using state feedback is used with energy-scheduled gains. The gains are obtained offline using Matlab's steady state linear quadratic regulator function. Lateral trajectory control is effected by performing periodic bank sign reversals based on a heading error corridor. A description and results of the AG&C test cases on which it has been tested are given. Although it is not anticipated that the algorithm will be quite as robust as algorithms with onboard trajectory re-generation capability, the results nevertheless show it to be very robust with respect to varying initial conditions and works satisfactorily even for entries from widely different orbits than that of the reference profile. Moreover, the commanded bank and angle of attack histories are very smooth, making it easier for the attitude control system to implement the guidance commands. Finally, results indicate that the guidance gains are more or less trajectory-independent which is a potentially useful property.
Quadratic Optimization in the Problems of Active Control of Sound
NASA Technical Reports Server (NTRS)
Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).
Linear quadratic optimal controller for cable-driven parallel robots
NASA Astrophysics Data System (ADS)
Abdolshah, Saeed; Shojaei Barjuei, Erfan
2015-12-01
In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work-space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional- integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.
Monitoring bioeroding sponges: using rubble, Quadrat, or intercept surveys?
Schönberg, C H L
2015-04-01
Relating to recent environmental changes, bioerosion rates of calcium carbonate materials appear to be increasing worldwide, often driven by sponges that cause bioerosion and are recognized bioindicators for coral reef health. Various field methods were compared to encourage more vigorous research on bioeroding sponges and their inclusion in major monitoring projects. The rubble technique developed by Holmes et al. (2000) had drawbacks often due to small specimen sizes: it was time-costly, generated large variation, and created a biased impression about dominant species. Quadrat surveys were most rapid but overestimated cover of small specimens. Line intercepts are recommended as easiest, least spatially biased, and most accurate, especially when comparing results from different observers. Intercepts required fewer samples and provided the best statistical efficiency, evidenced by better significances and test power. Bioeroding sponge abundances and biodiversities are influenced by water depth, sediment quality, and most importantly by availability of suitable attached substrate. Any related data should thus be standardized to amount of suitable substrate to allow comparison between different environments, concentrating on dominant, easily recognized species to avoid bias due to experience of observers. PMID:25920717
Quadratic Fermi node in a 3D strongly correlated semimetal
Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.
2015-01-01
Strong spinâ€“orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spinâ€“orbit and strong electronâ€“electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114
Quadratic Fermi node in a 3D strongly correlated semimetal.
Kondo, Takeshi; Nakayama, M; Chen, R; Ishikawa, J J; Moon, E-G; Yamamoto, T; Ota, Y; Malaeb, W; Kanai, H; Nakashima, Y; Ishida, Y; Yoshida, R; Yamamoto, H; Matsunami, M; Kimura, S; Inami, N; Ono, K; Kumigashira, H; Nakatsuji, S; Balents, L; Shin, S
2015-01-01
Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114
Mechanical cooling in single-photon optomechanics with quadratic nonlinearity
NASA Astrophysics Data System (ADS)
Gu, Wen-ju; Yi, Zhen; Sun, Li-hui; Xu, Da-hai
2015-08-01
In the paper we study the nonlinear mechanical cooling processes in an intrinsic quadratically optomechanical coupling system without linearizing the optomechanical interaction. We apply scattering theory to calculate the transition rates between different mechanical Fock states using the resolvent of the Hamiltonian, which allows for a direct identification of the underlying physical processes, where only even-phonon transitions are permitted and odd-phonon transitions are forbidden. We verify the feasibility of the approach by comparing the steady-state mean phonon number obtained from transition rates with the simulation of the full quantum master equation, and also discuss the analytical results in the weak coupling limit that coincide with two-phonon mechanical cooling processes. Furthermore, to evaluate the statistical properties of steady mechanical state, we respectively apply the Mandel Q parameter to show that the oscillator can be in nonclassical mechanical states, and the phonon number fluctuations F to display that the even-phonon transitions favor suppressing the phonon number fluctuations compared to the linear coupling optomechanical system.
Gap solitons in a nonlinear quadratic negative-index cavity
NASA Astrophysics Data System (ADS)
Scalora, Michael; de Ceglia, Domenico; D'Aguanno, Giuseppe; Mattiucci, Nadia; Akozbek, Neset; Centini, Marco; Bloemer, Mark J.
2007-06-01
We predict the existence of gap solitons in a nonlinear, quadratic Fabry-Pérot negative index cavity. A peculiarity of a single negative index layer is that if magnetic and electric plasma frequencies are different it forms a photonic band structure similar to that of a multilayer stack composed of ordinary, positive index materials. This similarity also results in comparable field localization and enhancement properties that under appropriate conditions may be used to either dynamically shift the band edge, or for efficient energy conversion. We thus report that an intense, fundamental pump pulse is able to shift the band edge of a negative index cavity, and make it possible for a weak second harmonic pulse initially tuned inside the gap to be transmitted, giving rise to a gap soliton. The process is due to cascading, a well-known phenomenon that occurs far from phase matching conditions that limits energy conversion rates, it resembles a nonlinear third-order process, and causes pulse compression due to self-phase modulation. The symmetry of the equations of motion under the action of either an electric or a magnetic nonlinearity suggests that both nonlinear polarization and magnetization, or a combination of both, can lead to solitonlike pulses. More specifically, the antisymmetric localization properties of the electric and magnetic fields cause a nonlinear polarization to generate a dark soliton, while a nonlinear magnetization spawns a bright soliton.
Phase Transitions in the Quadratic Contact Process on Complex Networks
NASA Astrophysics Data System (ADS)
Varghese, Chris; Durrett, Rick
2013-03-01
The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where a single infected (1) individual can infect a susceptible (0) neighbor and infected individuals are allowed to recover (1 --> 0). In the QCP, a combination of two 1's is required to effect a 0 --> 1 change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks as a model for the change in a population via sexual reproduction and death. We define two versions of the QCP - vertex centered (VQCP) and edge centered (EQCP) with birth events 1 - 0 - 1 --> 1 - 1 - 1 and 1 - 1 - 0 --> 1 - 1 - 1 respectively, where ` -' represents an edge. We investigate the effects of network topology by considering the QCP on regular, ErdÅ‘s-RÃ©nyi and power law random graphs. We perform mean field calculations as well as simulations to find the steady state fraction of occupied vertices as a function of the birth rate. We find that on the homogeneous graphs (regular and ErdÅ‘s-RÃ©nyi) there is a discontinuous phase transition with a region of bistability, whereas on the heavy tailed power law graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter.
Generation and dynamics of quadratic birefringent spatial gap solitons
Anghel-Vasilescu, P.; Dorignac, J.; Geniet, F.; Leon, J.; Taki, A.
2011-04-15
A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe{sub 2} (LGT) crystals. Once irradiated by a cw laser beam of 10 {mu}m wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold.
Linear versus quadratic portfolio optimization model with transaction cost
NASA Astrophysics Data System (ADS)
Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah
2014-06-01
Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.
Intense turquoise colors of apatite-type compounds with Mn5+ in tetrahedral coordination
NASA Astrophysics Data System (ADS)
Medina, Elena A.; Li, Jun; Stalick, Judith K.; Subramanian, M. A.
2016-02-01
The solid solutions of chlorapatite compounds Ba5Mn3-xVxO12Cl (x = 0-3.0) and Ba5Mn3-xPxO12Cl (x = 0-3.0) have been synthesized through solid state reactions and Pechini or sol-gel method using citric acid. The colors of the samples change from white (x = 3.0) through turquoise (x = 1.5) to dark green (x = 0) with increasing amount of manganese. Optical measurements reveal that the origin of the color is presumably a combination of d-d transitions of Mn5+ and cation-anion charge transfer from transition metals to oxygens. Near IR reflectance measurements indicate that synthesized compounds are promising materials for "cool pigments" applications. Magnetic measurements verify that manganese has two unpaired electrons and exhibits 5 + oxidation state. The IR spectra change systematically with sample compositions and the fingerprint region (700 cm-1 to 1100 cm-1) indicates characteristic bands belonging to (MnO4)3-, (VO4)3- and (PO4)3- functional groups. Structure refinements using neutron data confirm that Mn5+, V5+ and P5+ cations occupy the tetrahedral sites in the apatite structure.
AEM investigation of tetrahedrally coordinated Ti{sup 4+} in nickel-titanate spinel
Anderson, I.M. |; Bentley, J.; Carter, C.B.
1994-12-31
Stoichiometry and site distribution of metastable nickel-titanate spinel was studied with AEM. Results of EDXS and EELS agree that the metastable spinel is nonstoichiometric and titanium-deficient relative to its hypothetical endmember composition, ``Ni{sub 2}TiO{sub 4}``. The titanium deficiency has been determined by EELS to be {Delta} = 0.025 {plus_minus} 0.005. Channeling-enhanced microanalysis and ELNES studies indicate that the Ti{sup 4+} and Ni{sup 2+} cations are in tetrahedral and octahedral coordination, respectively, so that the metastable spinel has the normal cation distribution: Ti{sub l-{Delta}}[Ni{sub 2(1+{Delta})}]O{sub 4}. This is consistent with neutron powder-diffraction studies and SiO{sub 2}-solubility measurements of similar equilibrated and quenched spinel-containing specimens. Metastable nickel-titanate spinel therefore contrasts with stable stoichiometric spinels which tend to the inverse cation distribution, Me[MeTi]O{sub 4}.
Multiple-Armed Tetrahedral DNA Nanostructures for Tumor-Targeting, Dual-Modality in Vivo Imaging.
Jiang, Dawei; Sun, Yanhong; Li, Jiang; Li, Qian; Lv, Min; Zhu, Bing; Tian, Tian; Cheng, Dengfeng; Xia, Jiaoyun; Zhang, Lan; Wang, Lihua; Huang, Qing; Shi, Jiye; Fan, Chunhai
2016-02-24
In this work, we have developed multiple-armed DNA tetrahedral nanostructures (TDNs) for dual-modality in vivo imaging using near-infrared (NIR) fluorescence and single-photon emission computed tomography (SPECT). We found that the presence of arm strands in TDNs remarkably enhanced their in vitro stability, allowing them to stay intact for at least 12 h in serum. By using NIR fluorescence imaging, we evaluated in mice the pharmacokinetics of TDNs, which exhibited distinctly different in vivo biodistribution patterns compared with those of double-stranded (ds)DNA. We also noticed that TDNs had twofold longer circulation time in the blood system than that of dsDNA. With the use of multiple-armed TDNs, we could precisely anchor an exact number of functional groups including tumor-targeting folic acid (FA), NIR emitter Dylight 755, and radioactive isotope (99m)Tc on prescribed positions of TDNs, which showed the capability of targeted imaging ability in cancer cells. Furthermore, we realized noninvasive tumor-targeting imaging in tumor-bearing mice by using both NIR and SPECT modalities. PMID:26878704
Friedmann, T.A.; Siegal, M.P.; Tallant, D.R.; Simpson, R.L.; Dominguez, F.
1994-05-01
We are studying carbon thin films by using a pulsed excimer laser to ablate pyrolytic graphite targets to form highly tetrahedral coordinated amorphous carbon ({alpha}t-C) films. These films have been grown on room temperature p-type Si (100) substrates without the intentional incorporation of hydrogen. In order to understand and optimize the growth of {alpha}t-C films, parametric studies of the growth parameters have been performed. We have also introduced various background gases (H{sub 2}, N{sub 2} and Ar) and varied the background gas pressure during deposition. The residual compressive stress levels in the films have been measured and correlated to changes in the Raman spectra of the {alpha}t-C band near 1565 cm{sup {minus}1}. The residual compressive stress falls with gas pressure, indicating a decreasing atomic sp{sup 3}-bonded carbon fraction. We find that reactive gases such as hydrogen and nitrogen significantly alter the Raman spectra at higher pressures. These effects are due to a combination of chemical incorporation of nitrogen and hydrogen into the film as well as collisional cooling of the ablation plume. In contrast, films grown in non-reactive Ar background gases show much less dramatic changes in the Raman spectra at similar pressures.
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.
Pascucci, V
2004-02-18
This paper presents a simple approach for rendering isosurfaces of a scalar field. Using the vertex programming capability of commodity graphics cards, we transfer the cost of computing an isosurface from the Central Processing Unit (CPU), running the main application, to the Graphics Processing Unit (GPU), rendering the images. We consider a tetrahedral decomposition of the domain and draw one quadrangle (quad) primitive per tetrahedron. A vertex program transforms the quad into the piece of isosurface within the tetrahedron (see Figure 2). In this way, the main application is only devoted to streaming the vertices of the tetrahedra from main memory to the graphics card. For adaptively refined rectilinear grids, the optimization of this streaming process leads to the definition of a new 3D space-filling curve, which generalizes the 2D Sierpinski curve used for efficient rendering of triangulated terrains. We maintain the simplicity of the scheme when constructing view-dependent adaptive refinements of the domain mesh. In particular, we guarantee the absence of T-junctions by satisfying local bounds in our nested error basis. The expensive stage of fixing cracks in the mesh is completely avoided. We discuss practical tradeoffs in the distribution of the workload between the application and the graphics hardware. With current GPU's it is convenient to perform certain computations on the main CPU. Beyond the performance considerations that will change with the new generations of GPU's this approach has the major advantage of avoiding completely the storage in memory of the isosurface vertices and triangles.
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 Ëœ20 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 Ã— 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 (Ëœ72%) 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.
McGuire, John J; Bartley, David M; Tomsho, John W; Haile, William H; Coward, James K
2009-08-15
Phosphorus-containing pseudopeptides, racemic at the C-terminal alpha-carbon, are potent mechanism-based inhibitors of folylpolyglutamate synthetase (FPGS). They are mimics of the tetrahedral intermediate postulated to form during FPGS-catalyzed biosynthesis of poly(gamma-l-glutamates). In the present paper, the FPGS inhibitory activity of each diastereomer coupled to three heterocycles is reported. The high R(f) pseudopeptide containing the 5,10-dideazatetrahydropteroyl (DDAH(4)Pte) heterocycle is most potent (K(is) = 1.7 nM). While the heterocyclic portion affects absolute FPGS inhibitory potency, the high R(f) species is more potent in each pair containing the same heterocycle. This species presumably has the same stereochemistry as the natural folate polyglutamate, i.e., (l-Glu-gamma-l-Glu). Unexpectedly, the low R(f) (presumed l-Glu-gamma-d-Glu) species are only slightly less potent (<30-fold) than their diastereomers. Further study of this phenomenon comparing l-Glu-gamma-l-Glu and l-Glu-gamma-d-Glu dipeptide-containing FPGS substrates shows that <1% contamination of commercial d-Glu precursors by l-Glu may give misleading information if l-Glu-gamma-l-Glu substrates have low K(m) values. PMID:19563773
Non-Axial Octupole Deformations and Tetrahedral Symmetry in Heavy Nuclei
Mazurek, Katarzyna; Dudek, Jerzy
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.
Chen, Yuanyuan; Farquhar, Erik R.; Chance, Mark R.; Palczewski, Krzysztof; Kiser, Philip D.
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.
Raman scattering from the filled tetrahedral semiconductor LiMgAs
NASA Astrophysics Data System (ADS)
Kuriyama, K.; Yamashita, Y.; Suzuki, Y.; Matsumoto, K.; Kushida, K.
2010-01-01
Ordered LiMgAs (space group: F-43m), viewed theoretically as a zinc-blende-AlAs-like (MgAs)- lattice partially filled with He-like Li+ interstitials, is studied using a Raman-scattering method. The band gap of as-grown crystals is found to be 2.309 eV with a direct gap from the photoluminescence measurements at 20 K, in consistency with that estimated by the optical absorption. From Raman scattering, two LO and TO phonons at kËœ0 for Li-As and Mg-As pair are found to be 656 and 638 cm-1 and 329 and 307 cm-1, respectively, indicating that LiMgAs crystallizes with the ordered Li and Mg atoms at their tetrahedral sites. These results confirm a prediction that the ordered LiMgAs is attributed to the low ionic character of both Li-As (Pauling's ionicity fi = 0.22) and Mg-As (fi = 0.15) bonds.
Dynamics in a tetrahedral network glassformer: Vibrations, network rearrangements, and diffusion
NASA Astrophysics Data System (ADS)
Kawasaki, Takeshi; Kim, Kang; Onuki, Akira
2014-05-01
We perform molecular dynamics simulation on a tetrahedral network glassformer using a model for viscous SiO2 by Coslovich and Pastore [J. Phys.: Condens. Matter 21, 285107 (2009)]. In this system, Si and O particles form a random network at low temperature T. We attach an ellipsoid to each particle to represent its time-averaged vibration tensor. We then examine the anisotropic vibrations of Si and O, where the ellipsoid orientations are correlated with the network. The ellipsoids exhibit marked vibrational heterogeneity. The configuration changes occur as breakage and reorganization of the network, where only one or two particles undergo large jumps at each rearrangement leading to diffusion. To the time-correlation functions, however, the particles surrounding these largely displaced ones yield significantly T-dependent contributions, resulting in a weak violation of the Stokes-Einstein relation. This crossover is mild in silica due to the small Si-O bond numbers per particle, while it is strong in fragile glassformers with large coordination numbers. On long timescales, jump events tend to occur in the same regions forming marked dynamic heterogeneity. We also calculate the diffusion constants and the viscosity. The diffusion obeys activation dynamics and may be studied by short-time analysis of irreversible jumps.
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.
Sondergaard, Thomas; Wille, Morten
2015-11-01
Recent times have seen the introduction of small spherical arrays whose usefulness as sound intensity probes is the focus of this paper. The presented probe consists of a spherical shell, 30â€‰mm in diameter, housing four 14 in. microphones arranged in a regular tetrahedral configuration. Classical formulae may be used to estimate the sound intensity vector, as may methods based on spherical harmonics decomposition. Results are shown to be comparable to those obtained from classical sound intensity probes. The existence of an analytical model for a plane wave's diffraction about a sphere provides a means for adopting common optimization techniques for potentially improving the intensity vector estimate, however. This paper examines the validity of non-linear least squares optimization in conjunction with the proposed spherical sound intensity probe when placed in the following sound fields: (1) a simple plane wave; (2) a plane wave corrupted by noise; and (3) multiple incident plane waves. Under certain conditions, the probe is shown to greatly extend the operational frequency range of classical sound intensity probes. The optimization algorithm is found to lack robustness against deviations from plane wave conditions, however. PMID:26627758
Senthil Kumar, C M; Jacob, T K; Devasahayam, S; D'Silva, Sharon; Jinsha, J; Rajna, S
2015-11-01
Spilarctia obliqua Walker (Lepidoptera: Arctiidae) is a polyphagous insect pest damaging pulses, oil seeds, cereals, vegetables and medicinal and aromatic plants in India. The pest also infests turmeric and ginger sporadically in Kerala. We observed an epizootic caused by a nucleopolyhedrovirus (NPV) in field populations of the insects in December 2013. The NPV was purified and characterized. The isolate was tetrahedral in shape and belonged to multicapsid NPV. The REN profile of the SpobNPV genome with Pst I, Xho I and HindIII enzymes showed a genome size of 99.1Â±3.9 kbp. Partialpolh, lef-8 and lef-9 gene sequences of the isolate showed a close relationship with HycuNPV and SpphNPV. Phylogram and K-2-P distances between similar isolates suggested inclusion of the present SpobNPV isolate to group I NPV. The biological activity of the isolate was tested under laboratory conditions against third instar larvae of S. obliqua and the LC50 was 4.37Ã—10(3)OBs/ml occlusion bodies (OBs) per ml. The median survival time (ST50) was 181 h at a dose of 1Ã—10(6)OBs/ml and 167 h at a dose of 1Ã—10(8)OBs/ml. SpobNPV merits further field evaluation as a potential biological control agent of S. obliqua, a serious pest of many agriculturally important crops in the Oriental region. PMID:26449395
Hoia An, Le Thi; Tao, P.D.
1994-12-31
We present new algorithm of d.c. optimization (DCA) for globally minimizing a (convex or nonconvex) quadratic form on an Euclidean ball or sphere: min{l_brace}{1/2}x{sup T} A x + b{sup T}x : {parallel}x{parallel} {<=} r{r_brace} (Q1) min{l_brace}{1/2}x{sup T} Ax + b{sup T}x : {parallel}x{parallel} = r{r_brace} (Q2) where A is n {times} n real symmetrix matrix, b {element_of} IR{sup n}, r is a positive number. DCA is attractive because it is computationally inexpensive and quite reliable. For a {open_quotes}good{close_quotes} d.c. decomposition of the objective function, we propose a simple DCA to solve (Q1). This algorithm can be also applied to solving (Q2). Numerical simulations on a series of test problems are reported. They show robustness, stability and superiority of DCA with respect to known standard methods in the literature. The use of DCA in Trust Region methods, in Constrained Eigenvalue problem and in Least Squares with Quadratic constraints is consequently very interesting.
New type of Weyl semimetal with quadratic double Weyl fermions
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid
2016-01-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spinâ€“orbit coupling and that, after the inclusion of spinâ€“orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of Â±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914
New type of Weyl semimetal with quadratic double Weyl fermions.
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M Zahid
2016-02-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914
Moments for general quadratic densities in n dimensions
Furman, Miguel A.
2002-03-20
We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.
Gravity waves from non-minimal quadratic inflation
Pallis, Constantinos; Shafi, Qaisar
2015-03-12
We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio râ‰ƒ(2âˆ’4)â‹…10{sup âˆ’3}, and an inflaton mass close to 3â‹…10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic KÃ¤hler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the KÃ¤hler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s}â‰ƒ0.963 and râ‰ƒ0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the KÃ¤hler potential, and the prefactor encountered in it. Increasing slightly the latter above (âˆ’3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5âˆ’9)â‹…10{sup 13} GeV.
Mondal, Amit Kumar; Parmar, Vijay Singh; Biswas, Soumava; Konar, Sanjit
2016-03-21
A rare class of dinuclear double-stranded helicates having tetrahedral metal centres with formulae [Co2(L(1))2]Â·2(CH3CN) (1), [Co2(L(2))2]Â·6(CH3CN) (2), [Zn2(L(1))2]Â·2(CH3CN)Â·(CH3OH) (3) and [Zn2(L(2))2]Â·4(CH3CN) (4) were synthesized and characterized. Detailed dc and ac magnetic susceptibility measurements reveal the presence of field induced slow magnetic relaxation behaviour in high spin tetrahedral Co(II) centres with an easy-plane magnetic anisotropy. Complexes 1 and 2 are the rare examples of transition metal based helicates showing such behaviour. Furthermore, 3 and 4 exhibit fluorescence emission in different solvents that are analyzed in terms of fluorescence quantum yields and lifetimes. PMID:26842007
Hepburn, Iain; Cannon, Robert; De Schutter, Erik
2013-01-01
We describe a novel method for calculating the quasi-static electrical potential on tetrahedral meshes, which we call E-Field. The E-Field method is implemented in STEPS, which performs stochastic spatial reaction-diffusion computations in tetrahedral-based cellular geometry reconstructions. This provides a level of integration between electrical excitability and spatial molecular dynamics in realistic cellular morphology not previously achievable. Deterministic solutions are also possible. By performing the Rallpack tests we demonstrate the accuracy of the E-Field method. Efficient node ordering is an important practical consideration, and we find that a breadth-first search provides the best solutions, although principal axis ordering suffices for some geometries. We discuss potential applications and possible future directions, and predict that the E-Field implementation in STEPS will play an important role in the future of multiscale neural simulations. PMID:24194715
Berg, J.W. van der; Maseland, J.E.J.; Oskam, B.
1996-12-31
In this paper an assessment of CFD methods based on the underlying grid type is made. It is safe to say that emerging CFD methods based on hybrid body-fitted grids of tetrahedral and prismatic cells using unstructured data storage schemes have the potential to satisfy the basic requirements of problem-turnaround-time and accuracy for complex geometries. The CFD system described in this paper is based on the hybrid prismatic-tetrahedral grid approach. In an analysis it is shown that the cells in the prismatic layer have to satisfy a central symmetry property in order to obtain a second-order accurate approximation of the viscous terms in the Reynolds-averaged Navier-Stokes equations. Prismatic grid generation is demonstrated for the ONERA M6 wing-alone configuration and the AS28G wing/body configuration.
Tetrahedral magnetic order and the metal-insulator transition in the pyrochlore lattice of Cd2Os2O7.
Yamaura, J; Ohgushi, K; Ohsumi, H; Hasegawa, T; Yamauchi, I; Sugimoto, K; Takeshita, S; Tokuda, A; Takata, M; Udagawa, M; Takigawa, M; Harima, H; Arima, T; Hiroi, Z
2012-06-15
Cd2Os2O7 shows a peculiar metal-insulator transition at 227 K with magnetic ordering in a frustrated pyrochlore lattice, but its magnetic structure in the ordered state and the transition origin are yet uncovered. We observed a commensurate magnetic peak by resonant x-ray scattering in a high-quality single crystal. X-ray diffraction and Raman scattering experiments confirmed that the transition is not accompanied with any spatial symmetry breaking. We propose a noncollinear all-in-all-out spin arrangement on the tetrahedral network made of Os atoms. Based on this we suggest that the transition is not caused by the Slater mechanism as believed earlier but by an alternative mechanism related to the formation of the specific tetrahedral magnetic order on the pyrochlore lattice in the presence of strong spin-orbit interactions. PMID:23004317
Synthesis of tetrahedral quasi-type-II CdSe-CdS core-shell quantum dots.
Sugunan, Abhilash; Zhao, Yichen; Mitra, Somak; Dong, Lin; Li, Shanghua; Popov, Sergei; Marcinkevicius, Saulius; Toprak, Muhammet S; Muhammed, Mamoun
2011-10-21
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. PMID:21941036
Mohanty, Debasish; Li, Jianlin; Abraham, Daniel P; Huq, Ashfia; Payzant, E Andrew; Wood III, David L; Daniel, Claus
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.
Zhang, Feng-Li; Chen, Jia-Qian; Qin, Long-Fang; Tian, Lei; Li, Zaijun; Ren, Xuehong; Gu, Zhi-Guo
2016-04-01
An effective single crystal to single crystal transformation from a tetrahedral Ni cage to an FeNi cage was demonstrated. The iron(ii) centers of the FeNi cage can be induced to display spin crossover behaviors with an increasing amount of Fe(ii) ions. The SCSC metal-center exchange provides a powerful approach to modify solid magnetic properties. PMID:26955799
Temporal Dynamics and Nonclassical Photon Statistics of Quadratically Coupled Optomechanical Systems
NASA Astrophysics Data System (ADS)
Singh, Shailendra Kumar; Muniandy, S. V.
2016-01-01
Quantum optomechanical system serves as an interface for coupling between photons and phonons due to mechanical oscillations. We used the Heisenberg-Langevin approach under Markovian white noise approximation to study a quadratically coupled optomechanical system which contains a thin dielectric membrane quadratically coupled to the cavity field. A decorrelation method is employed to solve for a larger number of coupled equations. Transient mean numbers of cavity photons and phonons that provide dynamical behaviour are computed for different coupling regime. We have also obtained the two-boson second-order correlation functions for the cavity field, membrane oscillator and their cross correlations that provide nonclassical properties governed by quadratic optomechanical system.
Newton's method for solving a quadratic matrix equation with special coefficient matrices
NASA Astrophysics Data System (ADS)
Seo, Sang-Hyup; Seo, Jong Hyun; Kim, Hyun-Min
2014-03-01
We consider the iterative method for solving a quadratic matrix equation with special coefficient matrices which arises in the quasi-birth-death problem. In this paper, we show that the elementwise minimal positive solvents to quadratic matrix equations can be obtained using Newton's method. We also prove that the convergence rate of the Newton iteration is quadratic if the FrÃ©chet derivative at the elementwise minimal positive solvent is nonsingular. However, if the FrÃ©chet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.(This is summarized a paper which is to appear in Honam Mathematical Journal.)
Gong K.; Vukmirovic M.B.; Ma C.; Zhu Y.; Adzic R.R.
2011-11-01
We synthesized the Pt monolayer shell-Pd tetrahedral core electrocatalysts that are notable for their high activity and stable performance. A small number of low-coordination sites and defects, and high content of the (1 1 1)-oriented facets on Pd tetrahedron makes them a suitable support for a Pt monolayer to obtain an active O{sub 2} reduction reaction (ORR) electrocatalyst. The surfactants, used to control size and shape of Pd tetrahedral nanoparticles, are difficult to remove and cause adverse effects on the ORR. We describe a simple and noninvasive method to synthesize high-purity tetrahedral Pd nanocrystals (TH Pd) by combining a hydrothermal route and CO adsorption-induced removal of surfactants. Poly(vinylpyrrolidone) (PVP), used as a protecting and reducing agent in hydrothermal reactions, is strongly bonded to the surface of the resulting nanocrystals. We demonstrate that PVP was displaced efficiently by adsorbed CO. A clean surface was achieved upon CO stripping at a high potential (1.0 V vs RHE). It played a decisive role in improving the activity of the Pt monolayer/TH Pd electrocatalyst for the ORR. Furthermore, the results demonstrate a versatile method for removal of surfactants from various nanoparticles that severely limited their applications.
NASA Astrophysics Data System (ADS)
Paiva Fonseca, Gabriel; Landry, Guillaume; White, Shane; D'Amours, Michel; Yoriyaz, HÃ©lio; 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 50â€‰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.
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
Thermal expansion and structural complexity of Ba silicates with tetrahedrally coordinated Si atoms
NASA Astrophysics Data System (ADS)
Gorelova, Liudmila A.; Bubnova, Rimma S.; Krivovichev, Sergey V.; Krzhizhanovskaya, Maria G.; Filatov, Stanislav K.
2016-03-01
Thermal expansion of Ba silicates with tetrahedrally coordinated Si atoms in the temperature range of 25-1100 Â°C had been studied by high-temperature X-ray powder diffraction. The volume thermal expansion coefficients (TECs) are in the range 41-50Ã—10-6 Â°C-1 with an average value of <Î±V > = 45 Ã—10-6 Â°C-1. In the structures with chain and layered silicate anions, thermal expansion is anisotropic: the direction of maximal TEC is parallel to the extension of the zweier chains of silicate tetrahedra, which are strained owing to the interactions with Ba2+. The strain is released during thermal expansion due to the increasing effective size of Ba2+ induced by thermal vibrations. Information-theoretic analysis of the structural and topological complexities of Ba silicates indicates that their structural complexity is a function of the topological complexity of their silicate anions. The latter displays a non-linear behaviour with increasing SiO2 content (=the increasing degree of polymerization and increasing dimensionality): it starts from simple topologies, reaches a maximum at topologies of intermediate complexity, and ends up at simple topologies again. The specificity of the interactions of Ba2+ with the silicate anions results in higher complexity of high-temperature Î±-BaSi2O5 compared to that of low-temperature Î²-BaSi2O5. This uncommon behaviour may be explained by the vibrational advantages provided by flatter and more complex silicate layers in the Î±-phase, which overcome negative differences in configurational entropies of the two modifications apparent in the differences of their structural Shannon information.
Correlation of structure and triboluminescence for tetrahedral manganese(II) compounds.
Cotton, F A; Daniels, L M; Huang, P
2001-07-01
To investigate the structural basis of triboluminescence, several known tetrahedrally coordinated Mn(II) complexes have been synthesized according to literature methods and their crystal structures have been determined by X-ray diffraction. Among them, (MePh(3)P)(2)[MnCl(4)] (2), a = 15.4804(4) A, cubic, space group P2(1)3, Z = 4; (Et(4)N)(2)[MnBr(4)] (4), a = 13.362(1) A, c = 14.411(1) A, tetragonal, space group P42(1)m, Z = 4; MnBr(2)(OPPh(3))(2) (7), a = 9.974(1) A, b = 10.191(3) A, c = 10.538(2) A, alpha = 65.32(1) degrees, beta = 63.49(1) degrees, gamma = 89.44(2) degrees, triclinic, space group P1, Z = 1; and MnBr(2)(OAsPh(3))(2) (10), a = 17.816(3) A, b = 10.164(1) A, c = 18.807(3) A, orthorhombic, space group Pca2(1), Z = 4 were reported to be triboluminescent and (Me(4)N)(2)[MnCl(4)] (3), a = 9.016(3) A, b = 36.90(2) A, c = 15.495(3) A, beta = 90.72(3) degrees, monoclinic, space group P2(1)/n, Z = 12, and MnI(2)(OAsPh(3))(2) (11), a = 10.094(4) A, b = 10.439(2) A, c = 34.852(2) A, alpha = 83.17(4) degrees, beta = 86.09(2) degrees, gamma = 75.16(3) degrees, triclinic, space group P1, Z = 4, were reported to be not triboluminescent. The result supports the correlation between space group acentricity and triboluminescence activity. PMID:11421708
Simple shearing flow of dry soap foams with TCP structure[Tetrahedrally Close-Packed
REINELT,DOUGLAS A.; KRAYNIK,ANDREW M.
2000-02-16
The microrheology of dry soap foams subjected to large, quasistatic, simple shearing deformations is analyzed. Two different monodisperse foams with tetrahedrally close-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Laves (C15). The elastic-plastic response is evaluated by calculating foam structures that minimize total surface area at each value of strain. The minimal surfaces are computed with the Surface Evolver program developed by Brakke. The foam geometry and macroscopic stress are piecewise continuous functions of strain. The stress scales as T/V{sup 1/3} where T is surface tension and V is cell volume. Each discontinuity corresponds to large changes in foam geometry and topology that restore equilibrium to unstable configurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a small increase in strain changes the energy profile in the neighborhood of a foam structure from a local minimum to a saddle point, which can lead to symmetry-breaking bifurcations. In general, the new foam topology associated with each stable solution branch results from a cascade of local topology changes called T1 transitions. Each T1 cascade produces different cell neighbors, reduces surface energy, and provides an irreversible, film-level mechanism for plastic yield behavior. Stress-strain curves and average stresses are evaluated by examining foam orientations that admit strain-periodic behavior. For some orientations, the deformation cycle includes Kelvin cells instead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and can even cause strain localization.
Simple shearing flow of dry soap foams with tetrahedrally close-packed structure
Reinelt, Douglas A.; Kraynik, Andrew M.
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.
Schweinfurth, David; Demeshko, Serhiy; Khusniyarov, Marat M; Dechert, Sebastian; Gurram, Venkatanarayana; Buchmeiser, Michael R; Meyer, Franc; Sarkar, Biprajit
2012-07-16
The 'Click'-derived tripodal ligand tris[(1-benzyl-1H-1,2,3-triazole-4-yl)methyl]amine, tbta, was used to synthesize the complexes [Fe(tbta)Cl]BF(4), 1, and [Co(tbta)Cl]BF(4), 2. Both complexes were characterized by (1)H NMR spectroscopy and elemental analysis. Single-crystal X-ray structural determination of 2 shows a 4 + 1 coordination around the cobalt(II) center with a rather long bond between Co(II) and the central amine nitrogen atom of tbta. Such a coordination geometry is best described as capped tetrahedral. 1 and 2 are thus the first examples of pseudotetrahedral coordinated Fe(II) and Co(II) complexes with tbta. A combination of SQUID susceptometry, EPR spectroscopy, Mössbauer spectroscopy, and DFT calculations was used to elucidate the electronic structures of these complexes and determine the spin state of the metal center. Comparisons are made between the complexes presented here with related complexes of other ligands such as tris(2-pyridylmethyl)amine, tmpa, hydrotris(pyrazolyl) borate, Tp, and tris(2-(1-pyrazolyl)methyl)amine, amtp. 1 and 2 were tested as precatalysts for the homopolymerization of ethylene, and both complexes delivered distinctly different products in this reaction. Blind catalyst runs were carried out with the metal salts to prove the importance of the tripodal ligand for product formation. PMID:22731779
Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis
2005-12-01
This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.
Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures
NASA Astrophysics Data System (ADS)
Burger, Sven; Gutsche, Philipp; Hammerschmidt, Martin; Herrmann, Sven; Pomplun, Jan; Schmidt, Frank; Wohlfeil, Benjamin; Zschiedrich, Lin
2015-09-01
The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for computation of electromagnetic fields in a device with rough textures. The method allows for efficient computations on meshes with strong variations in element sizes. This enables to use precise geometry resolution of the rough textures. Convergence to highly accurate results is observed.
Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Martin, Corless
2004-01-01
We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.
New trace formulae for a quadratic pencil of the Schroedinger operator
Yang Chuanfu
2010-03-15
This work deals with the eigenvalue problem for a quadratic pencil of the Schroedinger operator on a finite closed interval with the two-point boundary conditions. We will obtain new regularized trace formulas for this class of differential pencil.
Note: Probing quadratic magneto-optical Kerr effects with a dual-beam system.
Trudel, Simon; Wolf, Georg; Schultheiss, Helmut; Hamrle, Jaroslav; Hillebrands, Burkard; Kubota, Takahide; Ando, Yasuo
2010-02-01
In this Note, we present a dual-beam magneto-optical Kerr effect (MOKE) magnetometer for the study of quadratic MOKE in magnetic thin films. The two beams simultaneously probe the sample, located in the middle of a quadrupole magnet, at two angles of incidence (0 degrees and 45 degrees). This combination of two systems allows one to automatically and routinely perform measurements that are sensitive to the combined longitudinal and quadratic MOKE signals (45 degrees), or the quadratic effect alone (0 degrees). Orientation-dependent and automated quantitative analyses of the quadratic effect's amplitude are also implemented. We present representative measurements on Heusler compound thin films to illustrate the newly combined capabilities of this instrument. PMID:20192522
Kelly, S. D.; Kemner, K. M.; Fryxell, Glen E. ); Liu, Jun ); Mattigod, Shas V. )
2000-12-01
X-ray absorption fine structure (XAFS) spectroscopy is used to investigate the chemical interaction between the end member of the self assembled monolayers on mesoporous supports[Cu(NH2)6] and the tetrahedral anion SO4.
Akinoglu, B.G.; Ecevit, A. )
1990-01-01
In this paper, a new correlation for the estimation of monthly average daily global solar radiation will be presented and compared with the correlations of Rietveld, Benson et al., Oegelman et al., and a recent formulation by Gopinathan. The overall results show that the quadratic form gives better performance in terms of global applicability. The new quadratic model should be preferred for the monthly average global solar radiation estimation when the data for bright sunshine hours are available.
Sequential design of discrete linear quadratic regulators via optimal root-locus techniques
NASA Technical Reports Server (NTRS)
Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar
1989-01-01
A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.
Hendrickx, Christophe; Mateus, OctÃ¡vio; Buffetaut, Eric
2016-01-01
Six quadrate bones, of which two almost certainly come from the Kem Kem beds (Cenomanian, Upper Cretaceous) of south-eastern Morocco, are determined to be from juvenile and adult individuals of Spinosaurinae based on phylogenetic, geometric morphometric, and phylogenetic morphometric analyses. Their morphology indicates two morphotypes evidencing the presence of two spinosaurine taxa ascribed to Spinosaurus aegyptiacus and? Sigilmassasaurus brevicollis in the Cenomanian of North Africa, casting doubt on the accuracy of some recent skeletal reconstructions which may be based on elements from several distinct species. Morphofunctional analysis of the mandibular articulation of the quadrate has shown that the jaw mechanics was peculiar in Spinosauridae. In mature spinosaurids, the posterior parts of the two mandibular rami displaced laterally when the jaw was depressed due to a lateromedially oriented intercondylar sulcus of the quadrate. Such lateral movement of the mandibular ramus was possible due to a movable mandibular symphysis in spinosaurids, allowing the pharynx to be widened. Similar jaw mechanics also occur in some pterosaurs and living pelecanids which are both adapted to capture and swallow large prey items. Spinosauridae, which were engaged, at least partially, in a piscivorous lifestyle, were able to consume large fish and may have occasionally fed on other prey such as pterosaurs and juvenile dinosaurs. PMID:26734729
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.
Sandia Higher Order Elements (SHOE) v 0.5 alpha
Energy Science and Technology Software Center (ESTSC)
2013-09-24
SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please notemoreÂ Â» that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likely exist.Â«Â less
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.
Computing intersections between non-compatible curves and finite elements
NASA Astrophysics Data System (ADS)
Durand, Raul; Farias, Márcio M.; Pedroso, Dorival M.
2015-09-01
This paper presents a method to find all intersections between curved lines such as structural line elements and finite element meshes with intentions to generate smaller, non-compatible, line cells (e.g. bar elements) between crossings. The intersection finding algorithm works for two and three-dimensional meshes constituted by linear, quadratic or higher order elements. Using the proposed algorithm, meshes can then be automatically prepared for finite element analyses with techniques for embedding elements within others or analyses that require lines within solids. The application of the method is demonstrated by a number of numerical examples illustrating its capabilities in handling complex geometries, relative speed and convenience.
NASA Astrophysics Data System (ADS)
Yang, Xingyi
Tetrahedral amorphous carbon (ta-C) is a diamond-like carbon (DLC) material comprised of a mixture of sp2 (˜40%) and sp3-bonded (˜60%) carbon domains. The physicochemical structure and electrochemical properties depend strongly on the sp2/sp3 bonding ratio as well as the incorporation of impurities, such as hydrogen or nitrogen. The ability to grow ta-C films at lower temperatures (25-100 °C) on a wider variety of substrates is a potential advantage of these materials as compared with diamond films. In this project, the basic structural and electrochemical properties of nitrogen-incorporated ta-C thin films will be discussed. The major goal of this work was to determine if the ta-C:N films exhibit electrochemical properties more closely aligned with those of boron-doped diamond (sp 3 carbon) or glassy carbon (amorphous sp2 carbon). Much like diamond, ta-C:N thin-film electrodes are characterized by a low background voltammetric current, a wide working potential window, relatively rapid electron-transfer kinetics for aqueous redox systems, such as Fe(CN) 6-3/-4 and Ru(NH3)6+3/+2 , and weak adsorption of polar molecules from solution. For example, negligible adsorption of methylene blue was found on the ta-C:N films in contrast to glassy carbon; a surface on which this molecule strongly adsorbs. The film microstructure was studied with x-ray photoelectron microscopy (XPS), visible Raman spectroscopy and electron-energy loss spectroscopy (EELS); all of which revealed the sp2-bonded carbon content increased with increasing nitrogen. The electrical properties of ta-C:N films were studied by four-point probe resistance measurement and conductive-probe AFM (CP-AFM). The incorporation of nitrogen into ta-C films increased the electrical conductivity primarily by increasing the sp2-bonded carbon content. CP-AFM showed the distribution of the conductive sp2-carbon on the film surface was not uniform. These films have potential to be used in field emission area. The heterogeneous electrochemical properties were studied with scanning electron microscopy (SECM). If was found that more electrically conducting sites were isolated by less conducting or even insulating sites. Consistent with the heterogeneous electrical properties, heterogeneous electrochemical activity was observed for different aqueous redox analytes. Flow injection analysis with electrochemical detection (EC-FIA) of dopamine and norepinephrine were carried out using the N-ta:C films. Detection figures of merit for these biomolecules were determined. These biomolecules can be detected stably and reproducible in PBS buffer at constant potential by N-ta:C film. The N-ta:C films provide good limits of detection for these biomolecules. N-ta:C films show great promise in the electroanalytical field. Compared with the diamond, the growth condition is much milder. These N-ta:C films are commercially available and could be produced in large scale. All of these virtues make N-ta:C films excellent choices for electroanalytical measurements.
Vibrational spectroscopy and analysis of pseudo-tetrahedral complexes with metal imido bonds.
Mehn, Mark P; Brown, Steven D; Jenkins, David M; Peters, Jonas C; Que, Lawrence
2006-09-01
A number of assignments have been previously posited for the metal-nitrogen stretch (nu(M-NR)), the N-R stretch (nu(MN-R)), and possible ligand deformation modes associated with terminally bound imides. Here we examine mononuclear iron(III) and cobalt(III) imido complexes of the monoanionic tridentate ligand [PhBP3] ([PhBP3] = [PhB(CH2PPh2)3]-) to clarify the vibrational features for these trivalent metal imides. We report the structures of [PhBP3]FeNtBu and [PhBP3]CoNtBu. Pseudo-tetrahedral metal imides of these types exhibit short bond lengths (ca. 1.65 A) and nearly linear angles about the M-N-C linkages, indicative of multiple bond character. Furthermore, these compounds give rise to intense, low-energy visible absorptions. Both the position and the intensity of the optical bands in the [PhBP3]MNR complexes depend on whether the substituent is an alkyl or aryl group. Excitation into the low-energy bands of [PhBP3]FeNtBu gives rise to two Raman features at 1104 and 1233 cm(-1), both of which are sensitive to 15N and 2H labeling. The isotope labeling suggests the 1104 cm(-1) mode has the greatest Fe-N stretching character, while the 1233 cm(-1) mode is affected to a lesser extent by (15)N substitution. The spectra of the deuterium-labeled imides further support this assertion. The data demonstrate that the observed peaks are not simple diatomic stretching modes but are extensively coupled to the vibrations of the ancillary organic group. Therefore, describing these complexes as simple diatomic or even triatomic oscillators is an oversimplification. Analogous studies of the corresponding cobalt(III) complex lead to a similar set of isotopically sensitive resonances at 1103 and 1238 cm(-1), corroborating the assignments made in the iron imides. Very minimal changes in the vibrational frequencies are observed upon replacement of cobalt(III) for iron(III), suggesting similar force constants for the two compounds. This is consistent with the previously proposed electronic structure model in which the added electron resides in a relatively nonbonding orbital. Replacement of the tBu group with a phenyl ring leads to a significantly more complicated resonance Raman spectrum, presumably due to coupling with the vibrations of the phenyl ring. Polarization studies demonstrate that the observed modes have A(1) symmetry. In this case, a clearer resonance enhancement of the signals is observed, supporting a charge transfer designation for the electronic transitions. A series of isotope-labeling experiments has been carried out, and the modes with the greatest metal-nitrogen stretching character have been assigned to peaks at approximately 960 and approximately 1300 cm(-1) in both the iron and cobalt [PhBP3]MNPh complexes. These results are consistent with a multiple M-N bond for these metal imides. PMID:16933946
Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu
2014-01-01
The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281
Daskaloyannis, C. Tanoudis, Y.
2008-05-15
The two-dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar to the classical ones multiplied by a quantum coefficient -{h_bar}{sup 2} plus a quantum deformation of order {h_bar}{sup 4} and {h_bar}{sup 6}. The systems inside the classes are transformed using Staeckel transforms in the quantum case as in the classical case. The general form of the Staeckel transform between superintegrable systems is discussed.
Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu
2014-01-01
The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281
Shi, Muling; Zheng, Jing; Liu, Changhui; Tan, Guixiang; Qing, Zhihe; Yang, Sheng; Yang, Jinfeng; Tan, Yongjun; Yang, Ronghua
2016-03-15
As an important biomarker and therapeutic target, telomerase has attracted extensive attention concerning its detection and monitoring. Recently, enzyme-assisted amplification approaches have provided useful platforms for the telomerase activity detection, however, further improvement in sensitivity is still hindered by the single-step signal amplification. Herein, we develop a quadratic signal amplification strategy for ultrasensitive surface-enhanced Raman scattering (SERS) detection of telomerase activity. The central idea of our design is using telomerase-induced silver nanoparticles (AgNPs) assembly and silver ions (Ag(+))-mediated cascade amplification. In our approach, each telomerase-aided DNA sequence extension could trigger the formation of a long double-stranded DNA (dsDNA), making numerous AgNPs assembling along with this long strand through specific Ag-S bond, to form a primary ampliï¬cation element. For secondary ampliï¬cation, each conjugated AgNP was dissolved into Ag(+), which can effectively induce the 4-aminobenzenethiol (4-ABT) modified gold nanoparticles (AuNPs@4-ABT) to undergo aggregation to form numerous "hot-spots". Through quadratic ampliï¬cations, a limit of detection down to single HeLa cell was achieved. More importantly, this method demonstrated good performance when applied to tissues from colon cancer patients, which exhibits great potential in the practical application of telomerase-based cancer diagnosis in early stages. To demonstrate the potential in screening the telomerase inhibitors and telomerase-targeted drugs, the proposed design is successfully employed to measure the inhibition of telomerase activity by 3'-azido-3'-deoxythymidine. PMID:26496221
Karamanis, Panaghiotis; Otero, Nicolás; Pouchan, Claude
2014-05-21
In an attempt to diversify the options in designing graphene-based systems bearing large second order nonlinear optical (NLO) responses of octupolar and/or dipolar character, the subject of the quadratic NLO properties of hybrid boron nitride (BN) graphene flakes is opened up. State of the art ab initio and density functional theory methods applied on a toolbox of book-text octupolar and arbitrary dipolar planar hybrid h-BN-graphene nanosized systems reveal that by confining finite h-BN sections in the internal network of graphene, the capacity of the ?-electron network of graphene species in delivering giant second order NLO responses could be fully exploited. Configuration interaction (CIS) and time-dependent density functional (TD) computations, within the sum-overstate (SOS) perturbational approach, expose that the prevailing (hyper)polarization mechanism, lying under the sizable computed octupolar hyperpolarizabilities, is fueled by alternating positive and negative atomic charges located in the internal part of the hybrid flakes, and more precisely at the BN/graphene intersections. This type of charge transfer mechanism distinguishes, in fact, the elemental graphene dipoles/octupoles we report here from other conventional NLO dipoles or octupoles. More interestingly, it is shown that by controlling the shape, size, and covering area of the h-BN domain (or domains), one can effectively regulate "à volonté" both the magnitudes and types of the second order NLO responses switching from dipolar to octupolar and vice versa. Especially in the context of the latter class of NLO properties, this communication brings into surface novel, graphene-based, octupolar planar or quasiplanar motifs. The take home message of this communication is summarized as follows: When the right BN segment is incorporated in the right section of the right graphene flake, systems of giant quadratic NLO octupolar and/or dipolar responses may emerge. PMID:24779531
NASA Astrophysics Data System (ADS)
Peng, Haowei; Ndione, Paul F.; Ginley, David S.; Zakutayev, Andriy; Lany, Stephan
2015-04-01
Transition metal oxides play important roles as contact and electrode materials, but their use as active layers in solar energy conversion requires achieving semiconducting properties akin to those of conventional semiconductors like Si or GaAs. In particular, efficient bipolar carrier transport is a challenge in these materials. Based on the prediction that a tetrahedral polymorph of MnO should have such desirable semiconducting properties, and the possibility to overcome thermodynamic solubility limits by nonequilibrium thin-film growth, we exploit both structure-property and composition-structure relationships to design and realize novel wurtzite-structure Mn1 -xZnxO alloys. At Zn compositions above x ?0.3 , thin films of these alloys assume the tetrahedral wurtzite structure instead of the octahedral rocksalt structure of MnO, thereby enabling semiconductor properties that are unique among transition metal oxides, i.e., a band gap within the visible spectrum, a band-transport mechanism for both electron and hole carriers, electron doping, and a band lineup suitable for solar hydrogen generation. A proof of principle is provided by initial photo-electrocatalytic device measurements, corroborating, in particular, the predicted favorable hole-transport properties of these alloys.
Peng, Haowei; Ndione, Paul F.; Ginley, David S.; Zakutayev, Andriy; Lany, Stephan
2015-05-18
Transition metal oxides play important roles as contact and electrode materials, but their use as active layers in solar energy conversion requires achieving semiconducting properties akin to those of conventional semiconductors like Si or GaAs. In particular, efficient bipolar carrier transport is a challenge in these materials. Based on the prediction that a tetrahedral polymorph of MnO should have such desirable semiconducting properties, and the possibility to overcome thermodynamic solubility limits by nonequilibrium thin-film growth, we exploit both structure-property and composition-structure relationships to design and realize novel wurtzite-structure Mnâ‚â‚‹xZnxO alloys. At Zn compositions above x â‰ˆ 0.3, thin films ofmoreÂ Â» these alloys assume the tetrahedral wurtzite structure instead of the octahedral rocksalt structure of MnO, thereby enabling semiconductor properties that are unique among transition metal oxides, i.e., a band gap within the visible spectrum, a band-transport mechanism for both electron and hole carriers, electron doping, and a band lineup suitable for solar hydrogen generation. A proof of principle is provided by initial photo-electrocatalytic device measurements, corroborating, in particular, the predicted favorable hole-transport properties of these alloys.Â«Â less
NASA Astrophysics Data System (ADS)
Lian, Y.-Y.; Hsu, K.-H.; Shao, Y.-L.; Lee, Y.-M.; Jeng, Y.-W.; Wu, J.-S.
2006-12-01
The development of a parallel three-dimensional (3-D) adaptive mesh refinement (PAMR) scheme for an unstructured tetrahedral mesh using dynamic domain decomposition on a memory-distributed machine is presented in detail. A memory-saving cell-based data structure is designed such that the resulting mesh information can be readily utilized in both node- or cell-based numerical methods. The general procedures include isotropic refinement from one parent cell into eight child cells and then followed by anisotropic refinement which effectively removes hanging nodes. A simple but effective mesh-quality control mechanism is employed to preserve the mesh quality. The resulting parallel performance of this PAMR is found to scale approximately as N for N?32. Two test cases, including a particle method (parallel DSMC solver for rarefied gas dynamics) and an equation-based method (parallel Poisson-Boltzmann equation solver for electrostatic field), are used to demonstrate the generality of the PAMR module. It is argued that this PAMR scheme can be applied in any numerical method if the unstructured tetrahedral mesh is adopted.
Scheiner, S; Kleier, D A; Lipscomb, W N
1975-01-01
The charge relay ststem and its role in the acylation of serine proteinases is studied using the partial retention of diatomic differential overlap (PRDDO) technique to perform approximate ab initio molecular orbital calculations on a model of the enzyme-substrate complex. The aspartate in the charge relay system is seen to act as the ultimate proton acceptor during the charging of the serine nucleophile. A projection of the potential energy surface is obtained in a subspace corresponding to this charge transfer and to the coupled motions of active site residues and the substrate. These results together with extended basis set results for cruder models suggest that a concerted transfer of protons from Ser-195 to His-57 and from His-57 to Asp-102 occurs with an energy barrier of 20-25 kcal/mole (84-105 kJ/mole). The subsequent nucleophilic attack on the scissile peptide linkage by the charged serine is then seen to proceed energetically downhill to the tetrahedral intermediate. The formation of the tetrahedral intermediate from the Michaelis complex is calculated to be nearly thermoneutral. PMID:1058476
Do, Hackwon; Lee, Chang Woo; Lee, Sung Gu; Kang, Hara; Park, Chul Min; Kim, Hak Jun; Park, Hyun; Park, HaJeung; Lee, Jun Hyuck
2016-02-01
The gene product of dddC (Uniprot code G5CZI2), from the Gram-negative marine bacterium Oceanimonas doudoroffii, is a methylmalonate-semialdehyde dehydrogenase (OdoMMSDH) enzyme. MMSDH is a member of the aldehyde dehydrogenase superfamily, and it catalyzes the NADdependent decarboxylation of methylmalonate semialdehyde to propionyl-CoA. We determined the crystal structure of OdoMMSDH at 2.9 Ã… resolution. Among the twelve molecules in the asymmetric unit, six subunits complexed with NAD, which was carried along the protein purification steps. OdoMMSDH exists as a stable homodimer in solution; each subunit consists of three distinct domains: an NAD-binding domain, a catalytic domain, and an oligomerization domain. Computational modeling studies of the OdoMMSDH structure revealed key residues important for substrate recognition and tetrahedral intermediate stabilization. Two basic residues (Arg103 and Arg279) and six hydrophobic residues (Phe150, Met153, Val154, Trp157, Met281, and Phe449) were found to be important for tetrahedral intermediate binding. Modeling data also suggested that the backbone amide of Cys280 and the side chain amine of Asn149 function as the oxyanion hole during the enzymatic reaction. Our results provide useful insights into the substrate recognition site residues and catalytic mechanism of OdoMMSDH. PMID:26832667
Resurrecting quadratic inflation in no-scale supergravity in light of BICEP2
Ellis, John; García, Marcos A.G.; Olive, Keith A.; Nanopoulos, Dimitri V. E-mail: garciagarcia@physics.umn.edu E-mail: olive@physics.umn.edu
2014-05-01
The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential ? ?{sup n} : n ? 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R+R{sup 2} model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N = 1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focusing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.
A new color space to discriminate skin regions using fuzzy quadratic programming
NASA Astrophysics Data System (ADS)
Mazaherie, Amir; Mirghasemi, Saeed; Lotfizad, Mojtaba
2011-10-01
This paper presents a new color space through linear conversion in which the cost function has fuzzy quadratic (FQ) characteristic. Training samples are used to create an efficient color space with respect to desired application. Quadratic Programming (QP) technique is engaged to extract the conversion matrix. According to fuzzy feature of the cost function, several matrices are introduced to generate the new color space for skin segmentation. The proposed method involves two steps. First a second order cost function established based on separating target pixels from non-target ones while followed by some constraints. In the second stage, a quadratic optimization is used to solve problem efficiently. Finally, the results of fuzzy approach are compared to non-fuzzy methods.
Shafii, Mohammad Ali Meidianti, Rahma Wildian, Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto
2014-09-30
Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.
NASA Astrophysics Data System (ADS)
Popescu, Mihai; Dumitrache, Alexandru
2011-05-01
This study refers to minimization of quadratic functionals in infinite time. The coefficients of the quadratic form are quadratic matrix, function of the state variable. Dynamic constraints are represented by bilinear differential systems of the form x?=A(x)x+B(x)u,x(0)=x0. One selects an adequate factorization of A( x) such that the analyzed system should be controllable. Employing the Hamilton-Jacobi equation it results the matrix algebraic equation of Riccati associated to the optimum problem. The necessary extremum conditions determine the adjoint variables ? and the control variables u as functions of state variable, as well as the adjoint system corresponding to those functions. Thus one obtains a matrix differential equation where the solution representing the positive defined symmetric matrix P( x), verifies the Riccati algebraic equation. The stability analysis for the autonomous systems solution resulting for the determined feedback control is performed using the Liapunov function method. Finally we present certain significant cases.
Gupta, Arvind K; Yadav, Ashok; Srivastava, Anant Kumar; Ramya, Kormathmadam Raghupathy; Paithankar, Harshad; Nandi, Shyamapada; Chugh, Jeetender; Boomishankar, Ramamoorthy
2015-04-01
A charge-neutral tetrahedral [(Pd3X)4L6] cage assembly built from a trinuclear polyhedral building unit (PBU), [Pd3X](3+), cis-blocked with an imido P(V) ligand, [(N(i)Pr)3PO](3-) (X(3-)), and oxalate dianions (L(2-)) is reported. Use of benzoate or ferrocene dicarboxylate anions, which do not offer wide-angle chelation as that of oxalate dianions, leads to smaller prismatic clusters instead of polyhedral cage assemblies. The porosity of the tetrahedral cage assembly was determined by gas adsorption studies, which show a higher uptake capacity for CO2 over N2 and H2. The tetrahedral cage was shown to encapsulate a wide range of neutral guest solvents from polar to nonpolar such as dimethyl sulfoxide, benzene, dichloromethane, chloroform, carbon tetrachloride, and cyclopentane as observed by mass spectral and single-crystal X-ray diffraction studies. The (1)H two-dimensional diffusion ordered spectroscopy NMR analysis shows that the host and guest molecules exhibit similar diffusion coefficients in all the studied host-guest systems. Further, the tetrahedral cage shows selective binding of benzene, CCl4, and cyclopentane among other solvents from their categories as evidenced from mass spectral analysis. A preliminary density functional theory analysis gave a highest binding energy for benzene among the other solvents that were structurally shown to be encapsulated at the intrinsic cavity of the tetrahedral cage. PMID:25781912
Origin of the giant quadratic electro-optic effect in KTa1-xNbxO3 single crystals
NASA Astrophysics Data System (ADS)
Yu, Xiaoyan; Wang, Haoyu; Rong, Xianwei
2015-08-01
The quadratic electro-optic (EO) effect of KTa1-xNbxO3 single crystals were investigated in this paper. The quadratic EO coefficient (R11-R12) could reach as high as 1.07 Ã— 10-14 m2/V2, which means that the induced refractive index change under an 500 V/mm electric field is 200 times bigger than that of LiNbO3. A Sellmeier dispersion model of the quadratic EO effect was proposed to analyze the origin of the giant quadratic EO effect in KTa1-xNbxO3 single crystals.
Hendrickx, Christophe; Araújo, Ricardo; Mateus, Octávio
2015-01-01
The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber-invaded by the quadrate diverticulum of the mandibular arch pneumatic system-was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455
AraÃºjo, Ricardo; Mateus, OctÃ¡vio
2015-01-01
The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamberâ€”invaded by the quadrate diverticulum of the mandibular arch pneumatic systemâ€”was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455
NASA Astrophysics Data System (ADS)
Swaidan, Waleeda; Hussin, Amran
2015-10-01
Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.
NASA Technical Reports Server (NTRS)
Fleming, P.
1983-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.
Generation of Knot Net for Calculation of Quadratic Triangular B-spline Surface of Human Head
NASA Astrophysics Data System (ADS)
Mihalík, Ján
2011-09-01
This paper deals with calculation of the quadratic triangular B-spline surface of the human head for the purpose of its modeling in the standard videocodec MPEG-4 SNHC. In connection with this we propose an algorithm of generation of the knot net and present the results of its application for triangulation of the 3D polygonal model Candide. Then for the model and generated knot net as well as an established distribution of control points we show the results of the calculated quadratic triangular B-spline surface of the human head including its textured version for the texture of the selected avatar.
Quasi-Deterministic Properties of Random Gaussian Fields Constrained by a Large Quadratic Form
NASA Astrophysics Data System (ADS)
Mounaix, Philippe
2015-08-01
Completing the study initiated by Mounaix and Collet (J Stat Phys 143:139-147, 2011), we investigate the realizations of a Gaussian random field in the limit where a given (general) quadratic form of the field is large. Concentration in and in probability is proved under mild conditions and the resulting quasi-deterministic behavior of the field is given. Applications to a large local quadratic form are considered in two specific cases. In particular, the quasi-deterministic structure of a Gaussian random flow with a large local helicity at some given point is determined explicitly.
Parameter estimation of optical fringes with quadratic phase using the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Lu, Ming-Feng; Zhang, Feng; Tao, Ran; Ni, Guo-Qiang; Bai, Ting-Zhu; Yang, Wen-Ming
2015-11-01
Optical fringes with a quadratic phase are often encountered in optical metrology. Parameter estimation of such fringes plays an important role in interferometric measurements. A novel method is proposed for accurate and direct parameter estimation using the fractional Fourier transform (FRFT), even in the presence of noise and obstacles. We take Newton's rings fringe patterns and electronic speckle pattern interferometry (ESPI) interferograms as classic examples of optical fringes that have a quadratic phase and present simulation and experimental results demonstrating the performance of the proposed method.
Sequential design of linear quadratic state regulators via the optimal root-locus techniques
NASA Technical Reports Server (NTRS)
Shieh, L. S.; Dib, H. M.; Yates, R. E.
1988-01-01
The use of well-known root-locus techniques for sequentially finding the weighting matrices and the linear quadratic state regulators of multivariable control systems in the frequency domain is considered. This sequential design method permits the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system; it also allows some optimal closed-loop poles to be placed in a specific region of the complex plane. In addition, it provides a design procedure for determining the weighting matrices and linear quadratic state regulators for the optimal control of multivariable systems in the frequency domain.
User's guide for SOL/QPSOL: a Fortran package for quadratic programming
Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.
1983-07-01
This report forms the user's guide for Version 3.1 of SOL/QPSOL, a set of Fortran subroutines designed to locate the minimum value of an arbitrary quadratic function subject to linear constraints and simple upper and lower bounds. If the quadratic function is convex, a global minimum is found; otherwise, a local minimum is found. The method used is most efficient when many constraints or bounds are active at the solution. QPSOL treats the Hessian and general constraints as dense matrices, and hence is not intended for large sparse problems. This document replaces the previous user's guide of June 1982.
OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE
Xie, Xianchao; Kou, S. C.; Brown, Lawrence
2015-01-01
This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results.
A variable-metric algorithm employing linear and quadratic penalties. [for optimal control
NASA Technical Reports Server (NTRS)
Kelley, H. J.; Lefton, L.; Johnson, I. L., Jr.
1975-01-01
A variable-metric algorithm is described that uses both linear and quadratic penalty terms for handling nonlinear constraints. Quadratic penalty coefficients are adjusted in a process which maintains a positive-definite matrix of second partial derivatives of the function without generating the large positive eigenvalues which cause zigzagging and slow convergence. The schemes suggested use inferred second-order properties not only in terms of the variable metric of the Davidson-Fletcher-Powell algorithm (or its relatives) but by estimating of second directional derivatives by fitting cubics to various functions along search directions.
Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.
McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T
2013-12-13
Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model. PMID:24483652
Linear Quadratic Gaussian-Based Closed-Loop Control of Type 1 Diabetes
Patek, Stephen D.; Breton, Marc D.; Chen, Yuanda; Solomon, Chad; Kovatchev, Boris
2007-01-01
Background We investigated the applicability of linear quadratic Gaussian (LQG) methodology to the subcutaneous blood glucose regulation problem. We designed an LQG-based feedback control algorithm using linearization of a previously published metabolic model of type 1 diabetes. A key feature of the controller is a Kalman filter used to estimate metabolic states of the patient based on continuous glucose monitoring. Insulin infusion is computed from linear quadratic regulator feedback gains applied to these estimates, generally seeking to minimize squared deviations from a target glucose concentration and basal insulin rate. We evaluated in silico subject-specific LQG control and compared it to preexisting proportional-integral-derivative control. PMID:19756210
A PC program for unbiased and predictive linear and quadratic discriminant analysis.
Grouven, U; Bergel, F; Schultz, B; Schultz, A
1995-07-01
Discriminant analysis plays an important role in biological and medical research. The most popular methods of discrimination in practical applications are parametric methods like linear and quadratic discriminant analysis. However, there exist modifications of these approaches, namely unbiased and predictive discriminant analysis, which lead to reduced error rates in certain situations. In this paper a menu-driven, user-friendly PC program written in Borland Pascal 7.0 is introduced which performs unbiased and predictive linear and quadratic discriminant analysis. PMID:7497704
Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Loehner, Rainald; Morgan, Ken; Peraire, Jaime; Vahdati, Mehdi
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.
Finite element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Lohner, Rainald; Morgan, Ken; Peraire, Jaime; Vahdati, Mehdi
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.
A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models
ERIC Educational Resources Information Center
Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen
2012-01-01
Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…
Optical synthetic-aperture radar processor archietecture with quadratic phase-error correction
Dickey, F.M.; Mason, J.J. )
1990-10-15
Uncompensated phase errors limit the image quality of synthetic-aperture radar. We present an acousto-optic synthetic-aperture radar processor architecture capable of measuring the quadratic phase error. This architecture allows for the error signal to be fed back to the processor to generate the corrected image.
Graphical Representation of Complex Solutions of the Quadratic Equation in the "xy" Plane
ERIC Educational Resources Information Center
McDonald, Todd
2006-01-01
This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.
NASA Technical Reports Server (NTRS)
Wong, P.-K.; Stein, G.; Athans, M.
1979-01-01
Strong sufficient conditions are derived for the robustness of optimal linear-quadratic (LQ) regulators to large parameter perturbations. In particular, it is shown that under certain conditions LQ designs remain stable in the presence of actuator channel failures. The general results can be specialized to provide insight into the gain margin, gain reduction, and phase margin properties of optimal LQ regulators.
A Method for Selecting between Linear and Quadratic Classification Models in Discriminant Analysis.
ERIC Educational Resources Information Center
Meshbane, Alice; Morris, John D.
1995-01-01
A method for comparing the cross-validated classification accuracies of linear and quadratic classification rules is presented under varying data conditions for the "k"-group classification problem. Separate-group and total-group proportions of correct classifications can be compared for the two rules, as is illustrated. (Author/SLD)
Linear and Quadratic Rules: What Are They and When Are They Used?
ERIC Educational Resources Information Center
Altman, Daniel R.
Discriminant analysis is a multivariate method of analysis with two purposes: (1) to describe differences among groups; or (2) to classify participants into groups. Either linear or quadratic rules can be used in both descriptive discriminant analysis (DDA) and predictive discriminant analysis (PDA). In both DDA and PDA the researcher wants to useâ€¦
ERIC Educational Resources Information Center
Vial, Alexandre
2007-01-01
We investigate the problem of the horizontal distance travelled by a mobile experiencing a quadratic drag force. We show that by introducing a normalized distance, the problem can be greatly simplified. In order to parametrize this distance, we use the Pearson VII function, and we find that the optimal launch angle as a function of the initial…
DIVERSITY OF EPIDEMIC POPULATIONS OF GIBBERELLA ZEAE FROM SMALL QUADRATS IN KANSAS AND NORTH DAKOTA
Technology Transfer Automated Retrieval System (TEKTRAN)
Gibberella zeae (anamorph Fusarium graminearum) causes Fusarium head blight (FHB) of wheat and barley. We isolated G. zeae from the top, middle, and bottom positions of wheat heads from 0.25 m² quadrats during severe FHB epidemics in Kansas in 1993 (KS) and North Dakota in 1994 (ND). We used three...
Solution to Projectile Motion with Quadratic Drag and Graphing the Trajectory in Spreadsheets
ERIC Educational Resources Information Center
Benacka, Jan
2010-01-01
This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and…
Failures and Inabilities of High School Students about Quadratic Equations and Functions
ERIC Educational Resources Information Center
Memnun, Dilek Sezgin; Aydin, Bünyamin; Dinç, Emre; Çoban, Merve; Sevindik, Fatma
2015-01-01
In this research study, it was aimed to examine failures and inabilities of eleventh grade students about quadratic equations and functions. For this purpose, these students were asked ten open-ended questions. The analysis of the answers given by the students to these questions indicated that a significant part of these students had failures and…
Quantization of a particle with a force quadratic in the velocity
Sa Borges, J.; Epele, L.N.; Fanchiotti, H.; Garcia Canal, C.A.; Sima-tildeo, F.R.A.
1988-09-15
The quantization of a system subject to a force quadratic in the velocity and position dependence is carried out in the phase-space path-integral framework. The resulting Hamiltonian coincides with that obtained by using the Weyl-ordering canonical prescription.
Granda, L.N.
2011-04-01
We study a scalar field with non-minimal kinetic coupling to itself and to the curvature. The slow rolling conditions allowing an inflationary background have been found. The quadratic and Higgs type potentials have been considered, and the corresponding values for the scalar fields at the end of inflation allows to recover the connection with particle physics.
Endicott, Julia S.; Joubert-Doriol, LoÃ¯c; Izmaylov, Artur F.
2014-07-21
We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.
Robust Ellipse Fitting via Half-Quadratic and Semidefinite Relaxation Optimization.
Liang, Junli; Wang, Yunlong; Zeng, Xianju
2015-11-01
Ellipse fitting is widely applied in the fields of computer vision and automatic manufacture. However, the introduced edge point errors (especially outliers) from image edge detection will cause severe performance degradation of the subsequent ellipse fitting procedure. To alleviate the influence of outliers, we develop a robust ellipse fitting method in this paper. The main contributions of this paper are as follows. First, to be robust against the outliers, we introduce the maximum correntropy criterion into the constrained least-square (CLS) ellipse fitting method, and apply the half-quadratic optimization algorithm to solve the nonlinear and nonconvex problem in an alternate manner. Second, to ensure that the obtained solution is related to an ellipse, we introduce a special quadratic equality constraint into the aforementioned CLS model, which results in the nonconvex quadratically constrained quadratic programming problem. Finally, we derive the semidefinite relaxation version of the aforementioned problem in terms of the trace operator and thus determine the ellipse parameters using semidefinite programming. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach. PMID:26219096
ERIC Educational Resources Information Center
Bandele, Samuel Oye; Adekunle, Adeyemi Suraju
2015-01-01
The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used forâ€¦
Solution to Projectile Motion with Quadratic Drag and Graphing the Trajectory in Spreadsheets
ERIC Educational Resources Information Center
Benacka, Jan
2010-01-01
This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles andâ€¦
ERIC Educational Resources Information Center
Han, Kyung T.; Rudner, Lawrence M.
2014-01-01
This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal informationâ€¦
The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; Um, Chung IN; George, T. F.
1994-01-01
The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.
Closed-loop structural stability for linear-quadratic optimal systems
NASA Technical Reports Server (NTRS)
Wong, P. K.; Athans, M.
1975-01-01
This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.
Lu, C.N.; Chen, S.S.; Ong, C.M. )
1988-08-01
This paper presents the formulation and solution method of an optimal power flow problem using sequential quadratic programming technique for an ac-dc power system with one or more multiterminal dc systems. The economic advantage of being able to coordinate the dc system power transfers is illustrated by numerical examples based on the modified IEEE 30 and 118 bus systems.
Structural and Thermal Properties of Elementary and Binary Tetrahedral Semiconductor Nanoparticles
NASA Astrophysics Data System (ADS)
Omar, M. S.
2016-01-01
We report an equation free from fitting parameters as a direct calculation of size-dependent mean bond length for group IV and compounds from the III-V and II-VI binary groups. Size-dependent melting temperature and thermal expansion are also investigated for some materials forming the groups mentioned above. The empirical relation, which is obtained from fitting experimental data of melting enthalpy, is used to recalculate their values as well as entropy. The nanosize dependence of lattice thermal expansion for elements forming group IV is analyzed according to the hard sphere model, while mean ionicity is used for groups III-V and II-VI.
Water Adsorption at the Tetrahedral Titania Surface Layer of SrTiO3(110)-(4 × 1)
2013-01-01
The interaction of water with oxide surfaces is of great interest for both fundamental science and applications. We present a combined theoretical (density functional theory (DFT)) and experimental (scanning tunneling microscopy (STM) and photoemission spectroscopy (PES)) study of water interaction with the two-dimensional titania overlayer that terminates the SrTiO3(110)-(4 × 1) surface and consists of TiO4 tetrahedra. STM and core-level and valence band PES show that H2O neither adsorbs nor dissociates on the stoichiometric surface at room temperature, whereas it does dissociate at oxygen vacancies. This is in agreement with DFT calculations, which show that the energy barriers for water dissociation on the stoichiometric and reduced surfaces are 1.7 and 0.9 eV, respectively. We propose that water weakly adsorbs on two-dimensional, tetrahedrally coordinated overlayers. PMID:24353755
Jiang, Shang-Da; Maganas, Dimitrios; Levesanos, Nikolaos; Ferentinos, Eleftherios; Haas, Sabrina; Thirunavukkuarasu, Komalavalli; Krzystek, J; Dressel, Martin; Bogani, Lapo; Neese, Frank; Kyritsis, Panayotis
2015-10-14
The high-spin (S = 1) tetrahedral Ni(II) complex [Ni{(i)Pr2P(Se)NP(Se)(i)Pr2}2] was investigated by magnetometry, spectroscopic, and quantum chemical methods. Angle-resolved magnetometry studies revealed the orientation of the magnetization principal axes. The very large zero-field splitting (zfs), D = 45.40(2) cm(-1), E = 1.91(2) cm(-1), of the complex was accurately determined by far-infrared magnetic spectroscopy, directly observing transitions between the spin sublevels of the triplet ground state. These are the largest zfs values ever determined--directly--for a high-spin Ni(II) complex. Ab initio calculations further probed the electronic structure of the system, elucidating the factors controlling the sign and magnitude of D. The latter is dominated by spin-orbit coupling contributions of the Ni ions, whereas the corresponding effects of the Se atoms are remarkably smaller. PMID:26352187
Jiang, Long; Ju, Ping; Meng, Xian-Rui; Kuang, Xiao-Jun; Lu, Tong-Bu
2012-01-01
Mechanically Interlocked molecules, such as catenanes and rotaxanes, are of great interest due to their fascinating structures and potential applications, while such molecules have been mainly restricted to comprising components of interlocked rings or polygons. The constructions of infinite polycatenanes and polyrotaxanes by discrete cages remain great challenge, and only two infinite polycatenanes fabricated by discrete cages have been reported so far, while the structures of polyrotaxanes and polypseudo-rotaxanes fabricated by discrete build units have not been documented to date. Herein we report the first example of a two-dimensional (2D) polypseudo-rotaxane fabricated by stool-like build units, the second example of a one-dimensional (1D) polycatenane, and the second example of a three-dimensional (3D) polycatenane, which were assemblied by discrete tetrahedral cages. The pores of dehydrated 3D polycatenane are dynamic, and display size-dependent adsorption/desorption behaviors of alcohols. PMID:22993693
Technology Transfer Automated Retrieval System (TEKTRAN)
This historical dataset consists of a series of permanent 1-m2 quadrats located on the sagebrush steppe in eastern Idaho, USA. The key aspect of the data is that during each growing season, all individual plants in each quadrat were identified and mapped. The combination of a long time-series with f...
NASA Astrophysics Data System (ADS)
Hansen, Mikkel Bo; Christiansen, Ove; Hättig, Christof
2009-10-01
Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H2O, CH2O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented.
NASA Astrophysics Data System (ADS)
Mehta, Jugal V.; Gajera, Sanjay B.; Patel, Mohan N.
2015-02-01
The mononuclear copper(II) complexes with P, O-donor ligand and different fluoroquinolones have been synthesized and characterized by elemental analysis, electronic spectra, TGA, EPR, FT-IR and LC-MS spectroscopy. An antimicrobial efficiency of the complexes has been tested against five different microorganisms in terms of minimum inhibitory concentration (MIC) and displays very good antimicrobial activity. The binding strength and binding mode of the complexes with Herring Sperm DNA (HS DNA) have been investigated by absorption titration and viscosity measurement studies. The studies suggest the classical intercalative mode of DNA binding. Gel electrophoresis assay determines the ability of the complexes to cleave the supercoiled form of pUC19 DNA. Synthesized complexes have been tested for their SOD mimic activity using nonenzymatic NBT/NADH/PMS system and found to have good antioxidant activity. All the complexes show good cytotoxic and in vitro antimalarial activities.
StreÄka, Jozef; Rojas, Onofre; Verkholyak, Taras; Lyra, Marcelo L
2014-02-01
The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model. PMID:25353458
NASA Astrophysics Data System (ADS)
StreÄka, Jozef; Rojas, Onofre; Verkholyak, Taras; Lyra, Marcelo L.
2014-02-01
The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model.
NASA Technical Reports Server (NTRS)
Jurenko, Robert J.; Bush, T. Jason; Ottander, John A.
2014-01-01
A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.
NASA Astrophysics Data System (ADS)
Parravicini, Valeriano; Morri, Carla; Ciribilli, Giada; Montefalcone, Monica; Albertelli, Giancarlo; Bianchi, Carlo Nike
2009-02-01
The performances of two commonly used non-destructive sampling procedures for rocky benthic assemblages (i.e. photography and visually assessed quadrats) were compared. A damaging human activity, date mussel ( Lithophaga lithophaga) harvesting (DMH), was chosen. Directly impacted sites were compared with reference conditions (controls). Both visual quadrats and photography were equally able to detect differences between impacted situations and controls. However, visual quadrats showed high variability among replicates and estimated higher species richness for controls, while photography did so for impacts. Pooling photos in a 'sum photo quadrat' showed that differences between the two methods are due to sampling unit size rather than sampling procedure itself. As a small sampling unit is unavoidable with photography, visual quadrats should be preferred in investigating shallow rocky reefs for their larger size; however, longer working time underwater with quadrats does not allow for numerous replicates. Pooling many photos to reach sampling sizes comparable with those of quadrats may be a valid alternative to reconcile image resolution and areal coverage.
The quadratically damped oscillator: A case study of a non-linear equation of motion
NASA Astrophysics Data System (ADS)
Smith, B. R.
2012-09-01
The equation of motion for a quadratically damped oscillator, where the damping is proportional to the square of the velocity, is a non-linear second-order differential equation. Non-linear equations of motion such as this are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions. Like all second-order ordinary differential equations, it has a corresponding first-order partial differential equation, whose independent solutions constitute the constants of the motion. These constants readily provide an approximate solution correct to first order in the damping constant. They also reveal that the quadratically damped oscillator is never critically damped or overdamped, and that to first order in the damping constant the oscillation frequency is identical to the natural frequency. The technique described has close ties to standard tools such as integral curves in phase space and phase portraits.
Moments and distribution of central $L$ L -values of quadratic twists of elliptic curves
NASA Astrophysics Data System (ADS)
Radziwi??, Maksym; Soundararajan, K.
2015-12-01
We show that if one can compute a little more than a particular moment for some family of L-functions, then one has upper bounds of the conjectured order of magnitude for all smaller (positive, real) moments and a one-sided central limit theorem holds. We illustrate our method for the family of quadratic twists of an elliptic curve, obtaining sharp upper bounds for all moments below the first. We also establish a one sided central limit theorem supporting a conjecture of Keating and Snaith. Our work leads to a conjecture on the distribution of the order of the Tate-Shafarevich group for rank zero quadratic twists of an elliptic curve, and establishes the upper bound part of this conjecture (assuming the Birch-Swinnerton-Dyer conjecture).
Quadratic Herman-Wallis factors in the fundamental bands of linear molecules
NASA Astrophysics Data System (ADS)
Watson, James K. G.
1987-10-01
General theoretical formulas are derived for the coefficients in the terms M˜12 and M˜13 of the effective molecular dipole moment operator, and applied to the parallel and perpendicular fundamentals of linear molecules. The Herman-Wallis factors for P- and R-branch lines are F PR = [1 + A 1m + A 2PRm 2] 2, m = ? J( J' + J? + 1)/2 and for Q-branch lines F Q = [1 + A 2QJ ( J + 1)] 2 The quadratic coefficients A2PR and A2Q depend on up to cubic potential derivatives and quadratic dipole derivatives. Calculated A2PR and A2Q values for the fundamentals of CO 2 do not agree well with recent measurements of Johns, and possible reasons for the discrepancies are discussed.
Reconstruction of quadratic curves in 3D using two or more perspective views: simulation studies
NASA Astrophysics Data System (ADS)
Kumar, Sanjeev; Sukavanam, N.; Balasubramanian, R.
2006-01-01
The shapes of many natural and man-made objects have planar and curvilinear surfaces. The images of such curves usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we describe a method of reconstruction of a quadratic curve in 3-D space as an intersection of two cones containing the respective projected curve images. The correspondence between this pair of projections of the curve is assumed to be established in this work. Using least-square curve fitting, the parameters of a curve in 2-D space are found. From this we are reconstructing the 3-D quadratic curve. Relevant mathematical formulations and analytical solutions for obtaining the equation of reconstructed curve are given. The result of the described reconstruction methodology are studied by simulation studies. This reconstruction methodology is applicable to LBW decision in cricket, path of the missile, Robotic Vision, path lanning etc.
Harnessing quadratic optical response of two-dimensional materials through active microcavities
NASA Astrophysics Data System (ADS)
Ciattoni, Alessandro; Rizza, Carlo
2014-09-01
We propose a method for efficiently harnessing the quadratic optical response of two-dimensional graphenelike materials by theoretically investigating second-harmonic generation from a current biased sheet placed within a planar active microcavity. We show that, by tuning the cavity to resonate at the second-harmonic frequency, a highly efficient frequency doubling process is achieved (several orders of magnitude more efficient than the free-standing sheet). The efficiency of the process is not due to phase matching, which is forbidden by the localization of the nonlinear quadratic response on the two-dimensional atomic layered material, but stems from the interplay between the two-dimensional planar geometry of the nonlinear medium and the field oscillation within the active cavity near its threshold. The suggested method can easily be extended to different wave interactions and nonlinearities, and therefore it can represent a basic tool for efficiently exploiting nonlinear optical properties of two-dimensional materials.
Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching
NASA Astrophysics Data System (ADS)
Janssen, Lukas; Herbut, Igor F.
2015-07-01
We construct and discuss the field theory for tensorial nematic order parameter coupled to gapless four-component fermions at the quadratic band touching point in three (spatial) dimensions. Within a properly formulated epsilon-expansion this theory is found to have a quantum critical point, which describes the (presumably continuous) transition from the semimetal into a (nematic) Mott insulator. The latter phase breaks the rotational, but not the time-reversal, symmetry and may be relevant to materials such as gray tin or mercury telluride at low temperatures. The critical point represents a simple quantum analog of the familiar classical isotropic-to-nematic transition in liquid crystals. The properties and the consequences of this quantum critical point are discussed. Its existence supports the scenario of the "fixed-point collision," according to which three-dimensional Fermi systems with quadratic band touching and long-range Coulomb interactions are unstable towards the gapped nematic ground state at low temperatures.
Multivariable design of improved linear quadratic regulation control for MIMO industrial processes.
Zhang, Ridong; Lu, Renquan; Jin, Qibing
2015-07-01
In this study, a multivariable linear quadratic control system using a new state space structure was developed for the chamber pressure in the industrial coke furnace. Such processes typically have complex and nonlinear dynamic behavior, which causes the performance of controllers using conventional design and tuning to be poor or to require significant effort in practice. The process model is first treated into a new state space form and the implementation of linear quadratic control is designed using this new model structure. Performance in terms of regulatory/servo, disturbance rejection and measurement noise problems were all compared with the recent model predictive control strategy. Results revealed that the control system showed more robustness and improved the closed-loop process performance under model/process mismatches. PMID:25896826
Magneto-optical conductivity of Weyl semimetals with quadratic term in momentum
NASA Astrophysics Data System (ADS)
Shao, J. M.; Yang, G. W.
2016-02-01
Weyl semimetal is a three-dimensional Dirac material whose low energy dispersion is linear in momentum. Adding a quadratic (SchrÃ¶dinger) term to the Weyl node breaks the original particle-hole symmetry and also breaks the mirror symmetry between the positive and negative Landau levels in present of magnetic field. This asymmetry splits the absorption line of the longitudinal magneto-optical conductivity into a two peaks structure. It also results in an oscillation pattern in the absorption part of the Hall conductivity. The two split peaks in ReÏƒxx (or the positive and negative oscillation in ImÏƒxy) just correspond to the absorptions of left-handed (Ïƒ-) and right-handed (Ïƒ+) polarization light, respectively. The split in ReÏƒxx and the displacement between the absorption of Ïƒ+ and Ïƒ- are decided by the magnitude of the quadratic term and the magnetic field.
The algebraic decoding of the (41, 21, 9) quadratic residue code
NASA Technical Reports Server (NTRS)
Reed, Irving S.; Truong, T. K.; Chen, Xuemin; Yin, Xiaowei
1992-01-01
A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.
Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory
NASA Technical Reports Server (NTRS)
Koppang, Paul; Leland, Robert
1996-01-01
Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.
NASA Astrophysics Data System (ADS)
Duarte-Mermoud, Manuel A.; Aguila-Camacho, Norelys; Gallegos, Javier A.; Castro-Linares, Rafael
2015-05-01
This paper presents two new lemmas related to the Caputo fractional derivatives, when Î± âˆˆ(0, 1 ] , for the case of general quadratic forms and for the case where the trace of the product of a rectangular matrix and its transpose appear. Those two lemmas allow using general quadratic Lyapunov functions and the trace of a matrix inside a Lyapunov function respectively, in order to apply the fractional-order extension of Lyapunov direct method, to analyze the stability of fractional order systems (FOS). Besides, the paper presents a theorem for proving uniform stability in the sense of Lyapunov for fractional order systems. The theorem can be seen as a complement of other methods already available in the literature. The two lemmas and the theorem are applied to the stability analysis of two Fractional Order Model Reference Adaptive Control (FOMRAC) schemes, in order to prove the usefulness of the results.
Remark on the subtractive renormalization of the quadratically divergent scalar mass
Fujikawa, Kazuo
2011-05-15
The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We reexamine some technical aspects of the subtractive renormalization, in particular, the mass-independent renormalization of massive {lambda}{phi}{sup 4} theory with higher derivative regularization. We then discuss an unconventional scheme to introduce the notion of renormalization point {mu} to the subtractive renormalization in a theory defined by a large fixed cutoff M. The resulting renormalization group equation generally becomes inhomogeneous, but it is transformed to be homogeneous. The renormalized scalar mass consists of two components in this scheme, one with the ordinary anomalous dimension and the other which is proportional to the renormalization scale {mu}. This scheme interpolates between the theory defined by dimensional regularization and the theory with unsubtracted quadratic divergences.
KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry
Hollenbach, D.F.; Petrie, L.M.; Landers, N.F.
1993-07-01
This report discusses KENO-VI which is a new version of the KENO monte Carlo Criticality Safety developed at Oak Ridge National Laboratory. The purpose of KENO-VI is to provide a criticality safety code similar to KENO-V.a that possesses a more general and flexible geometry package. KENO-VI constructs and processes geometry data as sets of quadratic equations. A lengthy set of simple, easy-to-use geometric functions, similar to those provided in KENO-V.a., and the ability to build more complex geometric shapes represented by sets of quadratic equations are the heart of the geometry package in KENO-VI. The code`s flexibility is increased by allowing intersecting geometry regions, hexagonal as well as cuboidal arrays, and the ability to specify an array boundary that intersects the array.
A robust aCGH data recovery framework based on half quadratic minimization.
Mohammadi, Majid; Abed Hodtani, Ghosheh
2016-03-01
This paper presents a general half quadratic framework for simultaneous analysis of the whole array comparative genomic hybridization (aCGH) profiles in a data set. The proposed framework accommodates different M-estimation loss functions and two underlying assumptions for aCGH profiles of a data set: sparsity and low rank. Using M-estimation loss functions, this framework is more robust to various types of noise and outliers. The solution of the proposed framework is given by half quadratic (HQ) minimization. To hasten this procedure, accelerated proximal gradient (APG) is utilized. Experimental results support the robustness of the proposed framework in comparison to the state-of-the-art algorithms. PMID:26803290
The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter
NASA Technical Reports Server (NTRS)
Townsend, Barbara K.
1986-01-01
A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.
Dupuis, JÃ©rÃ´me A; Joachim, Jean
2006-09-01
We consider the problem of estimating the number of species of an animal community. It is assumed that it is possible to draw up a list of species liable to be present in this community. Data are collected from quadrat sampling. Models considered in this article separate the assumptions related to the experimental protocol and those related to the spatial distribution of species in the quadrats. Our parameterization enables us to incorporate prior information on the presence, detectability, and spatial density of species. Moreover, we elaborate procedures to build the prior distributions on these parameters from information furnished by external data. A simulation study is carried out to examine the influence of different priors on the performances of our estimator. We illustrate our approach by estimating the number of nesting bird species in a forest. PMID:16984311
Learning control for minimizing a quadratic cost during repetitions of a task
NASA Technical Reports Server (NTRS)
Longman, Richard W.; Chang, Chi-Kuang
1990-01-01
In many applications, control systems are asked to perform the same task repeatedly. Learning control laws have been developed over the last few years that allow the controller to improve its performance each repetition, and to converge to zero error in tracking a desired trajectory. This paper generates a new type of learning control law that learns to minimize a quadratic cost function for tracking. Besides being of interest in its own right, this objective alleviates the need to specify a desired trajectory that can actually be performed by the system. The approach used here is to adapt appropriate methods from numerical optimization theory in order to produce learning control algorithms that adjust the system command from repetition to repetition in order to converge to the quadratic cost optimal trajectory.
Layden, B.; Cairns, Iver H.; Robinson, P. A.; Percival, D. J.
2012-07-15
The quadratic longitudinal response function describes the second-order nonlinear response of a plasma to electrostatic wave fields. An explicit expression for this function in the weak-turbulence regime requires the evaluation of velocity-space integrals involving the velocity distribution function and various resonant denominators. Previous calculations of the quadratic longitudinal response function were performed by approximating the resonant denominators to facilitate the integration. Here, we evaluate these integrals exactly for a non-relativistic collisionless unmagnetized isotropic Maxwellian plasma in terms of generalized plasma dispersion functions, and correct certain aspects of expressions previously derived for these functions. We show that in the appropriate limits the exact expression reduces to the approximate form used for interactions between two fast waves and one slow wave, such as the electrostatic decay of Langmuir waves into Langmuir waves and ion sound waves, and the scattering of Langmuir waves off thermal ions.
Spontaneous quantum Hall effect via a thermally induced quadratic Fermi point.
Chern, Gia-Wei; Batista, C D
2012-10-12
Gapless electronic systems containing topologically nontrivial Fermi points are sources of various topological insulators. Whereas, most of these special band-crossing points are built in the electronic structure of the noninteracting lattice models, we show that a quadratic Fermi point characterized by a nonzero winding number emerges with a collinear triple-Q spin-density-wave state that arises from a perfectly nested but topologically trivial Fermi surface. We obtain a universal low-energy Hamiltonian for the quadratic Fermi point and show that such collinear orderings are unstable against the onset of scalar spin chirality that opens a gap and induces a spontaneous quantum Hall insulator as the temperature tends to zero. PMID:23102349
Photonic EPR State from Quadratic Waveguide Array with Alternating Positive and Negative Couplings
NASA Astrophysics Data System (ADS)
Yang, Ying; Xu, Ping; Lu, Liang-Liang; Zhu, Shi-Ning
2016-02-01
We propose the generation of photonic EPR state from quadratic waveguide array. Both the propagation constant and the nonlinearity in the array are designed to possess a periodical modulation along the propagation direction. This ensures that the photon pairs can be generated efficiently through the quasi-phase-matching spontaneous parametric down conversion by holding the spatial EPR entanglement in the fashion of correlated position and anticorrelated momentum. The Schmidt number which denotes the degree of EPR entanglement is calculated and it can approach a high value when the number of illuminated waveguide channels and the length of the waveguide array are properly chosen. These results suggest the quadratic waveguide array as a compact platform for engineering photonic quantum states in a high-dimensional Hilbert space. Supported by the State Key Program for Basic Research in China under Grant No. 2012CB921802, the National Natural Science Foundations of China under Grant Nos. 91321312, 11321063 and 11422438
Kernels, Degrees of Freedom, and Power Properties of Quadratic Distance Goodness-of-Fit Tests.
Lindsay, Bruce G; Markatou, Marianthi; Ray, Surajit
2014-03-01
In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests. First, we introduce the concept of a root kernel and discuss the considerations that enter the selection of this kernel. We derive an easy to use normal approximation to the power of quadratic distance goodness-of-fit tests and base the construction of a noncentrality index, an analogue of the traditional noncentrality parameter, on it. This leads to a method akin to the Neyman-Pearson lemma for constructing optimal kernels for specific alternatives. We then introduce a midpower analysis as a device for choosing optimal degrees of freedom for a family of alternatives of interest. Finally, we introduce a new diffusion kernel, called the Pearson-normal kernel, and study the extent to which the normal approximation to the power of tests based on this kernel is valid. Supplementary materials for this article are available online. PMID:24764609
Grouven, U; Bergel, F; Schultz, A
1996-01-01
Discriminant analysis plays an important role in biological and medical research. In practice, standard linear and quadratic methods are often applied which assume equal costs of misclassification. However, there can be situations where misclassifications between certain groups may be more serious than between other groups. Such considerations can be taken into account by using classification methods which incorporate misclassification costs. The widely applied statistical packages BMDP, SAS, and SPSS do not offer the possibility of using unequal misclassification costs for discriminant analysis with more than two groups. In this paper a menu-driven, user-friendly PC program written in Borland Pascal is introduced which performs linear and quadratic discriminant analysis for g > or = 2 groups allowing for the incorporation of misclassification costs. PMID:8646839
NASA Astrophysics Data System (ADS)
Artés, Joan C.; Rezende, Alex C.; Oliveira, Regilene D. S.
Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. Our goal is to make a global study of the family QsnSN of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the collision of two infinite singular points. This family can be divided into three different subfamilies, all of them with the finite saddle-node in the origin of the plane with the eigenvectors on the axes and with the eigenvector associated with the zero eigenvalue on the horizontal axis and (A) with the infinite saddle-node in the horizontal axis, (B) with the infinite saddle-node in the vertical axis and (C) with the infinite saddle-node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and time homotheties are three-dimensional and we give the bifurcation diagram of their closure with respect to specific normal forms, in the three-dimensional real projective space. The subfamilies (A) and (B) have already been studied [Artés et al., 2013b] and in this paper we provide the complete study of the geometry of the last family (C). The bifurcation diagram for the subfamily (C) yields 371 topologically distinct phase portraits with and without limit cycles for systems in the closure /line{QsnSN(C)} within the representatives of QsnSN(C) given by a chosen normal form. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincaré disk. The bifurcation set of /line{QsnSN(C)} is not only algebraic due to the presence of some surfaces found numerically. All points in these surfaces correspond to either connections of separatrices, or the presence of a double limit cycle.
A garden of orchids: a generalized Harper equation at quadratic irrational frequencies
NASA Astrophysics Data System (ADS)
Mestel, B. D.; Osbaldestin, A. H.
2004-10-01
We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.
NASA Astrophysics Data System (ADS)
Barrett, Dennis I.; Biggs, Rory; Remsing, Claudiu C.
2015-11-01
In this paper we consider quadratic Hamilton-Poisson systems on the semi-Euclidean Lie-Poisson space {s}{e}(1, 1)*-. The homogeneous positive semidefinite systems are classified; there are exactly six equivalence classes. In each case, the stability nature of the equilibrium states is determined. Explicit expressions for the integral curves are found. A characterization of the equivalence classes, in terms of the equilibria, is identified. Finally, the relation of this work to optimal control is briefly discussed.
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Range and flight time of quadratic resisted projectile motion using the Lambert W function
NASA Astrophysics Data System (ADS)
Belgacem, Chokri Hadj
2014-09-01
We study projectile motion with air resistance quadratic in speed. An approximation of a low-angle trajectory is considered where the horizontal velocity, v x , is assumed to be much larger than the vertical velocity, v y . The explicit solutions for the range and flight time are expressed in terms of the secondary branch of the Lambert function, {{W}_{-1}}. In addition to their theoretical importance, the results obtained will be of interest to teachers involved in undergraduate physics courses.
A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints
NASA Technical Reports Server (NTRS)
Hanson, R. J.; Krogh, Fred T.
1992-01-01
A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.
NASA Technical Reports Server (NTRS)
Sireteanu, T.
1974-01-01
An oscillating system with quadratic damping subjected to white noise excitation is replaced by a nonlinear, statistically equivalent system for which the associated Fokker-Planck equation can be exactly solved. The mean square responses are calculated and the optimum damping coefficient is determined with respect to the minimum mean square acceleration criteria. An application of these results to the optimization of automobile suspension damping is given.
Sequential design of a linear quadratic controller for the deep space network antennas
NASA Technical Reports Server (NTRS)
Gawronski, Wodek
1992-01-01
A linear quadratic controller design procedure is proposed for the NASA/JPL Deep Space Network antennas. The procedure is developed for an antenna model divided into tracking and flexible subsystems. Controllers for the flexible and tracking parts are designed separately by adjusting the performance index weights. The effect of weights on system performance is a crucial property, and is analytically described in this paper. The procedure is illustrated with the control system design for the DSS 13 antenna.
Classification of constraints and degrees of freedom for quadratic discrete actions
HÃ¶hn, Philipp A.
2014-11-15
We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form and employs the canonical formalism developed in Dittrich and HÃ¶hn [â€œConstraint analysis for variational discrete systems,â€ J. Math. Phys. 54, 093505 (2013); e-print http://arxiv.org/abs/arXiv:1303.4294 [math-ph
Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints
NASA Technical Reports Server (NTRS)
Juang, J.-N.; Turner, J. D.; Chun, H. M.
1984-01-01
Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.
NASA Astrophysics Data System (ADS)
Raju, Thokala Soloman; Hegde, Tejaswi; Kumar, C. N.; Panigrahi, Prasanta K.
2015-06-01
We demonstrate that the localized nonlinear gain induces stable chirped dissipative double-kink, fractional-transform, bell, and kink type solitons in optical mediawith quadratic nonlinearity. To compensate spatially uniform loss in both fundamental-frequency (FF) and second-harmonic (SH) component of the system, a strongly localized 'hot-spot', carrying the nonlinear gain, is added, acting either on FF component or on the SH one.
NASA Technical Reports Server (NTRS)
Ito, Kazufumi; Teglas, Russell
1987-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
NASA Astrophysics Data System (ADS)
Kortan, Victoria Ramaker
It has become increasingly apparent that the future of electronic devices can and will rely on the functionality provided by single or few dopant atoms. The most scalable physical system for quantum technologies, i.e. sensing, communication and computation, are spins in crystal lattices. Diamond is an excellent host crystal offering long room temperature spin coherence times and there has been exceptional experimental work done with the nitrogen vacancy center in diamond demonstrating many forms of spin control. Transition metal dopants have additional advantages, large spin-orbit interaction and internal core levels, that are not present in the nitrogen vacancy center. This work explores the implications of the internal degrees of freedom associated with the core d levels using a tight-binding model and the Koster-Slater technique. The core d levels split into two separate symmetry states in tetrahedral bonding environments and result in two levels with different wavefunction spatial extents. For 4 d semiconductors, e.g. GaAs, this is reproduced in the tight-binding model by adding a set of d orbitals on the location of the transition metal impurity and modifying the hopping parameters from impurity to its nearest neighbors. This model does not work in the case of 3d semiconductors, e.g. diamond, where there is no physical reason to drastically alter the hopping from 3 d dopant to host and the difference in wavefunction extent is not as pronounced. In the case of iron dopants in gallium arsenide the split symmetry levels in the band gap are responsible for a decrease in tunneling current when measured with a scanning tunneling microscope due to interference between two elastic tunneling paths and comparison between wavefunction measurements and tight-binding calculations provides information regarding material parameters. In the case of transition metal dopants in diamond there is less distinction between the symmetry split d levels. When considering pairs of transition metal dopants an important quantity is the exchange interaction between the two, which is a measure of how fast a gate can be operated between the pair and how well entanglement can be created. The exchange interaction between pairs of transition metal dopants has been calculated in diamond for several directions in the (110) plane, and for select transition metal dopants in gallium arsenide. In tetrahedral semiconductors transition metal dopants provide an internal degree of freedom due to the symmetry split d levels and this included functionality makes them special candidates for single spin based quantum technologies as well as physical systems to learn about fundamental physics.
NASA Astrophysics Data System (ADS)
Sun, Jun-Qiang; Ruedenberg, Klaus
1993-10-01
A novel second-order algorithm is formulated for determining steepest-descent lines on potential energy surfaces. The reaction path is deduced from successive exact steepest-descent lines of local quadratic approximations to the surface. At each step, a distinction is made between three points: the center for the local quadratic Taylor expansion of the surface, the junction of the two adjacent local steepest-descent line approximations, and the predicted approximation to the true steepest-descent line. This flexibility returns a more efficient yield from the calculated information and increases the accuracy of the local quadratic approximations by almost an order of magnitude. In addition, the step size is varied with the curvature and, if desired, can be readjusted by a trust region assessment. Applications to the Gonzalez-Schlegel and the Müller-Brown surfaces show the method to compare favorably with existing methods. Several measures are given for assessing the accuracy achieved without knowledge of the exact steepest-descent line. The optimal evaluation of the predicted gradient and curvature for dynamical applications is discussed.
Entanglement in a model for Hawking radiation: An application of quadratic algebras
Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.
2013-03-15
Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.
On Pure Quasi-Quantum Quadratic Operators of 𝕄2(?) II
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh
2015-11-01
In this paper we study quasi quantum quadratic operators (QQO) acting on the algebra of 2×2 matrices 𝕄2(?). We consider two kinds of quasi QQO the corresponding quadratic operator maps from the unit circle into the sphere and from the sphere into the unit circle, respectively. In our early paper we have defined a q-purity of quasi QQO. This notion is equivalent to the invariance of the unit sphere in ?3. But to check this condition, in general, is tricky. Therefore, it would be better to find weaker conditions to check the q-purity. One of the main results of this paper is to provide a criterion of q-purity of quasi QQO in terms of the unit circles. Moreover, we are able to classify all possible kinds of quadratic operators which can produce q-pure quasi QQO. We think that such result will allow one to check whether a given mapping is a pure channel or not. This finding suggests us to study such a class of nonpositive mappings. Correspondingly, the complement of this class will be of potential interest for physicist since this set contains all completely positive mappings.
Fast-rolling shutter compensation based on piecewise quadratic approximation of a camera trajectory
NASA Astrophysics Data System (ADS)
Lee, Yun Gu; Kai, Guo
2014-09-01
Rolling shutter effect commonly exists in a video camera or a mobile phone equipped with a complementary metal-oxide semiconductor sensor, caused by a row-by-row exposure mechanism. As video resolution in both spatial and temporal domains increases dramatically, removing rolling shutter effect fast and effectively becomes a challenging problem, especially for devices with limited hardware resources. We propose a fast method to compensate rolling shutter effect, which uses a piecewise quadratic function to approximate a camera trajectory. The duration of a quadratic function in each segment is equal to one frame (or half-frame), and each quadratic function is described by an initial velocity and a constant acceleration. The velocity and acceleration of each segment are estimated using only a few global (or semiglobal) motion vectors, which can be simply predicted from fast motion estimation algorithms. Then geometric image distortion at each scanline is inferred from the predicted camera trajectory for compensation. Experimental results on mobile phones with full-HD video demonstrate that our method can not only be implemented in real time, but also achieve satisfactory visual quality.