A computational study of nodal-based tetrahedral element behavior.
Gullerud, Arne S.
2010-09-01
This report explores the behavior of nodal-based tetrahedral elements on six sample problems, and compares their solution to that of a corresponding hexahedral mesh. The problems demonstrate that while certain aspects of the solution field for the nodal-based tetrahedrons provide good quality results, the pressure field tends to be of poor quality. Results appear to be strongly affected by the connectivity of the tetrahedral elements. Simulations that rely on the pressure field, such as those which use material models that are dependent on the pressure (e.g. equation-of-state models), can generate erroneous results. Remeshing can also be strongly affected by these issues. The nodal-based test elements as they currently stand need to be used with caution to ensure that their numerical deficiencies do not adversely affect critical values of interest.
NASA Technical Reports Server (NTRS)
Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.
1992-01-01
A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.
A mesh generator for tetrahedral elements using Delaunay triangulation
Yuan, J.S.; Fitzsimons, C.J. )
1993-03-01
A tetrahedral mesh generator has been developed. The generator is based on the Delaunay triangulation which is implemented by employing the insertion polyhedron algorithm. In this paper some new methods to deal with the problems associated with the three-dimensional Delaunay triangulation and the insertion polyhedron algorithm are presented: degeneracy, the crossing situation, identification of the internal elements and internal point generation. The generator works both for convex and non-convex domains, including those with high aspect-ratio subdomains. Some examples are given in this paper to illustrate the capability of the generator.
On Curved Simplicial Elements and Best Quadratic Spline Approximation for
Hamann, Bernd
On Curved Simplicial Elements and Best Quadratic Spline Approximation for Hierarchical Data a method for hierarchical data approximation using curved quadratic simplicial elements for domain- cial elements make possible a better representation of curved geometry, domain boundaries
E. Cojocaru
2009-10-20
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic triangular elements may lead to an improved accuracy. Here we present a collection of elemental matrices evaluated analytically for quadratic triangular elements. They could be useful for the finite element method in advanced electromagnetics.
On Interpolation Errors over Quadratic Nodal Triangular Finite Elements
Kirby, Mike
On Interpolation Errors over Quadratic Nodal Triangular Finite Elements Shankar P. Sastry to interpolate a solution (within an element) of a partial differential equation obtained by the finite element the bounds on the error of the interpolated solution. For linear elements, the error bounds at a point have
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.
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
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.
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.
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
ROTATION-VIBRATION TETRAHEDRAL
SadovskiÃ, DmitriÃ
ANALYSIS OF ROTATION-VIBRATION RELATIVE EQUILIBRIA ON THE EXAMPLE OF A TETRAHEDRAL FOUR ATOM (RE) of a nonrigid molecule which vibrates about a well de#12;ned equilibrium con#12;guration and rotates as a whole. Our analysis uni#12;es the theory of rotational and vibrational RE. We rely
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…
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
Feature-Sensitive Tetrahedral Mesh Generation with Guaranteed Quality
Wang, Jun; Yu, Zeyun
2012-01-01
Tetrahedral meshes are being extensively used in finite element methods (FEM). This paper proposes an algorithm to generate feature-sensitive and high-quality tetrahedral meshes from an arbitrary surface mesh model. A top-down octree subdivision is conducted on the surface mesh and a set of tetrahedra are constructed using adaptive body-centered cubic (BCC) lattices. Special treatments are given to the tetrahedra near the surface such that the quality of the resulting tetrahedral mesh is provably guaranteed: the smallest dihedral angle is always greater than 5.71°. The meshes generated by our method are not only adaptive from the interior to the boundary, but also feature-sensitive on the surface with denser elements in high-curvature regions where geometric feature most likely reside. A variety of experimental results are presented to demonstrate the effectiveness and robustness of this algorithm. PMID:22328787
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
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 given…
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?.
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.
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.
Note on an Additive Characterization of Quadratic Residues Modulo p
Monico, Chris
Note on an Additive Characterization of Quadratic Residues Modulo p Chris Monico, Michele Elia, . . . , p - 1} of positive residues modulo an odd prime p is the partition into quadratic residues and quadratic non-residues if and only if the elements of A and B satisfy certain additive properties, thus
On differences of quadratic residues Guillermo Morales-Luna
International Association for Cryptologic Research (IACR)
On differences of quadratic residues Guillermo Morales-Luna Computer Science Cinvestav-IPN, Mexico of remainders, any element can be realized as the difference of two quadratic residues, and also that as difference of quadratic residues is non- decreasing with respect to the divisibility ordering in the odd
Generalized Linear Quadratic Control
Gattami, Ather Said
We consider the problem of stochastic finite- and infinite-horizon linear quadratic control under power constraints. The calculations of the optimal control law can be done off-line as in the classical linear quadratic ...
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…
Nonzero Quadrupole Moments of Candidate Tetrahedral Bands
Bark, R. A.; Lawrie, E. A.; Lawrie, J. J.; Mullins, S. M.; Murray, S. H. T.; Ncapayi, N. J.; Smit, F. D.; Sharpey-Schafer, J. F.; Lindsay, R.
2010-01-15
Negative-parity bands in the vicinity of {sup 156}Gd and {sup 160}Yb have been suggested as candidates for the rotation of tetrahedral nuclei. We report the observation of the odd and even-spin members of the lowest energy negative-parity bands in {sup 160}Yb and {sup 154}Gd. The properties of these bands are similar to the proposed tetrahedral band of {sup 156}Gd and its even-spin partner. Band-mixing calculations are performed and absolute and relative quadrupole moments deduced for {sup 160}Yb and {sup 154}Gd. The values are inconsistent with zero, as required for tetrahedral shape, and the bands are interpreted as octupole vibrational bands. The failure to observe the in-band E2 transitions of the bands at low spins can be understood using the measured B(E1) and B(E2) values.
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.
Quadratic eigenvalue problems.
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
Tetrahedrally coordinated carbonates in Earth's lower mantle.
Boulard, Eglantine; Pan, Ding; Galli, Giulia; Liu, Zhenxian; Mao, Wendy L
2015-01-01
Carbonates are the main species that bring carbon deep into our planet through subduction. They are an important rock-forming mineral group, fundamentally distinct from silicates in the Earth's crust in that carbon binds to three oxygen atoms, while silicon is bonded to four oxygens. Here we present experimental evidence that under the sufficiently high pressures and high temperatures existing in the lower mantle, ferromagnesian carbonates transform to a phase with tetrahedrally coordinated carbons. Above 80?GPa, in situ synchrotron infrared experiments show the unequivocal spectroscopic signature of the high-pressure phase of (Mg,Fe)CO3. Using ab-initio calculations, we assign the new infrared signature to C-O bands associated with tetrahedrally coordinated carbon with asymmetric C-O bonds. Tetrahedrally coordinated carbonates are expected to exhibit substantially different reactivity than low-pressure threefold coordinated carbonates, as well as different chemical properties in the liquid state. Hence, this may have significant implications for carbon reservoirs and fluxes, and the global geodynamic carbon cycle. PMID:25692448
Theory of prospective tetrahedral perovskite ferroelectrics
Roy, Anindya
2010-01-01
Using first-principles methods, we predict the energy landscape and ferroelectric states of double perovskites of the form AA$'$BB$'$O$_6$ in which the atoms on both the A and B sites are arranged in rock-salt order. While we are not aware of compounds that occur naturally in this structure, we argue that they might be realizable by directed synthesis. The high-symmetry structure formed by this arrangement belongs to the tetrahedral $F\\bar{4}3m$ space group. If a ferroelectric instability occurs, the energy landscape will tend to have minima with the polarization along tetrahedral directions, leading to a rhombohedral phase, or along Cartesian directions, leading to an orthorhombic phase. We find that the latter scenario applies to CaBaTiZrO$_6$ and KCaZrNbO$_6$, which are weakly ferroelectric, and the former one applies to PbSnTiZrO$_6$, which is strongly ferroelectric. The results are modeled with a fourth- or fifth-order Landau-Devonshire expansion, providing good agreement with the first-principles calcul...
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.
Optical Quadratic Measure Eigenmodes
Michael Mazilu; Joerg Baumgartl; Sebastian Kosmeier; Kishan Dholakia
2010-07-13
We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of their interaction with matter. In this manner we may decompose the respective fields into optical quadratic measure eigenmodes (QME). Key applications include the optimization of the size of a focused spot, the transmission through photonic devices, and the structured illumination of photonic and plasmonic structures. We verify the validity of the QME approach through a particular experimental realization where the size of a focused optical field is minimized using a superposition of Bessel beams.
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.
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]…
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2015-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
Luis Alvarez-Gaume; Alex Kehagias; Costas Kounnas; Dieter Lust; Antonio Riotto
2015-07-07
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-theory. We demonstrate that string theory on non-compact $CY_3$ manifolds, like a line bundle over $\\mathbb{CP}^2$, may indeed lead to gravity dynamics determined by a higher curvature action.
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.
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.
A Quadratic Basis Function, Quadratic Geometry, High Order Panel Method.
Peraire, Jaime
A Quadratic Basis Function, Quadratic Geometry, High Order Panel Method. David J. Willis Jaime, USA. Most panel method implementations use both low order basis function representations of the solution and flat panel representations of the body surface. Although several imple- mentations of higher
Hamiltonian Tetrahedralizations with Steiner Points Francisco Escalona
Urrutia, Jorge
(n log n) algorithm to solve this problem, where m is the number of elements of S on its convex hull. We. We prove that by adding to S at most m-2 2 Steiner points in the interior of the convex hull of S also prove that point sets with at most 20 convex hull points have a Hamiltonian tetrahedraliza- tion
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.
Efficient Query Processing on Unstructured Tetrahedral Stratos Papadomanolakis Anastassia Ailamaki
O'Hallaron, David R.
of high resolution and precision, to be queried by a visualization or analysis tool. Tetrahedral meshes to carry out simulations of unprecedented resolu- tion and scale. Accurate simulations improve our under.1 Querying Simulation Datasets To analyze and display simulation results, post-processing and visualization
The tetrahedral principle in kite design, Patrick Prosser
St Andrews, University of
@cs.strath.ac.uk Abstract I review an article by Alexander Graham Bell on the tertahedral principle in kite design, first of A.G. Bell. In June 1903 Alexander Graham Bell published a paper in the National Geo graphic prublished in 1903. Bell claims that as the tetrahedral kite is scaled up its density remains constant. I
Stereocontrolled Self-Assembly and Self-Sorting of Luminescent Europium Tetrahedral Cages.
Yan, Liang-Liang; Tan, Chun-Hong; Zhang, Guang-Lu; Zhou, Li-Peng; Bünzli, Jean-Claude; Sun, Qing-Fu
2015-07-01
Coordination-directed self-assembly has become a well-established technique for the construction of functional supramolecular structures. In contrast to the most often exploited transition metals, trivalent lanthanides Ln(III) have been less utilized in the design of polynuclear self-assembled structures despite the wealth of stimulating applications of these elements. In particular, stereochemical control in the assembly of lanthanide chiral cage compounds is not easy to achieve in view of the usually large lability of the Ln(III) ions. We report here the first examples of stereoselective self-assembly of chiral luminescent europium coordination tetrahedral cages and their intriguing self-sorting behavior. Two pairs of R and S ligands are designed on the basis of the pyridine-2,6-dicarboxamide coordination unit, bis(tridentate) L1 and tris(tridentate) L2. Corresponding chiral Eu4(L1)6 and Eu4(L2)4 topological tetrahedral cages are independently assembled via edge- and face-capping design strategies, respectively. The chirality of the ligand is transferred during the self-assembly process to give either ? or ? metal stereochemistry. The self-assembled cages are characterized by NMR, high-resolution ESI-TOF-MS, and in one case by X-ray crystallography. Strict control of stereoselectivity is confirmed by CD spectroscopy and NMR enantiomeric differentiation experiments. Narcissistic self-sorting is observed in the self-assembly process when two differently shaped ligands L1 and L2 are mixed. More impressively, distinct self-sorting behavior between Eu4(L1)6 and Eu4(L2)4 coordination cages is observed for the first time when racemic mixtures of ligands are used. We envisage that chiral luminescent lanthanide tetrahedral cages could be used in chiroptical probes\\sensors and enantioselective catalysis. PMID:26065490
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.
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.
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.
Variational Tetrahedral PierrePierre AlliezAlliez
California at Berkeley, University of
K's talk, Slides the authors posted, www.cs.uiuc.edu/class/fa05/cs598anh/slides/Bell2005_AlCoYvDe2005.pdf #12;2 Goals Â· 2D: Â· In: Non-intersecting closed curve Â· Out: Triangle Mesh Â· 3D: Â· In: Given a watertight, non- intersecting manifold triangle mesh Â· Out: Tetrahedral Mesh #12;3 Mesh quality
Mesh quality control for multiply-refined tetrahedral grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger
1994-01-01
A new algorithm for controlling the quality of multiply-refined tetrahedral meshes is presented in this paper. The basic dynamic mesh adaption procedure allows localized grid refinement and coarsening to efficiently capture aerodynamic flow features in computational fluid dynamics problems; however, repeated application of the procedure may significantly deteriorate the quality of the mesh. Results presented show the effectiveness of this mesh quality algorithm and its potential in the area of helicopter aerodynamics and acoustics.
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.
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
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
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.
Quadratic fractional age assumption revisited.
Hossain, Syed A
2011-04-01
This paper introduces a quadratic fractional age assumption which makes the force of mortality and survival function continuous at all ages. The necessary and sufficient condition for the assumption to be valid is derived. Important life table parameters are estimated and applications are shown using several life table data. PMID:20165913
Infrared absorption features for tetrahedral ammonia ice crystals
NASA Technical Reports Server (NTRS)
West, Robert A.; Orton, Glenn S.; Draine, Bruce T.; Hubbell, Earl A.
1989-01-01
An effort has been made to ascertain how particle shape and composition affect the strength and shape of resonant absorption features at 9.4 and 26 microns. A shifting of the peak of the resonance relative to that for spherical particles is noted in the computational results obtained for the extinction cross-sections of 0.5- and 1-micron, volume-equivalent radius tetrahedral NH3 ice crystals that either possessed or lacked foreign cores. It it judged unlikely that small, (less than 5-micron) NH3 particles could be the principal component of the haze in the 300-500 mbar region of Jupiter.
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.
Transport properties of tetrahedral, network-forming ionic melts.
Agarwal, Manish; Ganguly, Abir; Chakravarty, Charusita
2009-11-19
Molecular dynamics simulations of liquid silica and beryllium fluoride are performed using the van Beest-Kramer-van Santen and transferable rigid ion model potentials, respectively, in order to compare transport properties. The ionic conductivity (sigma), shear viscosity (eta) and ionic self-diffusivities (D(+/-)) are computed over a fairly wide range of temperatures and densities and deviations from Arrhenius behavior along different isochores is studied. The Stokes-Einstein relation is shown to hold over the entire range of state points, though the effective hydrodynamic radius shows small variations due to thermal fluctuations, compression, and local tetrahedral order. Several alternative tests of the Nernst-Einstein relation are implemented which show that significant network-formation in the anomalous regime leads to a breakdown of this relationship. The relaxation times, tau(sigma) and tau(M), associated with the decay of the charge-flux and pressure ACFs respectively, are computed. In the anomalous regime, as the tetrahedral network formation progresses, tau(M) increases rapidly while tau(sigma) shows very little variation, indicating a decoupling of charge and momentum transport processes. PMID:19860439
Geometrical Solutions of Quadratic Equations.
ERIC Educational Resources Information Center
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
Shan, Xiao; Connor, J N L
2012-11-26
A previous paper by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392) reported the surprising result that four simple parametrized S matrices can reproduce the forward-angle glory scattering of the H + D(2)(v(i)=0,j(i)=0) ? HD(v(f)=3,j(f)=0) + D reaction, whose differential cross section (DCS) had been computed in a state-of-the-art scattering calculation for a state-of-the-art potential energy surface. Here, v and j are vibrational and rotational quantum numbers, respectively, and the translational energy is 1.81 eV. This paper asks the question: Can we replace the analytic functions (of class C(?)) used by Shan-Connor with simpler mathematical functions and still reproduce the forward-angle glory scattering? We first construct S matrix elements (of class C(0)) using a quadratic phase and a piecewise-continuous pre-exponential factor consisting of three pieces. Two of the pieces are constants, with one taking the value N (a real normalization constant) at small values of the total angular momentum number, J; the other piece has the value 0 at large J. These two pieces are joined at intermediate values of J by either a straight line, giving rise to the linear parametrization (denoted param L), or a quadratic curve, which defines the quadratic parametrization (param Q). We find that both param L and param Q can reproduce the glory scattering for center-of-mass reactive scattering angles, ?(R) ? 30°. Second, we use a piecewise-discontinuous pre-exponential factor and a quadratic phase, giving rise to a step-function parametrization (param SF) and a top-hat parametrization (param TH). We find that both param SF and param TH can reproduce the forward-angle scattering, even though these class C(-1) parametrizations are usually considered too simplistic to be useful for calculations of DCSs. We find that an ultrasimplistic param THz, which is param TH with a phase of zero, can also reproduce the glory scattering at forward angles. The S matrix elements for param THz are real and consist of five nonzero equal values, given by S(J) = 0.02266, for the window, J = 21(1)25. Param THz is sufficiently simple that we can derive closed forms for the partial wave scattering amplitude, f(?(R)), and the near-side (N) and far-side (F) subamplitudes. We show that window representations of f(?(R)) provide important insights into the range of J values that contribute to the reaction dynamics. Other theoretical techniques used are NF theory for the analysis of DCSs and full and NF local angular momentum theory, in both cases including up to three resummations of f(?(R)) before making the NF decomposition. Finally, we investigate the accuracy of various semiclassical glory theories for the DCS of param L. By varying one phase parameter for param L, we show that the uniform semiclassical approximation is accurate from ?(R) = 0° to close to ?(R) = 180°. Our approach is an example of a "weak" form of Heisenberg's S matrix program, which does not use a potential energy surface(s); rather it focuses on the properties of the S matrix. Our method is easy to apply to DCSs from experimental measurements or from computer simulations. PMID:22876759
Self-assembly of tetrahedral plasmonic nanoclusters for optical metafluids
NASA Astrophysics Data System (ADS)
Schade, Nicholas; Manoharan, Vinothan
2015-03-01
We direct the assembly of clusters of gold nanospheres that behave as nanoscale electromagnetic resonators. We use spherical gold nanoparticles that are exceptionally smooth, monocrystalline, and monodisperse. These particles exhibit highly reproducible scattering spectra compared with gold colloids that are available commercially. We mix these positively charged particles with negatively charged dielectric particles. The gold particles stick to the dielectric particles permanently and randomly in a process that can be modeled mathematically as ``random parking,'' a type of non-equilibrium self-assembly. By controlling the particles' sizes, stoichiometry, and interactions, we maximize the yield of tetrahedral clusters, the ideal structures for isotropic metamaterials. We measure the optical properties of these structures with dark-field spectroscopy to characterize their suitability as building blocks for a bulk, isotropic, optical metafluid.
Nuclear Tetrahedral Symmetry: Possibly Present Throughout the Periodic Table
J. Dudek; A. Gozdz; N. Schunck; M. Miskiewicz
2002-05-21
More than half a century after the fundamental, spherical shell structure in nuclei has been established, theoretical predictions indicate that the shell-gaps comparable or even stronger than those at spherical shapes may exist. Group-theoretical analysis supported by realistic mean-field calculations indicate that the corresponding nuclei are characterized by the $T_d^D$ ('double-tetrahedral') group of symmetry, exact or approximate. The corresponding strong shell-gap structure is markedly enhanced by the existence of the 4-dimensional irreducible representations of the group in question and consequently it can be seen as a geometrical effect that does not depend on a particular realization of the mean-field. Possibilities of discovering the corresponding symmetry in experiment are discussed.
Intraframework migration of tetrahedral atoms in a zeolite.
Shin, Jiho; Ahn, Nak Ho; Camblor, Miguel A; Cho, Sung June; Hong, Suk Bong
2014-08-18
The transformation from a disordered into an ordered version of the zeolite natrolite occurs on prolonged heating of this material in the crystallizing medium, but not if the mother liquor is replaced by water or an alkaline solution. This process occurs for both aluminosilicate and gallosilicate analogues of natrolite. In cross experiments, the disordered Al-containing (or Ga-containing) analogue is heated while in contact with the mother liquor of the opposite analogue, that is, the Ga-containing (or Al-containing) liquor. Therefore, strong evidence for the mechanism of the ordering process was obtained, which was thus proposed to proceed by intraframework migration of tetrahedral atoms without diffusion along the pores. Migration is first triggered, then fuelled by surface rearrangement through reactions with the mother liquor, and stops when an almost fully ordered state is attained. Classical dissolution-recrystallization and Ostwald ripening processes do not appear to be relevant for this phase transformation. PMID:24931398
Shape Transformation and Surface Melting of Cubic and Tetrahedral Platinum Nanocrystals
Wang, Zhong L.
LETTERS Shape Transformation and Surface Melting of Cubic and Tetrahedral Platinum Nanocrystals is much lower than the melting point of bulk metallic platinum (1769 °C). The reduction in the melting Platinum nanocrystals with a high percentage of cubic-, tetrahedral-, or octahedral-like shapes have been
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.
Competing nonlinearities in quadratic nonlinear waveguide arrays
structure [8] we show that nonlinear phase cancellation is possible in both re- gimes of normal by quadratic nonlinear interactions. The presence of several SH modes is crucial for observation of com- petingCompeting nonlinearities in quadratic nonlinear waveguide arrays Frank Setzpfandt,1, * Dragomir N
Simplicity of quadratic Lie conformal algebras
Yanyong Hong; Zhixiang Wu
2015-07-07
In this paper, simplicity of quadratic Lie conformal algebras are investigated. From the point view of the corresponding Gel'fand-Dorfman bialgebras, some sufficient conditions and necessary conditions to ensure simplicity of quadratic Lie conformal algebras are presented. By these observations, we present several classes of new infinite simple Lie conformal algebras. These results will be useful for classification purposes.
STATISTICAL ANALYSIS OF QUADRATIC IN COMPUTER VISION
STATISTICAL ANALYSIS OF QUADRATIC PROBLEMS IN COMPUTER VISION BY YORAM LEEDAN A dissertation and Computer Engineering Written under the direction of Professor Peter Meer and approved by New Brunswick, New STATISTICAL ANALYSIS OF QUADRATIC PROBLEMS IN COMPUTER VISION by YORAM LEEDAN Dissertation Director: Professor
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…
Generalized quadratic weights for asymptotic regulator properties
NASA Technical Reports Server (NTRS)
Stein, G.
1979-01-01
The paper describes a generalized quadratic weight selection procedure based on asymptotic modal properties of linear-quadratic regulators as control weights tend to zero. Explicit formulas are developed for weighting matrices which produce an asymptotic eigenstructure consisting of p no greater than n - m finite modes, with the rest tending to infinity in selectable Butterworth patterns or determined by other secondary design considerations.
On the amelioration of quadratic divergences
Delbourgo, Robert
2002-01-01
Once massless quadratically divergent tadpole diagrams are discarded, because they contain no intrinsic scale, it is possible to convert other divergences into logarithmic form, using partial fraction identities; this includes the case of quadratic divergences, as has been applied to the linear sigma model. However the procedure must be carried out with due care, paying great attention to correct numerator factors.
On the amelioration of quadratic divergences
R. Delbourgo; M. D. Scadron
2002-02-17
Once massless quadratically divergent tadpole diagrams are discarded, because they contain no intrinsic scale, it is possible to convert other divergences into logarithmic form, using partial fraction identities; this includes the case of quadratic divergences, as has been applied to the linear sigma model. However the procedure must be carried out with due care, paying great attention to correct numerator factors.
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.
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.
Superlattice Quantum Dots of Self-assembled Tetrahedral Nanocrystals
NASA Astrophysics Data System (ADS)
Wang, Z. L.; Yin, J. S.
1998-03-01
Size and shape selected CoO nanocrystals dominated by tetrahedral shape have been synthesized and assembled to form superlattices with long-range translation order and short-range orientation order [1]. The crystallography of self-assembled nanocrystal superlattices (NCSs) is determined not only by the size of the nanocrystals and the length of the passivation thiolates, but by the shape of the nanocrystals. The structure of the nanocrystals are determined by high-resolution transmission electron microscopy (TEM). A model is suggested to explain the observed orientation order and the result supports that the thiolates molecules distributed on the nanocrystal surfaces form bundles, and the nanocrystals are assembled in such a way that the bundles tend to fill the entire space. The stability of the NCSs has been examined in-situ using TEM. The result suggests the strong effect of the substrate on NCSs. [1] J.S. Yin and Z.L. Wang, Phys. Rev. Lett., 79 (No. 13) (1997) 2570-2573. [2] J.S. Yin and Z.L. Wang, J. Phys. Chem., 101 (1997) 8979-8983.
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.
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 atmore »the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less
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 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.
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.
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.
High Order Nedelec Elements with local complete sequence properties
Zaglmayr, Sabine
High Order N´ed´elec Elements with local complete sequence properties Joachim Sch¨oberl and Sabine problems using high or- der H(curl) finite elements. We discuss a systematic strat- egy for the realization of arbitrary order hierarchic H(curl)- conforming finite elements for triangular and tetrahedral ele- ment
High order Nedelec elements with local complete sequence
Schoeberl, Joachim
High order Ne´de´lec elements with local complete sequence properties Joachim Scho¨berl and Sabine using high order H(curl) finite elements. Design/methodology/approach Discusses a systematic strategy for the realization of arbitrary order hierarchic H(curl)-conforming finite elements for triangular and tetrahedral
Ken-ichiro Arita; Yasunori Mukumoto
2014-05-09
Shell structures in single-particle energy spectra are investigated against regular tetrahedral type deformation using radial power-law potential model. Employing a natural way of shape parametrization which interpolates sphere and regular tetrahedron, we find prominent shell effects at rather large tetrahedral deformations, which bring about shell energies much larger than the cases of spherical and quadrupole type shapes. We discuss the semiclassical origin of these anomalous shell structures using periodic orbit theory.
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.)
PRIMES AND QUADRATIC RECIPROCITY ANGELICA WONG
May, J. Peter
PRIMES AND QUADRATIC RECIPROCITY ANGELICA WONG Abstract. We discuss number theory with the ultimate xi yp-i . It suffices to show that each term of the expansion Date: August 11, 2008. 1 #12;2 ANGELICA
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.
Generalized quadratic weights for asymptotic regulator properties
NASA Technical Reports Server (NTRS)
Stein, G.
1979-01-01
This paper describes a generalized quadratic weight selection procedure based on asymptotic modal properties of linear-quadratic regulators as control weights tend to zero. Explicit formulas are developed for weighting matrices which produce an asymptotic eigen-structure consisting of p less than or equal to n-m finite modes, with the rest tending to infinity in selectable Butterworth patterns or determined by other secondary design considerations.
MacLeod, Rob S.
D,c Rob MacLeod, PhDb a Department of Cardiology, Children's Hospital Boston, Boston, MA, USA b Scientific. © 2008 Published by Elsevier Inc. Keywords: ICD; Defibrillation; Modeling; Pediatric electrophysiology
THE DISTRIBUTION OF QUADRATIC RESIDUES AND NON-RESIDUES
Srinivasan, Aravind
106 THE DISTRIBUTION OF QUADRATIC RESIDUES AND NON-RESIDUES D. A. BURGESS 1. If p is a prime other than 2, half of the numbers 1, 2, ..., p-l are quadratic residues (modp) and the other half are quadratic non-residues. Various questions have been proposed concerning the distribution of the quadratic
Dr. Z.'s Number Theory Lecture 20 Handout: Quadratic residues and the law of Quadratic Reciprocity
Zeilberger, Doron
Dr. Z.'s Number Theory Lecture 20 Handout: Quadratic residues and the law of Quadratic Reciprocity By Doron Zeilberger Important Definition: a is a quadratic residue mod n is there is an integer x, 0 x such that x2 a (mod n) . Otherwise it is a quadratic non-residue. Note: every congruence class between 0
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
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.
Guises and disguises of quadratic divergences
Cherchiglia, A.L.; Vieira, A.R.; Hiller, Brigitte; Baêta 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 ?. 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.
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 ??.
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.
Indirect quantum tomography of quadratic Hamiltonians
NASA Astrophysics Data System (ADS)
Burgarth, Daniel; Maruyama, Koji; Nori, Franco
2011-01-01
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
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.
Learning from Examples with Quadratic Mutual Information
Slatton, Clint
Learning from Examples with Quadratic Mutual Information Dongxin Xu, Jose C .Principe Computational criteria (entropy or mutual information) directly from a training set. l'he method is based on a Parzen the algorithm for entropy estimation to the impor- tiint case of mutual information. The mutual information
Discrete calculus of variations for quadratic lagrangians
Ryckelynck, Philippe
2011-01-01
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical points of sampled actions. Then we characterize the discretization operators such that, for all quadratic lagrangian, the discrete Euler-Lagrange equations converge to the classical ones.
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…
Linear-quadratic fractional Gaussian control
Duncan, Tyrone E.; Pasik-Duncan, Bozenna
2013-01-01
In this paper a control problem for a linear stochastic system driven by a noise process that is an arbitrary zero mean, square integrable stochastic process with continuous sample paths and a cost functional that is quadratic in the system state...
Nikitin, A V; Rey, M; Tyuterev, Vl G
2015-03-01
A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB4 molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q)(-2) type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH4 molecule is demonstrated. PMID:25747072
Tetrahedral calcite crystals facilitate self-assembly at the air-water interface S. M. Hashmi
Tetrahedral calcite crystals facilitate self-assembly at the air-water interface S. M. Hashmi; published 26 October 2005 Calcite crystals often nucleate and grow in solutions of calcium carbonate out of aqueous solution is known to form fractal aggregates of micron-sized rhombohedral calcite
Aging of Tetrahedral Structure in a Lennard-Jones Glass1 Gianguido C. CIANCI2
Weeks, Eric R.
Aging of Tetrahedral Structure in a Lennard-Jones Glass1 Gianguido C. CIANCI2 and Eric R. WEEKS3,4 Summary We study the aging of a glassy Lennard-Jones binary mixture with molecular dy- namics simulations. We follow the evolution of the packing as a function of the system's age tw, the time passed since
A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection
Ming, Ping-bing
refinement of tetrahedral meshes using bisection. The algorithm is part of PHG, Parallel Hierarchical Grid is characterized by allowing simultaneous refinement of submeshes to arbitrary levels before synchronization, producing 4 smaller triangles or 8 smaller tetrahedra. Since the regular refinement cannot generate locally
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.
Assembly of Hydrogen Bonded Diamondoid Networks Based on Synthetic Metal-Organic Tetrahedral Nodes
Gao, Song
Bao-Qing Ma,* Hao-Ling Sun, and Song Gao* State Key Laboratory of Rare Earth Materials Chemistry and Applications and PKU-HKU Joint Laboratory on Rare Earth Materials and Bioinorganic Chemistry, CollegeAssembly of Hydrogen Bonded Diamondoid Networks Based on Synthetic Metal-Organic Tetrahedral Nodes
3D Harmonic Mapping and Tetrahedral Meshing of Brain Imaging Data
Thompson, Paul
3D Harmonic Mapping and Tetrahedral Meshing of Brain Imaging Data Yalin Wang1 , Xianfeng Gu2 , Paul Department, Harvard University, Cambridge, MA, USA Abstract. We developed two techniques to address 3D volume algorithm finds a harmonic map from a 3-manifold to a 3D solid sphere and the second is a novel sphere
Liquid-Liquid Phase Transitions in Tetrahedrally Coordinated Fluids via Wertheim Theory
Sciortino, Francesco
Liquid-Liquid Phase Transitions in Tetrahedrally Coordinated Fluids via Wertheim Theory Frank has been proposed as a mechanism for generating liquid-liquid phase transitions in one component be solved within Wertheim's theory for associating fluids and shows liquid-liquid phase separations (in
Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminium
Wadley, Haydn
Available online 17 June 2004 Abstract Open cell, lattice truss structures have been made by folding perforated 6061 aluminium alloy sheets. Simple air brazing is used to construct sandwich panels with cellular with compressive strength data for other cellular metals indicate that wrought aluminium alloy tetrahedral lattice
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…
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)
Anonymous IBE from Quadratic Residuosity with Improved Performance
International Association for Cryptologic Research (IACR)
Anonymous IBE from Quadratic Residuosity with Improved Performance Michael Clear , Hitesh Tewari Based Encryption, Anonymous IBE, Cocks Scheme, Quadratic Residuosity Abstract. Identity Based Encryption. Cocks constructed the first such scheme, and subsequent improvements have been made to achieve anonymity
Gorodylova, Nataliia; Kosinová, Veronika; Šulcová, Petra; B?lina, Petr; Vl?ek, 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
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.
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.
LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Lim, Andrew
LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ANDREW E. B. LIM AND XUN YU differential equations (BSDEs) with a quadratic cost criteria, or backward linear-quadratic (BLQ) control, an uncontrolled BSDE, and an uncontrolled forward stochastic differential equation (SDE), while the second
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 Sieve Factoring Method -part 1 Cryptology 2
Babinkostova, Liljana
algorithms that share a common strategy Trial division the sieve of Eratosthenes Quadratic Sieve Factoring of factorization algorithms that share a common strategy Trial division the sieve of Eratosthenes Fermat of Eratosthenes Fermat's algorithm Pomerance's Quadratic Sieve Quadratic Sieve Factoring Method - part 1 #12
Exploring {{W}}_{? } in the quadratic basis
NASA Astrophysics Data System (ADS)
Procházka, Tomáš
2015-09-01
We study the operator product expansions in the chiral algebra {W}_{? } , first using the associativity conditions in the basis of primary generating fields and then using a different basis coming from the free field representation in which the OPE takes a simpler quadratic form. The results in the quadratic basis can be compactly written using certain bilocal combinations of the generating fields and we conjecture a closed-form expression for the complete OPE in this basis. Next we show that the commutation relations as well as correlation functions can be easily computed using properties of these bilocal fields. In the last part we verify the consistency with results derived previously by studying minimal models of {W}_{? } and comparing them to known reductions of {W}_{? } to {W}_N . The results we obtain illustrate nicely the role of triality symmetry in the representation theory of {W}_{? }.
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.
Quadratic invariants of the elasticity tensor
Yakov Itin
2015-09-08
We study the quadratic invariants of the elasticity tensor in the framework of its unique irreducible decomposition. The key point is that this decomposition generates the direct sum reduction of the elasticity tensor space. The corresponding subspaces are completely independent and even orthogonal relative to the Euclidean (Frobenius) scalar product. We construct a basis set of seven quadratic invariants that emerge in a natural and systematic way. Moreover, the completeness of this basis and the independence of the basis tensors follow immediately from the direct sum representation of the elasticity tensor space. We define the Cauchy factor of an anisotropic material as a dimensionless measure of a closeness to a pure Cauchy material and a similar isotropic factor is as a measure for a closeness of an anisotropic material to its isotropic prototype. For cubic crystals, these factors are explicitly displayed and cubic crystal average of an arbitrary elastic material is derived.
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 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.
Shrinking the quadratic estimator of weak lensing
NASA Astrophysics Data System (ADS)
Anderes, Ethan; Paul, Debashis
2012-05-01
We study a regression characterization for the quadratic estimator of weak lensing, developed by Hu and Okamoto [W. Hu, Astrophys. J. 557, L79 (2001).ASJOAB0004-637X10.1086/323253][W. Hu and T. Okamoto, Astrophys. J. 574, 566 (2002).ASJOAB0004-637X10.1086/341110][T. Okamoto and W. Hu, Phys. Rev. DPRVDAQ0556-2821 67, 083002 (2003).10.1103/PhysRevD.67.083002], for cosmic microwave background observations. This characterization motivates a modification of the quadratic estimator by an adaptive Wiener filter which uses the robust Bayesian techniques described in [J. Berger, Ann. Stat.ASTSC70090-5364 8, 716 (1980).10.1214/aos/1176345068][J. Berger, Statistical Decision Theory and Bayesian Analysis (Springer, New York, 1980).][W. Strawderman, Ann. Stat.ASTSC70090-5364 42, 385 (1971).10.1214/aoms/1177693528]. This technique requires the user to propose a fiducial model for the spectral density of the unknown lensing potential but the resulting estimator is developed to be robust to mis-specification of this model. The role of the fiducial spectral density is to give the estimator superior statistical performance in a “neighborhood of the fiducial model” while controlling the statistical errors when the fiducial spectral density is drastically wrong. Our estimate also highlights some advantages provided by a Bayesian analysis of the quadratic estimator.
Numerical solution of quadratic matrix equations for free vibration analysis of structures
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1975-01-01
This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.
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
2015-01-01
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A2MSiO4 with A?=?Li or Na and M?=?Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. These structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs. PMID:26497381
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme
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.
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.
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
O'Connell, T P; Malthouse, J P
1995-01-01
Subtilisin and delta-chymotrypsin have been alkylated using 2-13C-enriched benzyloxycarbonylglycylglycylphenylalanylchloromethane. A single signal due to the 13C-enriched carbon was detected in both the intact subtilisin and delta-chymotrypsin derivatives. The signal titrated from 98.9 p.p.m. to 103.6 p.p.m. with a pKa value of 6.9 in the subtilisin derivative and it is assigned to a tetrahedral adduct formed between the hydroxy group of serine-221 and the inhibitor. The signal in the delta-chymotrypsin derivative titrated from 98.5 p.p.m. to 103.2 p.p.m. with a pKa value of 8.92 and it is assigned to a tetrahedral adduct formed between the hydroxy group of serine-195 and the inhibitor. In both derivatives the titration shift is assigned to the formation of the oxyanion of the tetrahedral adduct. delta-Chymotrypsin has been inhibited by benzyloxycarbonylphenylalanylchloromethane and two signals due to 13C-enriched carbons were detected. One of these signals titrated from 98.8 p.p.m. to 103.6 p.p.m. with a pKa value of 9.4 and it was assigned in the same way as in the previous delta-chymotrypsin derivative. The second signal had a chemical shift of 204.5 +/- 0.5 p.p.m. and it did not titrate from pH 3.5 to 9.0. This signal was assigned to alkylated methionine-192. We discuss how subtilisin and chymotrypsin could stabilize the oxyanion of tetrahedral adducts. PMID:7733869
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.
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.
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.
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 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
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.
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.
De Sitter stability in quadratic gravity
A. V. Toporensky; P. V. Tretyakov
2006-12-29
Quadratic curvature corrections to Einstein-Hilbert action lead in general to higher-order equations of motion, which can induced instability of some unperturbed solutions of General Relativity. We study conditions for stability of de Sitter cosmological solution. We argue that simple form of this condition known for FRW background in 3+1 dimensions changes seriously if at least one of these two assumptions is violated. In the present paper the stability conditions for de Sitter solution have been found for multidimensional FRW background and for Bianchi I metrics in 3+1 dimensions.
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.
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.
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
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.
R. M. Ferrer; Y. Y. Azmy
2009-05-01
We present a robust arbitrarily high order transport method of the characteristic type for unstructured tetrahedral grids. Previously encountered difficulties have been addressed through the reformulation of the method based on coordinate transformations, evaluation of the moments balance relation as a linear system of equations involving the expansion coefficients of the projected basis, and the asymptotic expansion of the integral kernels in the thin cell limit. The proper choice of basis functions for the high-order spatial expansion of the solution is discussed and its effect on problems involving scattering discussed. Numerical tests are presented to illustrate the beneficial effect of these improvements, and the improved robustness they yield.
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.
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.
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.
Compact stars with quadratic equation of state
NASA Astrophysics Data System (ADS)
Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi
2015-05-01
We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.
CPHD filters with unknown quadratic clutter generators
NASA Astrophysics Data System (ADS)
Mahler, Ronald
2015-05-01
Previous research has produced CPHD filters that can detect and track multiple targets in unknown, dynamically changing clutter. The .first such filters employed Poisson clutter generators and, as a result, were combinatorially complex. Recent research has shown that replacing the Poisson clutter generators with Bernoulli clutter generators results in computationally tractable CPHD filters. However, Bernoulli clutter generators are insufficiently complex to model real-world clutter with high accuracy, because they are statistically first-degree. This paper addresses the derivation and implementation of CPHD filters when first-degree Bernoulli clutter generators are replaced by second-degree quadratic clutter generators. Because these filters are combinatorially second-order, they are more easily approximated. They can also be implemented in exact closed form using beta-Gaussian mixture (BGM) or Dirichlet-Gaussian mixture (DGM) techniques.
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.
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…
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.)
Analysis of Students' Error in Learning of Quadratic Equations
ERIC Educational Resources Information Center
Zakaria, Effandi; Ibrahim; Maat, Siti Mistima
2010-01-01
The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…
GLOBAL OPTIMALITY CONDITIONS FOR QUADRATIC OPTIMIZATION PROBLEMS WITH BINARY CONSTRAINTS
Beck, Amir
GLOBAL OPTIMALITY CONDITIONS FOR QUADRATIC OPTIMIZATION PROBLEMS WITH BINARY CONSTRAINTS AMIR BECK main result identifies a class of quadratic problems for which a given feasible point is global optimal. We also establish a necessary global optimality condition. These conditions are expressed in a simple
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...
THE PARALLELIZED POLLARD KANGAROO METHOD IN REAL QUADRATIC FUNCTION FIELDS
Bernstein, Daniel
THE PARALLELIZED POLLARD KANGAROO METHOD IN REAL QUADRATIC FUNCTION FIELDS ANDREAS STEIN AND EDLYN TESKE Abstract. We show how to use the parallelized kangaroo method for computing invariants in real quadratic function #12;elds. Speci#12;cally, we show how to apply the kangaroo method to the infrastructure
Universally Anonymous IBE based on the Quadratic Residuosity Giuseppe Ateniese
International Association for Cryptologic Research (IACR)
Universally Anonymous IBE based on the Quadratic Residuosity Assumption Giuseppe Ateniese Johns introduce the first universally anonymous, thus key-private, IBE whose security is based on the standard quadratic residuosity assumption. Our scheme is a variant of Cocks IBE (which is not anonymous
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.
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
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
Neyrinck, Mark C
2015-01-01
We discuss an idealized model of halo formation, in which a collapsing halo node is tetrahedral, with a filament extruding from each of its four faces, and with a wall connecting each pair of filaments. In the model, filaments generally spin when they form, and the halo spins if and only if there is some rotation in filaments. This is the simplest-possible fully three-dimensional halo collapse in the 'origami approximation,' in which voids are irrotational, and the dark-matter sheet out of which dark-matter structures form is allowed to fold in position-velocity phase space, but not stretch (i.e., it cannot vary in density along a stream). Up to an overall scaling, the four filament directions, and only three other quantities, such as filament spins, suffice to determine all of the collapse's properties: the shape, mass, and spin of the halo; the densities per unit length and spins of all filaments; and masses per unit area of the walls. If the filaments are arranged regular-tetrahedrally, filament properties...
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.
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.
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.
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.
Are ghost surfaces quadratic-flux-minimizing?
S. R. Hudson; R. L. Dewar
2010-01-02
Two candidates for "almost-invariant" toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, $\\oint \\vec{A}\\cdot\\mathbf{dl}$. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other $1{1/2}$ degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.
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.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1986-01-01
An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.
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.
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.
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.
Single walled carbon nanotube network—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 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 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.
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.
The period function of reversible quadratic centers
NASA Astrophysics Data System (ADS)
Mardeši?, P.; Marín, D.; Villadelprat, J.
In this paper we investigate the bifurcation diagram of the period function associated to a family of reversible quadratic centers, namely the dehomogenized Loud's systems. The local bifurcation diagram of the period function at the center is fully understood using the results of Chicone and Jacobs [C. Chicone, M. Jacobs, Bifurcation of critical periods for plane vector fields, Trans. Amer. Math. Soc. 312 (1989) 433-486]. Most of the present paper deals with the local bifurcation diagram at the polycycle that bounds the period annulus of the center. The techniques that we use here are different from the ones in [C. Chicone, M. Jacobs, Bifurcation of critical periods for plane vector fields, Trans. Amer. Math. Soc. 312 (1989) 433-486] because, while the period function extends analytically at the center, it has no smooth extension to the polycycle. At best one can hope that it has some asymptotic expansion. Another major difficulty is that the asymptotic development has to be uniform with respect to the parameters, in order to prove that a parameter is not a bifurcation value. We study also the bifurcations in the interior of the period annulus and we show that there exist three germs of curves in the parameter space that correspond to this type of bifurcation. Moreover we determine some regions in the parameter space for which the corresponding period function has at least one or two critical periods. Finally we propose a complete conjectural bifurcation diagram of the period function of the dehomogenized Loud's systems. Our results can also be viewed as a contribution to the proof of Chicone's conjecture [C. Chicone, review in MathSciNet, ref. 94h:58072].
On a 'Mysterious' Case of a Quadratic Hamiltonian
Sergei Sakovich
2006-07-28
We show that one of the five cases of a quadratic Hamiltonian, which were recently selected by Sokolov and Wolf who used the Kovalevskaya-Lyapunov test, fails to pass the Painleve test for integrability.
Post-Newtonian, quasicircular binary inspirals in quadratic modified gravity
Stein, Leo Chaim
We consider a general class of quantum gravity-inspired, modified gravity theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to scalar fields ...
TWOPRIMARY ALGEBRAIC KTHEORY OF SOME QUADRATIC AND CYCLOTOMIC NUMBER RINGS
.5 that these are all simple when q #= 29 is an odd prime power with #(q) # 66, or a Sophie Germain prime, such that 2 and phrases. Algebraic KÂgroups, quadratic number fields, cyclotomic number fields, Sophie Germain primes
An efficiently solvable quadratic program for stabilizing dynamic locomotion
Kuindersma, Scott
We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while ...
DIAGONAL QUADRATIC APPROXIMATION FOR PARALLEL COMPUTING WITH ANALYTICAL TARGET CASCADING
Michalek, Jeremy J.
for convergence of the ATC inner loop . 10 4. Quadratic penalty method flow chart . . . . . . . . . . . . . . . . . . . 13 5. Ordinary Lagrangian method flow chart . . . . . . . . . . . . . . . . . 16 6. Augmented Lagrangian method flow chart . . . . . . . . . . . . . . . . 20 7. Augmented Lagrangian with alternating
Controlling the disorder properties of quadratic nonlinear photonic crystals
Arie, Ady
Controlling the disorder properties of quadratic nonlinear photonic crystals Idith Varon,* Gil demonstrate a modulation scheme for disordered nonlinear crystals that combines periodic modulation and disordered sections. The crystal is divided into a set of identical periodically poled building blocks
GENERATORS AND RELATIONS FOR K2OF , F IMAGINARY QUADRATIC
of integers* * in a number field has been adapted for the computer and gives explicit gene* *rators manipulations_to complete the analysis for the six first imaginary quadratic cases (i.e. the ones of smallest
A method of Weil sum in multivariate quadratic cryptosystem
Harayama, Tomohiro
2007-09-17
A new cryptanalytic application is proposed for a number theoretic tool Weil sum to the birthday attack against multivariate quadratic trapdoor function. This new customization of the birthday attack is developed by evaluating the explicit Weil sum...
Espinosa, Horacio D.
Elasticity, strength, and toughness of single crystal silicon carbide, ultrananocrystalline diamond report the mechanical properties of three emerging materials in thin film form: single crystal silicon carbide 3C-SiC , ultrananocrystalline diamond, and hydrogen-free tetrahedral amorphous carbon
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)
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
Catalytic Role of Proton Transfers in the Formation of a Tetrahedral Adduct in a Serine Carboxyl-acetyl-isoleucyl-prolyl- phenylalaninal (AcIPF) in a serine-carboxyl peptidase (kumamolisin-As) and elucidate the role of proton transfers-carboxyl peptidases have a fold resembling that of subtilisin, the proton transfer processes during the nucleophilic
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.
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.
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.
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.
Jiri Soucek
2010-08-26
In the paper the basic concepts of extended probability theory are introduced. The basic idea: the concept of an event as a subset of \\Omega is replaced with the concept of an event as a partition. The partition is any set of disjoint non-empty subsets of \\Omega (i.e. partition=subset+its decomposition). Interpretation: elements inside certain part are indistinguishable, while elements from different parts are distinguishable. There are incompatible events, e.g {{e1},{e2}} and {{e1,e2}}. This is logical incompatibility analogical to the impossibility to have and simultaneously not to have the which-way information in the given experiment. The context is the maximal set of mutually compatible events. Each experiment has associated its context. In each context the extended probability is reduced to classical probability. Then the quadratic representation of events, partitions and probability measures is developed. At the end the central concept of quadratic probability spaces (which extend Kolmogorov probability spaces) is defined and studied. In the next paper it will be shown that quantum mechanics can be represented as the theory of Markov processes in the extended probability theory (Einstein's vision of QM).
NASA Astrophysics Data System (ADS)
Khoreshok, A. A.; Mametyev, L. E.; Borisov, A. Yu; Vorobyev, A. V.
2015-09-01
Presents the results of modeling the stress-strain state in the mating structural elements of the attachment disk tools various design on triangular and tetrahedral prisms working bodies of roadheaders selective action in the destruction of coalface of heterogeneous structure.
A priori mesh quality metric error analysis applied to a high-order finite element method
A priori mesh quality metric error analysis applied to a high-order finite element method W. Lowrie-order finite element simulations. Most of the research to date has either been with finite volume methods [68] or linear finite element methods [13,9,5], though more recently quadratic finite elements have also been
Theory of transformation for the diagonalization of quadratic Hamiltonians
Ming-wen Xiao
2009-08-06
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and Bogoliubov-Valatin transformations, and thus provides us an operational procedure to answer, in a direct manner, the questions as to whether a quadratic Hamiltonian is diagonalizable, whether the diagonalization is unique, and how the transformation can be constructed if the diagonalization exists. The underlying idea is to consider the dynamic matrix. Each quadratic Hamiltonian has a dynamic matrix of its own. The eigenvalue problem of the dynamic matrix determines the diagonalizability of the quadratic Hamiltonian completely. In brief, the theory ascribes the diagonalization of a quadratic Hamiltonian to the eigenvalue problem of its dynamic matrix, which is familiar to all of us. That makes it much easy to use. Applications to various physical systems are discussed, with especial emphasis on the quantum fields, such as Klein-Gordon field, phonon field, etc..
Prehna,G.; Stebbins, E.
2007-01-01
The Rho family of small GTPases represent well characterized signaling molecules that regulate many cellular functions such as actin cytoskeletal arrangement and the cell cycle by acting as molecular switches. A Rac1-GDP-Zn complex has been crystallized in space group P3{sub 2}21 and its crystal structure has been solved at 1.9 {angstrom} resolution. These trigonal crystals reveal the unexpected ability of Rac1 to coordinate Zn atoms in a tetrahedral fashion by use of its biologically relevant switch I and switch II regions. Upon coordination of zinc, the switch I region is stabilized in the GDP-bound conformation and contributes to a Rac1 trimer in the asymmetric unit. Zinc coordination causes switch II to adopt a novel conformation with a symmetry-related molecule. Additionally, zinc was found to displace magnesium from its octahedral coordination at switch I, although GDP binding remained stable. This structure represents the first reported Rac1-GDP-Zn complex, which further underscores the conformational flexibility and versatility of the small GTPase switch regions.
Prehna, G.; Stebbins, C
2007-01-01
The Rho family of small GTPases represent well characterized signaling molecules that regulate many cellular functions such as actin cytoskeletal arrangement and the cell cycle by acting as molecular switches. A Rac1-GDP-Zn complex has been crystallized in space group P3221 and its crystal structure has been solved at 1.9 {angstrom} resolution. These trigonal crystals reveal the unexpected ability of Rac1 to coordinate Zn atoms in a tetrahedral fashion by use of its biologically relevant switch I and switch II regions. Upon coordination of zinc, the switch I region is stabilized in the GDP-bound conformation and contributes to a Rac1 trimer in the asymmetric unit. Zinc coordination causes switch II to adopt a novel conformation with a symmetry-related molecule. Additionally, zinc was found to displace magnesium from its octahedral coordination at switch I, although GDP binding remained stable. This structure represents the first reported Rac1-GDP-Zn complex, which further underscores the conformational flexibility and versatility of the small GTPase switch regions.
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.
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 99.1±3.9kbp. 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 4.37×10(3)OBs/ml occlusion bodies (OBs) per ml. The median survival time (ST50) was 181h at a dose of 1×10(6)OBs/ml and 167h at a dose of 1×10(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
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, 30?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
NASA Astrophysics Data System (ADS)
Yeo, Reuben J.; Dwivedi, Neeraj; Tripathy, S.; Bhatia, C. S.
2015-03-01
Developing ultrathin and highly wear-resistant overcoats for magnetic tape heads is one of the current research areas of interest, because of its potential to delay pole tip recession and increase the operational lifetime of high areal density tape drives. Using optimized process conditions and an appropriate overcoat design, we report on the development of a ˜20 nm thick silicon nitride/tetrahedral amorphous carbon (Si/SiNx/ta-C) bilayer overcoat, where the ta-C film was deposited by a filtered cathodic vacuum arc process. The bilayer overcoat deposited on a functional tape head survived 40-50 × 106 m of testing with commercial tape media under standard industrial testing conditions. The excellent wear resistance of the overcoat was attributed to the generation of high (˜72%) sp3 carbon content and the formation of strong interfacial bonds, such as Si-C, C=N, nitrile, and (Al, Ti)N at the interfaces, as confirmed by various spectroscopic techniques. This study demonstrates the pivotal role of high sp3 carbon bonding combined with enhanced interfacial bonding in developing an ultrathin yet durable protective overcoat for magnetic tape heads.
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.
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 notemore »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.« less
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 ? - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (V?)(A)?=??{sub X}?{sub X}P(x,y,A)d?(x)d?(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ? F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n??}?V{sup n?}(?) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel ? - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.
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
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.
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.
Frequency comb generation in quadratic nonlinear media
Ricciardi, Iolanda; Parisi, Maria; Maddaloni, Pasquale; Santamaria, Luigi; De Natale, Paolo; De Rosa, Maurizio
2014-01-01
Optical frequency combs are nowadays routinely used tools in a wide range of scientific and technological applications. Different techniques have been developed for generating optical frequency combs, like mode-locking in lasers and third-order interactions in microresonators, or to extend their spectral capabilities, using frequency conversion processes in nonlinear materials. Here, 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. We develop an elemental model which provides a deep physical insight into the observed dynamics. Moreover, 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. Finally, exploiting a nonlinearity intrinsically stronger than the third-order one, our work lays the groundw...
On Evgrafov-Fedoryuk's theory and quadratic differentials
NASA Astrophysics Data System (ADS)
Shapiro, Boris
2015-06-01
The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrödinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in -correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree the number of such accumulation rays can be any positive integer between and.
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Francisco M Fernández
2015-09-13
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.
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
NASA Astrophysics Data System (ADS)
Paiva Fonseca, Gabriel; Landry, Guillaume; White, Shane; D'Amours, Michel; Yoriyaz, Hélio; Beaulieu, Luc; Reniers, Brigitte; Verhaegen, Frank
2014-10-01
Accounting for brachytherapy applicator attenuation is part of the recommendations from the recent report of AAPM Task Group 186. To do so, model based dose calculation algorithms require accurate modelling of the applicator geometry. This can be non-trivial in the case of irregularly shaped applicators such as the Fletcher Williamson gynaecological applicator or balloon applicators with possibly irregular shapes employed in accelerated partial breast irradiation (APBI) performed using electronic brachytherapy sources (EBS). While many of these applicators can be modelled using constructive solid geometry (CSG), the latter may be difficult and time-consuming. Alternatively, these complex geometries can be modelled using tessellated geometries such as tetrahedral meshes (mesh geometries (MG)). Recent versions of Monte Carlo (MC) codes Geant4 and MCNP6 allow for the use of MG. The goal of this work was to model a series of applicators relevant to brachytherapy using MG. Applicators designed for 192Ir sources and 50?kV EBS were studied; a shielded vaginal applicator, a shielded Fletcher Williamson applicator and an APBI balloon applicator. All applicators were modelled in Geant4 and MCNP6 using MG and CSG for dose calculations. CSG derived dose distributions were considered as reference and used to validate MG models by comparing dose distribution ratios. In general agreement within 1% for the dose calculations was observed for all applicators between MG and CSG and between codes when considering volumes inside the 25% isodose surface. When compared to CSG, MG required longer computation times by a factor of at least 2 for MC simulations using the same code. MCNP6 calculation times were more than ten times shorter than Geant4 in some cases. In conclusion we presented methods allowing for high fidelity modelling with results equivalent to CSG. To the best of our knowledge MG offers the most accurate representation of an irregular APBI balloon applicator.
The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry
Eva G. Noya; Carlos Vega; Jonathan P. K. Doye; Ard A. Louis
2010-05-28
The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values for the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centred-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centred-cubic crystal becomes more stable than the body-centred-cubic crystal, and at higher temperatures a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centred-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centred-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centred-cubic crystal and between the fluid and the diamond crystal show that, at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles.
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.
Octahedral-tetrahedral equilibrium and solvent exchange of cobalt(II) ions in primary alkylamines.
Aizawa, Sen-ichi; Funahashi, Shigenobu
2002-08-26
The enthalpy differences (Delta H degrees ) of the equilibrium between the octahedral and tetrahedral solvated cobalt(II) complexes were obtained in some primary alkylamines such as propylamine (pa, 36.1 +/- 2.3 kJ mol(-1)), n-hexylamine (ha, 34.9 +/- 1.0 kJ mol(-1)), 2-methoxyethylamine (meea, 44.8 +/- 3.1 kJ mol(-1)), and benzylamine (ba, 50.1 +/- 3.6 kJ mol(-1)) by the spectrophotometric method. The differences in the energy levels between the two geometries of the cobalt(II) complexes in the spherically symmetric field (Delta E(spher)) were estimated from the values of Delta H degrees by offsetting the ligand field stabilization energies. It was indicated that the value of Delta E(spher) is the decisive factor in determining the value of Delta H degrees and is largely dependent on the electronic repulsion between the d-electrons and the donor atoms and the interelectronic repulsion in the d orbitals. The comparison between activation enthalpies (Delta H(++)) for the solvent exchange reactions of octahedral cobalt(II) ions in pa and meea revealed that the unexpectedly large rate constant and small Delta H(++) in pa are attributed to the strong electronic repulsion in the ground state and removal of the electronic repulsion in the dissociative transition state, which can give the small Delta E(spher) between the ground and transition states. Differences in the solvent exchange rates and the DeltaH(++) values of the octahedral metal(II) ions in some other solvents are discussed in connection with the electronic repulsive factors. PMID:12184774
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.
Confidence set interference with a prior quadratic bound. [in geophysics
NASA Technical Reports Server (NTRS)
Backus, George E.
1989-01-01
Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.
FUNCTION DIGRAPHS OF QUADRATIC MAPS MODULO p Christie L. Gilbert
Reiter, Clifford A.
. Storey 218 Sparrow Drive, Wake Forest, NC 27587 USA 1. INTRODUCTION In this paper we will consider distinct up to isomorphism. In Section 3 we investigate what appear to be tight bounds on number of cycles. In Section 4 we empirically compare these quadratic digraphs to "random" digraphs and this motivates our
Quadratic stabilization and tracking - Applications to the benchmark problem
NASA Technical Reports Server (NTRS)
Schmitendorf, W. E.; Dolphus, R. M.; Benson, R. W.
1992-01-01
Recent results regarding quadratic stabilization and disturbance attenuation are applied to the benchmark problem. The authors investigate the minimum achievable levels of disturbance attenuation for different disturbance inputs and controlled outputs. They then design a feedforward tracking controller which tracks step inputs while maintaining the disturbance attenuation properties of the regulator.
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…
Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses
Wlodek Bryc; Jacek Wesolowski
2015-11-03
We establish a correspondence between a family of Markov processes called quadratic harnesses and a family of finite state asymmetric exclusion processes with open boundaries. As applications, we give a quick proof of the large deviations principle for the total number of particles in the system, and show how explicit formulas for the average occupancy of a site arise for special choices of parameters.
Contingency Simulation Using Single Phase Quadratized Power Flow
methods based on the traditional power flow (TPF) model usually suffer from lack of the realistic system it provides accurate power flow solutions, this procedure, which involves a huge number of AC load flowContingency Simulation Using Single Phase Quadratized Power Flow Fang Yang, Student Member, IEEE, A
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 lowest…
Quadratic Programming and Impedance Control for Transfemoral Prosthesis
Ames, Aaron
Quadratic Programming and Impedance Control for Transfemoral Prosthesis Huihua Zhao, Shishir of improving both tracking performance and the stability of controllers implemented on transfemoral prosthesis prosthesis is attached to a robotic testbed, AMBER. The authors claim that the walking of AMBER is human like
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.
Front velocity in models with quadratic autocatalysis Vladimir K. Vanaga)
Epstein, Irving R.
Front velocity in models with quadratic autocatalysis Vladimir K. Vanaga) and Irving R. Epstein the dependence of the front velocity on the diffusion coefficients of X and R, the interconversion rates diffusion coef- ficients of X and R, DX and DR , respectively, raise the ques- tion of how the velocity
About Zhang's premodels for Siegel disks of quadratic rational maps.
Chéritat, Arnaud
About Zhang's premodels for Siegel disks of quadratic rational maps. Arnaud Ch´eritat CNRS, Univ. Toulouse Feb. 2011 A. Ch´eritat (CNRS, UPS) About Zhang's premodels Feb. 2011 1 / 33 #12;Let us show) About Zhang's premodels Feb. 2011 2 / 33 #12;A. Ch´eritat (CNRS, UPS) About Zhang's premodels Feb. 2011
Robustness of quadratic hedging strategies in finance via Fourier transforms
Vanmaele, Michèle
consider two models for the stock price process. The first model is a geometric L´evy process in which the robustness of the quadratic hedging strategies we use pricing and hedging formulas based on Fourier transform technically be performed under a related pricing measure that is a risk-neutral measure. Under this measure
Root Refinement for Real Polynomials using Quadratic Interval Refinement
Waldmann, Uwe
Root Refinement for Real Polynomials using Quadratic Interval Refinement Michael Kerber MPI consider the problem of approximating all real roots of a square-free polyno- mial f with real coefficients. Given isolating intervals for the real roots and an arbitrary positive integer L, the task
Spectral pulse transformations and phase transitions in quadratic nonlinear
. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveg- uide latticesSpectral pulse transformations and phase transitions in quadratic nonlinear waveguide arrays Frank, Germany 2Nonlinear Physics Centre, RSPE, Australian National University, Canberra, ACT 0200, Australia 3
A QUADRATIC TIME ALGORITHM FOR THE MINMAX LENGTH TRIANGULATION
Tan, Tiow Seng
A QUADRATIC TIME ALGORITHM FOR THE MINMAX LENGTH TRIANGULATION HERBERT EDELSBRUNNER \\Lambda AND TIOW SENG TAN y Abstract. We show that a triangulation of a set of n points in the plane that minimizes and is based on the theorem that there is a triangulation with minmax edge length that contains the relative
A QUADRATIC TIME ALGORITHM FOR THE MINMAX LENGTH TRIANGULATION
Tan, Tiow Seng
A QUADRATIC TIME ALGORITHM FOR THE MINMAX LENGTH TRIANGULATION HERBERT EDELSBRUNNER AND TIOW SENG TANy Abstract. We show that a triangulation of a set of n points in the plane that minimizes and is based on the theorem that there is a triangulation with minmax edge length that contains the relative
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)
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.
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.
Mesh considerations for finite element blast modelling in biomechanics.
Panzer, Matthew B; Myers, Barry S; Bass, Cameron R
2013-01-01
Finite element (FE) modelling is a popular tool for studying human body response to blast exposure. However, blast modelling is a complex problem owing to more numerous fluid-structure interactions (FSIs) and the high-frequency loading that accompanies blast exposures. This study investigates FE mesh design for blast modelling using a sphere in a closed-ended shock tube meshed with varying element sizes using both tetrahedral and hexahedral elements. FSI was consistent for sphere-to-fluid element ratios between 0.25 and 4, and acceleration response was similar for both element types (R(2) = 0.997). Tetrahedral elements were found to become increasingly volatile following shock loading, causing higher pressures and stresses than predicted with the hexahedral elements. Deviatoric stress response was dependent on the sphere mesh size (p < 0.001), while the pressure response was dependent on the shock tube mesh size (p < 0.001). The results of this study highlight the necessity for mesh sensitivity analysis in blast models. PMID:22185582
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.
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 ...
Implementation of an Evolving non Quadratic Anisotropic Behaviour for the Closed Packed Materials
Revil-Baudard, Benoit; Massoni, Elisabeth
2010-06-15
In this paper, the mechanical behaviour of alpha-titanium alloys is modelised for the cold forming processes. The elasto-plastic constitutive law is decomposed in an anisotropic plastic criterion, an isotropic hardening and a kinematic hardening. Non quadratic criteria have been developed by Cazacu et al.[1], to model the plasticity of hexagonal closed packed materials. The implementation of this model in a finite element software switch between two bases, the equilibrium is calculated in a reference basis and the anisotropy axes define a local basis, updated by the deformation gradient. An identification procedure, based on tensile tests, allows defining all the parameters needed to model the elasto-plastic behaviour. Simulations of cold forming processes (bulging and deep drawing) have been done to validate this model. Numerical results are compared with experimental data, obtained from speckles analysis.
Papalambros, Panos
Performance Enhancement of Bandgap Printed Antennas Using Finite Element Method and Size with antenna simulators based on the finite element and sequential quadratic programming method or genetic this task. In the topology optimization methods, the design domain is discretized into finite elements
Some Connections Between Primitive Roots and Quadratic Non-Residues Modulo a Prime
International Association for Cryptologic Research (IACR)
Some Connections Between Primitive Roots and Quadratic Non-Residues Modulo a Prime Sorin Iftene--In this paper we present some interesting connec- tions between primitive roots and quadratic non-residues--primitive roots, Legendre-Jacobi symbol, quadratic non-residues, square roots. I. INTRODUCTION Generating
On the distribution of quadratic residues and nonresidues modulo a prime number
Peralta, Rene
On the distribution of quadratic residues and nonresidues modulo a prime number Ren'e Peralta #12; Proposed running head : ``quadratic residues mod P ''. corresponding author: Ren'e Peralta the implications of this bound on the number of occurrences of arbitrary patterns of quadratic residues
Alignment-orientation conversion by quadratic Zeeman effect: Analysis and observation for Te2
Auzinsh, Marcis
Alignment-orientation conversion by quadratic Zeeman effect: Analysis and observation for Te2 I. P momenta into orientation due to quadratic correction to Zeeman effect. Circularity rate up to 0 of the quadratic correction to the Zeeman effect in diatomic mol- ecules. In particular, we direct now our
Hu, Tingshu
Nonlinear Control Design for Linear Differential Inclusions via Convex Hull Quadratic Lyapunov-quadratic Lyapunov function, the convex hull quadratic function, will be used for the construction of nonlinear state effectively by combining the path- following algorithm and the direct iterative algorithm. The design results
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...
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.
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.
NASA Astrophysics Data System (ADS)
Kaarour, A.; Ouardi, O.; Meskine, M.
2015-03-01
The use of tensor models adapted to tetrahedral molecules such CH4, SiH4, GeH4... that use mathematical tools (group theory, irreducible tensor operators) and the characteristics of symmetrical molecules, gives good results. Starting from an experimental spectrum, we can calculate some parameters of the Hamiltonian and consequently the energy levels. Once the line positions are determined, we calculate the parameters of the dipole moment of these molecules and consequently the rovibrational intensities. Both software STDS and SPVIEW, we determined the parameters of the Hamiltonian and those of the dipole moment.
Spinor condensates with a laser-induced quadratic Zeeman effect
Santos, L.; Fattori, M.; Stuhler, J.; Pfau, T.
2007-05-15
We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate {sup 52}Cr gas, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein-de Haas effect for relatively large magnetic fields, and may be employed to create S=1/2 systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exciting new control tool in spinor systems.
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)].
Nonlinear coupling in discrete optical waveguide arrays with quadratic nonlinearity
NASA Astrophysics Data System (ADS)
Setzpfandt, Frank; Sohler, Wolfgang; Schiek, Roland; Pertsch, Thomas
2015-10-01
We demonstrate nonlinear coupling in a discrete optical system. This is achieved in waveguide arrays with quadratic nonlinearity, where the symmetries of the nonlinearly interacting waveguide modes are used to suppress the usually dominating nonlinear effects within individual waveguides. We derive a mathematical model to describe the nonlinear coupling in such waveguide arrays and show experimentally the profound effects of this nonlinear coupling mechanism on second-harmonic generation.
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.
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.
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.
Central Control, Sewers and (0,1) quadratic programming
NASA Astrophysics Data System (ADS)
Kolechkina, Alla; van Nooijen, Ronald
2013-04-01
We consider small sewer systems that combine foul water and storm water sewer functions in flat terrain. These systems are a combination of local gravity flow networks connected by pumps. The pumps are usually fixed speed, so they are on or off. We formulate a (0,1) quadratic programming problem, provide an overview of known solution methods and examine the relative speed of different solution methods.
Gravitational instantons with faster than quadratic curvature decay (II)
Gao Chen; Xiuxiong Chen
2015-08-31
This is our second paper in a series to study gravitational instantons, i.e. complete hyperk\\"aler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models can be improved automatically. 2.Any ALF-D_k gravitational instanton must be the Cherkis-Hitchin-Ivanov-Kapustin-Lindstr\\"om-Ro\\v{c}ek metric.
FRW in quadratic form of $f(T)$ gravitational theories
G. G. L. Nashed
2015-06-26
We derive asymptote solution of a homogeneous and isotropic universe governed by the quadratic form of the field equation of $f(T)$ gravity. We explain how the higher order of the torsion can provide an origin for late accelerated phase of the universe in the FRW. The solution makes the scalar torsion $T$ to be a function of the cosmic time $t$. We show that for the equation of state $p=\\omega \\rho$ with $\\omega\
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 momentum dependence in the nucleon-nucleon interaction
R. B. Wiringa; A. Arriaga; V. R. Pandharipande
2003-09-05
We investigate different choices for the quadratic momentum dependence required in nucleon-nucleon potentials to fit phase shifts in high partial-waves. In the Argonne v18 potential L**2 and (L.S)**2 operators are used to represent this dependence. The v18 potential is simple to use in many-body calculations since it has no quadratic momentum-dependent terms in S-waves. However, p**2 rather than L**2 dependence occurs naturally in meson-exchange models of nuclear forces. We construct an alternate version of the Argonne potential, designated Argonne v18pq, in which the L**2 and (L.S)**2 operators are replaced by p**2 and Qij operators, respectively. The quadratic momentum-dependent terms are smaller in the v18pq than in the v18 interaction. Results for the ground state binding energies of 3H, 3He, and 4He, obtained with the variational Monte Carlo method, are presented for both the models with and without three-nucleon interactions. We find that the nuclear wave functions obtained with the v18pq are slightly larger than those with v18 at interparticle distances < 1 fm. The two models provide essentially the same binding in the light nuclei, although the v18pq gains less attraction when a fixed three-nucleon potential is added.
Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations
Holger R. Dullin; James D. Meiss
2008-07-04
We study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R^3. This family is the unfolded normal form for a bifurcation of a fixed point with a triple-one multiplier and also is the general form of a quadratic three-dimensional map with a quadratic inverse. Much of the nontrivial dynamics of this map occurs when its two fixed points are saddle-foci with intersecting two-dimensional stable and unstable manifolds that bound a spherical ``vortex-bubble''. We show that this occurs near a saddle-center-Neimark-Sacker (SCNS) bifurcation that also creates, at least in its normal form, an elliptic invariant circle. We develop a simple algorithm to accurately compute these elliptic invariant circles and their longitudinal and transverse rotation numbers and use it to study their bifurcations, classifying them by the resonances between the rotation numbers. In particular, rational values of the longitudinal rotation number are shown to give rise to a string of pearls that creates multiple copies of the original spherical structure for an iterate of the map.
Concerning Quadratic Interaction in the Quantum Cheshire Cat Experiment
W. M. Stuckey; Michael Silberstein; Timothy McDevitt
2015-11-04
In a July 2014 Nature Communications paper, Denkmayr et al. claim to have instantiated the so-called quantum Cheshire Cat experiment using neutron interferometry. Crucial to this claim are the weak values which must imply the quantum Cheshire Cat interpretation, i.e., "the neutron and its spin are spatially separated" in their experiment. While they measured the correct weak values for the quantum Cheshire Cat interpretation, the corresponding implications do not obtain because, as we show, those weak values were measured with both a quadratic and a linear magnetic field Bz interaction. We show explicitly how those weak values imply quantum Cheshire Cat if the Bz interaction is linear and then we show how the quadratic Bz interaction destroys the quantum Cheshire Cat implications of those weak values. Since both linear and quadratic Bz interactions contribute equally to the neutron intensity in this experiment, the deviant weak value implications are unavoidable. Because weak values were used successfully to compute neutron intensities for weak Bz in this experiment, it is clearly the case that one cannot make ontological inferences from weak values without taking into account the corresponding interaction strength.
NASA Astrophysics Data System (ADS)
Jenkins, D. M.; Lei, J.
2013-12-01
The sodium content in the M4 site of amphibole (BNa) was calibrated by Brown (1977, J Petrol, 18, 53-72) in a study that continues to be highly cited to this day. This study, based on empirical observations of amphibole compositional changes in the presence of the buffering assemblage plagioclase, chlorite, epidote, iron oxide, and water, demonstrated a systematic variation in the BNa and tetrahedral Al (TAl) content with pressure. Recent experimental work in this lab aimed at defining the extent of miscibility along the tremolite-glaucophane and hornblende-glaucophane joins in the Na2O-CaO-MgO-Al2O3-SiO2-H2O system has provided some additional information on the cation mixing along these joins. These joins also serve as the chemically-simplified framework of the BNa versus TAl correlation reported by Brown (1977). There are now sufficient, though still a bare minimum, of experimentally-confirmed mixing data for sodium-rich amphiboles to test this correlation and for quantifying the pressure-temperature (P-T) dependence of amphibole compositions in metamafic rocks relevant to subduction zones. From experimental results obtained over the range of 500-800°C, 1.5-2.0 GPa, and using a variety of amphibole synthesis and re-equilibration methods, the following set of asymmetric formalism (ASF) macroscopic interaction and mixing parameters have been derived that can be used with THERMOCALC dataset 55: Wtrgl = 70 kJ, Wglts = Wtrts =20 kJ, ?(tr) = 1.0, ?(ts) = 1.2, and ?(gl) = 0.52. Using a fixed MORB bulk composition, the composition of amphiboles within the P-T stability field of the buffering assemblage were calculated for the above chemical system with FeO added (i.e., NCFMASH) over the range of 0.2 - 2.0 GPa and 400 - 700°C. The following main observations can be made. First, the empirical amphibole compositions at low TAl and high BNa contents are well modeled by the miscibility gap in the amphibole ternary sub-system tremolite-glaucophane-tschermakite, particularly at temperatures of about 500-550°C. Second, amphiboles close to glaucophane in composition from the Shuksan metamorphic unit in the North Cascades of Washington are closely modeled by amphiboles equilibrated at about 1.0 GPa and 450°C. Third, the amphibole compositions from the Sanbagawa terrane, Japan, are modeled by the high-TAl members of coexisting low- and high TAl amphiboles (i.e., actinolite/winchite-barroisite) at 550-575°C with the compositions varying strongly with pressure (1.0-1.7 GPa), as opposed to the constant pressure proposed originally by Brown (1977). Better quantification of the BNa versus TAl variations in calcium-sodium requires improved knowledge of thermochemical properties and mixing of Fe2+ - and Fe3+ -bearing sodic amphiboles, for which there are still few experimental constraints, but these initial calculations provide important constraints on this classic diagram.
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.
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.
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 Mn??xZnxO alloys. At Zn compositions above x ? 0.3, thin films ofmore »these alloys assume the tetrahedral wurtzite structure instead of the octahedral rocksalt structure of MnO, thereby enabling semiconductor properties that are unique among transition metal oxides, i.e., a band gap within the visible spectrum, a band-transport mechanism for both electron and hole carriers, electron doping, and a band lineup suitable for solar hydrogen generation. A proof of principle is provided by initial photo-electrocatalytic device measurements, corroborating, in particular, the predicted favorable hole-transport properties of these alloys.« less
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.
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;
Discrete Calculus of Variations for Quadratic Lagrangians. Convergence Issues
Ryckelynck, Philippe
2011-01-01
We study in this paper the continuous and discrete Euler-Lagrange equations arising from a quadratic lagrangian. Those equations may be thought as numerical schemes and may be solved through a matrix based framework. When the lagrangian is time-independent, we can solve both continuous and discrete Euler-Lagrange equations under convenient oscillatory and non-resonance properties. The convergence of the solutions is also investigated. In the simplest case of the harmonic oscillator, unconditional convergence does not hold, we give results and experiments in this direction.
High Resolution Spectra of Novae and the Quadratic Zeeman Effect
Robert Williams; Elena Mason
2006-02-27
High resolution spectra of novae after outburst reveal distinctive characteristics in the line profiles and intensities. The higher Balmer lines are often broader than the lower members of the series, and the relative profiles and intensities of the [O I] \\lambda\\lambda6300, 6364 doublet differ from normal values. We suggest these features may be caused by the Quadratic Zeeman Effect from magnetic fields exceeding B=10^6 gauss. Taken together the emission and absorption lines point to multiple origins for the ejecta on both the erupting white dwarf and the cool secondary star.
The holographic entropy increases in quadratic curvature gravity
Srijit Bhattacharjee; Sudipta Sarkar; Aron C. Wall
2015-04-23
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is non stationary. 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.
The holographic entropy increases in quadratic curvature gravity
Bhattacharjee, Srijit; Wall, Aron
2015-01-01
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is non stationary. 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.
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.
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
Rigorous performance bounds for quadratic and nested dynamical decoupling
Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A.
2011-12-15
We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.
Toward Verification of USM3D Extensions for Mixed Element Grids
NASA Technical Reports Server (NTRS)
Pandya, Mohagna J.; Frink, Neal T.; Ding, Ejiang; Parlette, Edward B.
2013-01-01
The unstructured tetrahedral grid cell-centered finite volume flow solver USM3D has been recently extended to handle mixed element grids composed of hexahedral, prismatic, pyramidal, and tetrahedral cells. Presently, two turbulence models, namely, baseline Spalart-Allmaras (SA) and Menter Shear Stress Transport (SST), support mixed element grids. This paper provides an overview of the various numerical discretization options available in the newly enhanced USM3D. Using the SA model, the flow solver extensions are verified on three two-dimensional test cases available on the Turbulence Modeling Resource website at the NASA Langley Research Center. The test cases are zero pressure gradient flat plate, planar shear, and bump-inchannel. The effect of cell topologies on the flow solution is also investigated using the planar shear case. Finally, the assessment of various cell and face gradient options is performed on the zero pressure gradient flat plate case.
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
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
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
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.
Half-quadratic-based iterative minimization for robust sparse representation.
He, Ran; Zheng, Wei-Shi; Tan, Tieniu; Sun, Zhenan
2014-02-01
Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explores their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to performing both error correction and error detection. More specifically, by using the additive form of HQ, we propose an ?1-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative form of HQ, we propose an ?1-regularized error detection method by learning from uncorrupted data iteratively. We also show that the ?1-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the performance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings. PMID:24356348
Quadratic isocurvature cross-correlation, Ward identity, and dark matter
NASA Astrophysics Data System (ADS)
Chung, Daniel J. H.; Yoo, Hojin; Zhou, Peng
2013-06-01
Sources of isocurvature perturbations and large non-Gaussianities include field degrees of freedom whose vacuum expectation values are smaller than the expansion rate of inflation. The inhomogeneities in the energy density of such fields are quadratic in the fields to leading order in the inhomogeneity expansion. Although it is often assumed that such isocurvature perturbations and inflaton-driven curvature perturbations are uncorrelated, this is not obvious from a direct computational point of view due to the form of the minimal gravitational interactions. We thus compute the irreducible gravitational contributions to the quadratic isocurvature-curvature cross-correlation. We find a small but nondecaying cross-correlation, which in principle serves as a measurable prediction of this large class of isocurvature perturbations. We apply our cross-correlation result to two dark matter isocurvature perturbation scenarios: QCD axions and wimpzillas. On the technical side, we utilize a gravitational Ward identity in a novel manner to demonstrate the gauge invariance of the computation. Furthermore, the detailed computation is interpreted in terms of a soft-? theorem and a gravitational Ward identity. Finally, we also identify explicitly all the counterterms that are necessary for renormalizing the isocurvature perturbation composite operator in inflationary cosmological backgrounds.
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.
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.
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.
On a finite dynamic element method for free vibration analysis of structures
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1976-01-01
This paper explores the concept of finite dynamic elements involving higher order dynamic correction terms in the associated stiffness and mass matrices. Such matrices are then developed for a rectangular prestressed membrane element. Next, efficient analysis techniques for the eigenproblem solution of the resulting quadratic matrix equations are described in detail. These are followed by suitable numerical examples which indicate that employment of such dynamic elements in conjunction with an efficient quadratic matric solution technique will result in a most significant economy in the free vibration analysis of structures.
Minimal surface computation using a finite element method on an embedded surface
NASA Astrophysics Data System (ADS)
Cenanovic, Mirza; Hansbo, Peter; Larson, Mats G.
2015-11-01
We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is done on the piecewise planar isosurface using the shape functions from the background three dimensional mesh used to represent the distance function. A recently suggested stabilization scheme is a crucial component in the method.
and crosslinked polymers with diverse applications ranging from drug delivery2325 to electronics.26,27 Our groupsA ``click-based'' porous organic polymer from tetrahedral building blocks Prativa Pandey, Omar K and chemically stable ``click-based'' porous organic polymer with high surface area was synthesized from two
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.
Technology Transfer Automated Retrieval System (TEKTRAN)
Trace elements are defined as mineral elements that occur in living systems in micrograms per gram of body weight or less. Trace elements of greatest practical concern in human health are iodine, iron and zinc. Suggestive evidence is emerging that cobalt (as vitamin B12), copper, selenium, boron and...
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.
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.
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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.
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.
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
On global and local convergence of half-quadratic algorithms.
Allain, Marc; Idier, Jerôme; Goussard, Yves
2006-05-01
This paper provides original results on the global and local convergence properties of half-quadratic (HQ) algorithms resulting from the Geman and Yang (GY) and Geman and Reynolds (GR) primal-dual constructions. First, we show that the convergence domain of the GY algorithm can be extended with the benefit of an improved convergence rate. Second, we provide a precise comparison of the convergence rates for both algorithms. This analysis shows that the GR form does not benefit from a better convergence rate in general. Moreover, the GY iterates often take advantage of a low cost implementation. In this case, the GY form is usually faster than the GR form from the CPU time viewpoint. PMID:16671294
Active flutter suppression using eigenspace and linear quadratic design techniques
NASA Technical Reports Server (NTRS)
Garrard, W. L.; Liebst, B. S.
1983-01-01
Eigenspace (ES) and Linear Quadratic (LQ) techniques are used to design an active flutter suppression system for the DAST ARW-2 flight test vehicle. The performance of the ES and LQ controllers are very similar in meeting control surface activity specifications. The ES controller provides reduced wing root bending moment and shear but torsional stress is slightly higher than with the LQ controller. The ES controller also results in improved flutter boundaries compared with the LQ controller. The LQ controller exhibits significantly better phase margins at the flutter condition than does the ES controller but the LQ design requires large feedback gains on actuator states while the ES does not. This results in reduced overall actuator gain for the LQ design.
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.
Use of edge-based finite elements for solving three dimensional scattering problems
NASA Technical Reports Server (NTRS)
Chatterjee, A.; Jin, J. M.; Volakis, John L.
1991-01-01
Edge based finite elements are free from drawbacks associated with node based vectorial finite elements and are, therefore, ideal for solving 3-D scattering problems. The finite element discretization using edge elements is checked by solving for the resonant frequencies of a closed inhomogeneously filled metallic cavity. Great improvements in accuracy are observed when compared to the classical node based approach with no penalty in terms of computational time and with the expected absence of spurious modes. A performance comparison between the edge based tetrahedra and rectangular brick elements is carried out and tetrahedral elements are found to be more accurate than rectangular bricks for a given storage intensity. A detailed formulation for the scattering problem with various approaches for terminating the finite element mesh is also presented.
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.
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.
International Association for Cryptologic Research (IACR)
Yet another attack on a password authentication scheme based on quadratic residues with parameters proposed a password authentication scheme based on quadratic residues. However, in 1995, Chang, Wu and Laih residues. They claimed that their password authentication scheme can prevent the password from being
International Association for Cryptologic Research (IACR)
Yet another attack on a password authentication scheme based on quadratic residues with parameters proposed a password authentication scheme based on quadratic residues. However, in 1995, Chang, Wu and Laih residues. They claimed that their password authentication scheme can prevent the password from being
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…
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…
Chaotic solutions in the quadratic integrate-and-fire neuron with adaptation
models of integrate-and-fire type are commonly used to explore the dynamical properties of neuronsChaotic solutions in the quadratic integrate-and-fire neuron with adaptation Gang Zheng1 and Arnaud.Tonnelier@inrialpes.fr Abstract The quadratic integrate-and-fire (QIF) model with adaptation is commonly used as an elementary
Dislocation Parity Effects in Crystals with Quadratic Nonlinear Response Shani Sharabi,1,*
Arie, Ady
Dislocation Parity Effects in Crystals with Quadratic Nonlinear Response Shani Sharabi,1,* Noa 2014) The effect of edge topological dislocations on the phase matching spectrum of quadratic nonlinear of the dislocation's topological charge governs the transfer of energy between an input wave and its second harmonic
A Global Optimality Criterion for Nonconvex Quadratic Programming over a Ivo Nowak \\Lambda
Neumaier, Arnold
A Global Optimality Criterion for Nonconvex Quadratic Programming over a Simplex Ivo Nowak \\Lambda Abstract In this paper we propose a global optimality criterion for globally minimizing a quadratic form for checking the global optimality criterion and for computing the lower bound is reasonable. Numerical
A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
Vandenberghe, Lieven
, Stanford CA 94305 We consider nonlinear systems dx=dt = fxt where Dfxt is known to lie in the convex hull using convex programming techniques 1 . This paper de- scribes an algorithm that either nds a quadratic1 A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems L
MAXIMAL UNRAMIFIED EXTENSIONS OF IMAGINARY QUADRATIC NUMBER FIELDS OF SMALL CONDUCTORS
MAXIMAL UNRAMIFIED EXTENSIONS OF IMAGINARY QUADRATIC NUMBER FIELDS OF SMALL CONDUCTORS maximal unramified extensions Kur of imaginary quadratic number fields K * *of conductors5 420 (5 number one, the real abelian number fields of prime power conductors5 67 (see [56, Appendix]). For some
Blais, Brian
, and the quadratic form of BCM Brian S. Blais· N. Intrator H. Shouval Leon N Cooper Brown University Physics these with the quadratic form of BCM (Intrator and Cooper, 1992). By subjecting all of the learning rules to the same input
Bobrow, James E.
A Fast Sequential Linear Quadratic Algorithm for Solving Unconstrained Nonlinear Optimal Control a quadratic performance measure. We formulate the optimal control problem in discrete-time, but many-known necessary conditions for the optimal control. We also show that the algorithm is a Gauss-Newton method
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…
Are ghost-surfaces quadratic-flux minimizing? S.R. Hudsona
Hudson, Stuart
Are ghost-surfaces quadratic-flux minimizing? S.R. Hudsona and R.L. Dewarb aPrinceton Plasma through magnetic islands, namely quadratic-flux-minimizing (QFMIN) surfaces and ghost surfaces, use, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest
Dmitruk, A.V.
1994-12-31
For the control system {dot x} = f (x, t) + F (x, t)u a general optimal control problem is considered, involving terminal equality and inequality constraints, terminal functional to be minimized and a pointwise constraint u {element_of} U(t), where U(t) is a polyhedron. Given a singular extremal in this problem, necessary and sufficient conditions of a quadratic order {gamma} for a Pontryagin minimum are obtained. Here {gamma}({delta}x, {delta}u) is a quadratic function of estimation characteristics to this class of problems; it does`nt contain the control variations, but only variations of state variables. A Pontryagin minimum is an L{sub 1} - minimum with respect to the control on any uniformly bounded control set (thus, it allows to take needle-type variations of the control). The results are similar to those in the analysis and the classical calculus of variations in the sense that the necessary and sufficient conditions form an adjoining pair; the former transforms into the latter only by strengthening an inequality. These conditions include new Legendre type conditions, which take into account not only the second variations of Lagrange functions, but also their third variations and the admissible control set U (t).
Self-consistent linearization of non-linear BEM formulations with quadratic convergence
NASA Astrophysics Data System (ADS)
Fernandes, G. R.; de Souza Neto, E. A.
2013-11-01
In this work, a general technique to obtain the self-consistent linearization of non-linear formulations of the boundary element method (BEM) is presented. In the incremental-iterative procedure required to solve the non-linear problem the convergence is quadratic, being the solution obtained from the consistent tangent operator. This technique is applied to non-linear BEM formulations for plates where two independent problems are discussed: the plate bending and the stretching problem. For both problems an equilibrium equation is written in terms of strains and internal forces and then the consistent tangent operator is derived by applying the Newton-Raphson’s scheme. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness, although the presented formulations can be used with any non-linear model. Numerical examples are presented showing the accuracy of the results as well as the high convergence rate of the iterative procedure.
Geometry optimization with QM/MM methods II: Explicit quadratic coupling
NASA Astrophysics Data System (ADS)
Vreven, T.; Frisch, M. J.; Kudin, K. N.; Schlegel, H. B.; Morokuma, K.
2006-03-01
Geometry optimization of large QM/MM systems is usually carried out by alternating a second-order optimization of the QM region using internal coordinates ('macro-iterations'), and a first-order optimization of the MM region using Cartesian coordinates ('micro-iterations'), until self-consistency. However, the neglect of explicit coupling between the two regions (the Hessian elements that couple the QM coordinates with the MM coordinates) often interferes with a smooth convergence, while the Hessian update procedure can be unstable due to the presence of multiple minima in the MM region. A new geometry optimization scheme for QM/MM methods is proposed that addresses these problems. This scheme explicitly includes the coupling between the two regions in the QM optimization step, which makes it quadratic in the full space of coordinates. Analytical second derivatives are used for the MM contributions, with O(N) memory and CPU requirements (where N is the total number of atoms) by employing direct and fast multipole methods. The explicit coupling improves the convergence behaviour, while the Hessian update is stable since it no longer involves MM contributions. Examples show that the new procedure performs significantly better than the standard methods.
Mixed Element Type Unstructured Grid Generation for Viscous Flow Applications
NASA Technical Reports Server (NTRS)
Marcum, David L.; Gaither, J. Adam
2000-01-01
A procedure is presented for efficient generation of high-quality unstructured grids suitable for CFD simulation of high Reynolds number viscous flow fields. Layers of anisotropic elements are generated by advancing along prescribed normals from solid boundaries. The points are generated such that either pentahedral or tetrahedral elements with an implied connectivity can be be directly recovered. As points are generated they are temporarily attached to a volume triangulation of the boundary points. This triangulation allows efficient local search algorithms to be used when checking merging layers, The existing advancing-front/local-reconnection procedure is used to generate isotropic elements outside of the anisotropic region. Results are presented for a variety of applications. The results demonstrate that high-quality anisotropic unstructured grids can be efficiently and consistently generated for complex configurations.
Cation occupancies in Mg, Co, Ni, Zn, Al ferrite spinels: a multi-element EXAFS study.
Henderson, C M B; Charnock, J M; Plant, D A
2007-02-21
The distribution of cations between tetrahedral (A) sites and octahedral (B) sites in ferrite spinels has been studied using K-edge x-ray absorption spectroscopy. The samples include natural and synthetic end-member magnetites (Fe?O?), a natural Mn- and Zn-rich magnetite (franklinite) and synthetic binary, ternary and quaternary ferrites of stoichiometry M(²+)M?(³+)O?, where M(²+) = Mg, Co, Ni, Zn and M(³+) = Fe, Al. XAS data were obtained for all metals. Complete, unfiltered, EXAFS spectra were refined to determine the percentage distribution of each element over the A and B sites and these data were combined with microprobe analyses to quantify the tetrahedral occupancy for each element in each sample. Measured site occupancies and an internally consistent set of (M-O)(A) and (M-O)(B) bond lengths were used to calculate unit-cell parameters, which show excellent agreement with measured values, pointing to the reliability of the measured occupancy factors. The average occupancies determined for the tetrahedral sites in ferrites are (atoms per formula unit) Mg 0.44, Co 0.24, Ni 0.11, Zn 0.76, Al 0.11 and Fe(³+) 0.92-0.19. The wide range found for Fe(³+) is consistent with it playing a relatively passive role by making good any A-site deficit left by the other competing cations. PMID:22251601
Chua, Daniel H. C.; Hsieh, Jovan; Gao Xingyu; Qi Dongchen; Chen Shi; Varghese, Binni; Sow, Chorng Haur; Wee, A. T. S.; Lu Jiong; Loh, Kian Ping; Yu Xiaojiang; Moser, Herbert O.
2009-07-15
This paper reports a comprehensive experimental study on the effects of hydrogen microwave plasma treatment on nonhydrogenated high sp{sup 3} content tetrahedral amorphous carbon (ta-C) film. In this study, a surface C-H dipole layer was first observed by high resolution electron energy loss spectroscopy, showing the presence of C-H bonding states. This resulted in the enhancement of electron field emission of the plasma treated films by largely lowering the turn-on field. Thermal stability tests using in situ ultraviolet photoelectron spectroscopy confirm that the C-H dipole layer not only reduces the work function of the films, it is extremely stable in both ambient and vacuum conditions and can sustain up to 600 deg. C annealing in vacuum. Atomic force microscopy studies also show minimal modifications to the surface morphology, leading to the conclusion that the C-H dipole layer is responsible for lowering the work function. This has improved the electron emission properties which can lead to potential applications such as electron emission displays.
Wang, Z J
2012-12-06
The overriding objective for this project is to develop an efficient and accurate method for capturing strong discontinuities and fine smooth flow structures of disparate length scales with unstructured grids, and demonstrate its potentials for problems relevant to DOE. More specifically, we plan to achieve the following objectives: 1. Extend the SV method to three dimensions, and develop a fourth-order accurate SV scheme for tetrahedral grids. Optimize the SV partition by minimizing a form of the Lebesgue constant. Verify the order of accuracy using the scalar conservation laws with an analytical solution; 2. Extend the SV method to Navier-Stokes equations for the simulation of viscous flow problems. Two promising approaches to compute the viscous fluxes will be tested and analyzed; 3. Parallelize the 3D viscous SV flow solver using domain decomposition and message passing. Optimize the cache performance of the flow solver by designing data structures minimizing data access times; 4. Demonstrate the SV method with a wide range of flow problems including both discontinuities and complex smooth structures. The objectives remain the same as those outlines in the original proposal. We anticipate no technical obstacles in meeting these objectives.
Coslovich, D; Pastore, G
2009-07-15
We report molecular dynamics simulations for a new model of tetrahedral network glass-former, based on short-range spherical potentials. Despite the simplicity of the forcefield employed, our model reproduces some essential physical properties of silica, an archetypal network-forming material. Structural and dynamical properties, including dynamic heterogeneities and the nature of local rearrangements, are investigated in detail and a direct comparison with models of close-packed, fragile glass-formers is performed. The outcome of this comparison is rationalized in terms of the properties of the potential energy surface, focusing on the unstable modes of the stationary points. Our results indicate that the weak degree of dynamic heterogeneity observed in network glass-formers may be attributed to an excess of localized unstable modes, associated with elementary dynamical events such as bond breaking and reformation. In contrast, the more fragile Lennard-Jones mixtures are characterized by a larger fraction of extended unstable modes, which lead to a more cooperative and heterogeneous dynamics. PMID:21828513
NASA Astrophysics Data System (ADS)
Coslovich, D.; Pastore, G.
2009-07-01
We report molecular dynamics simulations for a new model of tetrahedral network glass-former, based on short-range spherical potentials. Despite the simplicity of the forcefield employed, our model reproduces some essential physical properties of silica, an archetypal network-forming material. Structural and dynamical properties, including dynamic heterogeneities and the nature of local rearrangements, are investigated in detail and a direct comparison with models of close-packed, fragile glass-formers is performed. The outcome of this comparison is rationalized in terms of the properties of the potential energy surface, focusing on the unstable modes of the stationary points. Our results indicate that the weak degree of dynamic heterogeneity observed in network glass-formers may be attributed to an excess of localized unstable modes, associated with elementary dynamical events such as bond breaking and reformation. In contrast, the more fragile Lennard-Jones mixtures are characterized by a larger fraction of extended unstable modes, which lead to a more cooperative and heterogeneous dynamics.
Tonneson, L.C.
1997-01-01
Trace elements used in nutritional supplements and vitamins are discussed in the article. Relevant studies are briefly cited regarding the health effects of selenium, chromium, germanium, silicon, zinc, magnesium, silver, manganese, ruthenium, lithium, and vanadium. The toxicity and food sources are listed for some of the elements. A brief summary is also provided of the nutritional supplements market.
NASA Astrophysics Data System (ADS)
Biryukov, V. A.; Muratov, M. V.; Petrov, I. B.; Sannikov, A. V.; Favorskaya, A. V.
2015-10-01
Seismic responses from fractured geological layers are mathematically simulated by applying the grid-characteristic method on unstructured tetrahedral meshes with the use of high-performance computer systems. The method is intended for computing complicated spatial dynamical processes in complex heterogeneous media and is characterized by exact formulation of contact conditions. As a result, it can be applied to the simulation of seismic exploration problems, including in regions with a large number of inhomogeneities, examples of which are fractured structures. The use of unstructured tetrahedral meshes makes it possible to specify geological cracks of various shapes and spatial orientations. As a result, problems are solved in a formulation maximally close to an actual situation. A cluster of computers is used to improve the accuracy of the computation by optimizing its duration.
Directionally adaptive finite element method for multidimensional Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Tan, Zhiqiang; Varghese, Philip L.
1993-01-01
A directionally adaptive finite element method for multidimensional compressible flows is presented. Quadrilateral and hexahedral elements are used because they have several advantages over triangular and tetrahedral elements. Unlike traditional methods that use quadrilateral/hexahedral elements, our method allows an element to be divided in each of the three directions in 3D and two directions in 2D. Some restrictions on mesh structure are found to be necessary, especially in 3D. The refining and coarsening procedures, and the treatment of constraints are given. A new implementation of upwind schemes in the constrained finite element system is presented. Some example problems, including a Mach 10 shock interaction with the walls of a 2D channel, a 2D viscous compression corner flow, and inviscid and viscous 3D flows in square channels, are also shown.
Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1997-01-01
An adaptive refinement strategy based on hierarchical element subdivision is formulated and implemented for meshes containing arbitrary mixtures of tetrahendra, hexahendra, prisms and pyramids. Special attention is given to keeping memory overheads as low as possible. This procedure is coupled with an algebraic multigrid flow solver which operates on mixed-element meshes. Inviscid flows as well as viscous flows are computed an adaptively refined tetrahedral, hexahedral, and hybrid meshes. The efficiency of the method is demonstrated by generating an adapted hexahedral mesh containing 3 million vertices on a relatively inexpensive workstation.
Hendrickx, Christophe; Mateus, Octávio; Buffetaut, Eric
2016-01-01
Six quadrate bones, of which two almost certainly come from the Kem Kem beds (Cenomanian, Upper Cretaceous) of south-eastern Morocco, are determined to be from juvenile and adult individuals of Spinosaurinae based on phylogenetic, geometric morphometric, and phylogenetic morphometric analyses. Their morphology indicates two morphotypes evidencing the presence of two spinosaurine taxa ascribed to Spinosaurus aegyptiacus and? Sigilmassasaurus brevicollis in the Cenomanian of North Africa, casting doubt on the accuracy of some recent skeletal reconstructions which may be based on elements from several distinct species. Morphofunctional analysis of the mandibular articulation of the quadrate has shown that the jaw mechanics was peculiar in Spinosauridae. In mature spinosaurids, the posterior parts of the two mandibular rami displaced laterally when the jaw was depressed due to a lateromedially oriented intercondylar sulcus of the quadrate. Such lateral movement of the mandibular ramus was possible due to a movable mandibular symphysis in spinosaurids, allowing the pharynx to be widened. Similar jaw mechanics also occur in some pterosaurs and living pelecanids which are both adapted to capture and swallow large prey items. Spinosauridae, which were engaged, at least partially, in a piscivorous lifestyle, were able to consume large fish and may have occasionally fed on other prey such as pterosaurs and juvenile dinosaurs. PMID:26734729
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).
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
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, Erd?s-Rényi 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 Erd?s-Rényi) 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.
Junction conditions in quadratic gravity: thin shells and double layers
Reina, Borja; Vera, Raül
2015-01-01
The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface -termed as thin shells, domain walls or braneworlds in the literature- as well as the proper matching conditions where only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in General Relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The ...
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
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.
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
Boundary element analysis of post-tensioned slabs
NASA Astrophysics Data System (ADS)
Rashed, Youssef F.
2015-06-01
In this paper, the boundary element method is applied to carry out the structural analysis of post-tensioned flat slabs. The shear-deformable plate-bending model is employed. The effect of the pre-stressing cables is taken into account via the equivalent load method. The formulation is automated using a computer program, which uses quadratic boundary elements. Verification samples are presented, and finally a practical application is analyzed where results are compared against those obtained from the finite element method. The proposed method is efficient in terms of computer storage and processing time as well as the ease in data input and modifications.
Membrane triangles with corner drilling freedoms. I - The EFF element
NASA Technical Reports Server (NTRS)
Alvin, Ken; De La Fuente, Horacio M.; Haugen, Bjorn; Felippa, Carlos A.
1992-01-01
The formulation of 3-node 9-DOF membrane elements with normal-to-element-plane rotations (drilling freedoms) is examined in the context of parametrized variational principles. In particular, attention is given to the application of the extended free formulation (EFF) to the construction of a triangular membrane element with drilling freedoms that initially has complete quadratic polynomial expansions in each displacement component. The main advantage of the EFF over the free formulation triangle is that an explicit form is obtained for the higher-order stiffness.
Indefinite quadratic forms and the invariance of the interval in Special Relativity
John H. Elton
2009-08-03
A simple theorem on proportionality of indefinite real quadratic forms is proved, and is used to clarify the proof of the invariance of the interval in Special Relativity from Einstein's postulate on the universality of the speed of light; students are often rightfully confused by the incomplete or incorrect proofs given in many texts. The result is illuminated and generalized using Hilbert's Nullstellensatz, allowing one form to be a homogeneous polynomial which is not necessarily quadratic. Also a condition for simultaneous diagonalizabilityof semi-definite real quadratic functions is given.
ERIC Educational Resources Information Center
Daniel, Esther Gnanamalar Sarojini; Saat, Rohaida Mohd.
2001-01-01
Introduces a learning module integrating three disciplines--physics, chemistry, and biology--and based on four elements: carbon, oxygen, hydrogen, and silicon. Includes atomic model and silicon-based life activities. (YDS)
Sieberer, M.; Turnovszky, S.; Redinger, J.; Mohn, P.
2007-12-01
In this paper, we study the structural properties of selected representatives of the so-called molybdenum cluster compounds. Belonging to this family are the GaM{sub 4}X{sub 8} compounds with M=Mo as a group VIB element and V, Nb, or Ta as a group VB element. X denotes either S or Se. These compounds are known to exhibit semiconducting behavior in the electrical resistivity, caused by hopping of electrons between well-separated metal clusters. The large separation of the tetrahedral metal (M{sub 4}) clusters is believed to be the origin of strong correlations. We show that recent calculations neglected an important type of structural distortion, namely, those happening only within the M{sub 4} unit at a fixed angle {alpha}=60 deg. of the trigonal (fcc-like) cell. These internal distortions gain a significant amount of energy compared to the cubic cell and they are--to our knowledge--almost undetectable with powder x-ray diffraction experiments. However, they strongly influence the band-structure by opening up a gap at the Fermi-energy. This, however, puts into question whether all compounds of this family are really Mott insulators as stated elsewhere. In particular, ferromagnetic GaMo{sub 4}S{sub 8} and GaV{sub 4}S{sub 8} are well described within density functional theory. Only the Nb- and Ta-based representatives require a large effort due to the lack of magnetic long-range order caused by frustrated antiferromagnetic M-M interactions.
Erratum to \\Feasible sequential quadratic programming for nely dicretized problems from
Tits, André L.
T. Lawrence and Andre L. Tits Department of Electrical Engineering and Institute for Systems. References 1] C. T. Lawrence and A. L. Tits. Feasible sequential quadratic program- ming for nely discretized
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.
TWO-PRIMARY ALGEBRAIC K-THEORY OF SOME QUADRATIC AND CYCLOTOMIC NUMBER RINGS
when q = 29 is an odd prime power with (q) 66, or a Sophie Germain prime, such that 2 is a primitive-groups, quadratic number fields, cyclotomic number fields, Sophie Germain primes, zeta-functions. Typeset by AMS
Quadratic Diffusion Monte-Carlo Algorithms for Solving Atomic Many-Body Problems
Chin, Siu A.
1990-01-01
. This failure can be simply circumvented by enforcing attractive cusp conditions on the trial function. Various new second-order diffusion Monte Carlo algorithms are systematically derived and their quadratic convergence numerically verified in cases of He and H...
QUASISYMMETRIC ROBUSTNESS OF THE COLLET-ECKMANN CONDITION IN THE QUADRATIC FAMILY
Avila, Artur
QUASISYMMETRIC ROBUSTNESS OF THE COLLET-ECKMANN CONDITION IN THE QUADRATIC FAMILY ARTUR AVILA as in the original argument of [AM1]. Date: August 28, 2003. 1 #12;2 ARTUR AVILA AND CARLOS GUSTAVO MOREIRA 2. Basic
OPTIMIZATION OF TURBOMACHINERY AIRFOILS WITH A GENETIC/SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM
Dennis, Brian
OPTIMIZATION OF TURBOMACHINERY AIRFOILS WITH A GENETIC/SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM words: shape optimization, aerodynamic design, turbomachinery, aerodynamics, genetic algorithms-magneto- gasdynamic effects. In the case of a turbomachinery aerodynamics, sources of entropy production other than
Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid
ERIC Educational Resources Information Center
Brilleslyper, Michael A.
2004-01-01
Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.
Brakerski, Zvika
The main results of this work are new public-key encryption schemes that, under the quadratic residuosity (QR) assumption (or Paillier’s decisional composite residuosity (DCR) assumption), achieve key-dependent message ...
Models of quadratic quantum algebras and their relation to classical superintegrable systems
Kalnins, E. G.; Miller, W.; Post, S.
2009-05-15
We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.
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.
ROOT-INDUCED INTEGRAL QUADRATIC FORMS M. BAROT AND J. A. DE LA PE~NA
Barot, Michael
ROOT-INDUCED INTEGRAL QUADRATIC FORMS M. BAROT AND J. A. DE LA PE~NA Abstract. Given an integral quadratic unit form q : Zn Z and a finite tuple of q-roots r = (rj )jJ the induced q-root form qr is con they are root-induced one from the other. Moreover, there are only finitely many unit forms without dou- ble
Application of edge-based finite elements and vector ABCs in 3D scattering
NASA Technical Reports Server (NTRS)
Chatterjee, A.; Jin, J. M.; Volakis, John L.
1992-01-01
A finite element absorbing boundary condition (FE-ABC) solution of the scattering by arbitrary 3-D structures is considered. The computational domain is discretized using edge-based tetrahedral elements. In contrast to the node-based elements, edge elements can treat geometries with sharp edges, are divergence-less, and easily satisfy the field continuity condition across dielectric interfaces. They do, however, lead to a higher unknown count but this is balanced by the greater sparsity of the resulting finite element matrix. Thus, the computation time required to solve such a system iteratively with a given degree of accuracy is less than the traditional node-based approach. The purpose is to examine the derivation and performance of the ABC's when applied to 2-D and 3-D problems and to discuss the specifics of our FE-ABC implementation.
Thermomechanical coupling during solidification: A 3D finite element approach
Menaie, M.; Bellet, M.
1995-12-31
This paper presents a thermo-mechanical approach of solidification in casting processes. A three-dimensional finite element analysis is presented. After a brief recall of the heat transfer computation, the mechanical model is detailed. The casting alloy behavior is modeled by a thermo-elastic-viscoplastic model, while the mould is assumed rigid. A mixed velocity-pressure formulation has been developed, using tetrahedral P1{sup +}-P1 elements. The complete thermo-mechanical coupling--not detailed here--has been implemented in Thercast3 software for 3D casting simulation. The validation is established on a cylindrical solidification test, and an example of application to an industrial casting is given.
Predicting random high-cycle fatigue life with finite elements
Preumont, A.; Piefort, V. )
1994-04-01
This paper extends the classical theory of random fatigue to multiaxial stress fields, using a quadratic criterion. An equivalent uniaxial random process is constructed by combining the power spectral densities of the normal and tangential stresses according to the von Mises criterion. This process, that we call the von Mises stress, is used to evaluate the damage with a uniaxial model of random fatigue. A finite element implementation is proposed. 17 refs.
Integrated Risk Information System (IRIS)
Mercury , elemental ; CASRN 7439 - 97 - 6 Human health assessment information on a chemical substance is included in the IRIS database only after a comprehensive review of toxicity data , as outlined in the IRIS assessment development process . Sections I ( Health Hazard Assessments for Noncarcinoge
ERIC Educational Resources Information Center
Herald, Christine
2001-01-01
Describes a research assignment for 8th grade students on the elements of the periodic table. Students use web-based resources and a chemistry handbook to gather information, construct concept maps, and present the findings to the full class using the mode of their choice: a humorous story, a slideshow or gameboard, a brochure, a song, or skit.…
Hu, Peigang; Luo, Qiong; Li, Qian-shu; Xie, Yaoming; King, R Bruce; Schaefer, Henry F
2014-05-19
The experimentally known but structurally uncharacterized Pt4(PF3)8 is predicted to have an S4 structure with a central distorted Pt4 tetrahedron having four short Pt?Pt distances, two long Pt-Pt distances, and all terminal PF3 groups. The structures of the lower nuclearity species Pt(PF3)n (n = 4, 3, 2), Pt2(PF3)n (n = 7, 6, 5, 4), and Pt3(PF3)6 were investigated by density functional theory to assess their possible roles as intermediates in the formation of Pt4(PF3)8 by the pyrolysis of Pt(PF3)4. The expected tetrahedral, trigonal planar, and linear structures are found for Pt(PF3)4, Pt(PF3)3, and Pt(PF3)2, respectively. However, the dicoordinate Pt(PF3)2 structure is bent from the ideal 180° linear structure to approximately 160°. Most of the low-energy binuclear Pt2(PF3)n (n = 7, 6, 5) structures can be derived from the mononuclear Pt(PF3)n (n = 4, 3, 2) structures by replacing one of the PF3 groups by a Pt(PF3)4 or Pt(PF3)3 ligand. In some of these binuclear structures one of the PF3 groups on the Pt(PF3)n ligand becomes a bridging group. The low-energy binuclear structures also include symmetrical [Pt(PF3)n]2 dimers (n = 2, 3) of the coordinately unsaturated Pt(PF3)n (n = 3, 2). The four low-energy structures for the trinuclear Pt3(PF3)6 include two structures with central equilateral Pt3 triangles and two structures with isosceles Pt3 triangles and various arrangements of terminal and bridging PF3 groups. Among these four structures the lowest-energy Pt3(PF3)6 structure has an unprecedented four-electron donor ?(2)-?3-PF3 group bridging the central Pt3 triangle through three Pt-P bonds and one Pt-F bond. Thermochemical studies on the aggregation of these Pt-PF3 complexes suggest the tetramerization of Pt(PF3)2 to Pt4(PF3)8 to be highly exothermic regardless of the mechanistic details. PMID:24801934
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 ampli?cation element. For secondary ampli?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 ampli?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
Finite Element approach for Density Functional Theory calculations on locally refined meshes
Fattebert, J; Hornung, R D; Wissink, A M
2007-02-23
We present a quadratic Finite Element approach to discretize the Kohn-Sham equations on structured non-uniform meshes. A multigrid FAC preconditioner is proposed to iteratively solve the equations by an accelerated steepest descent scheme. The method was implemented using SAMRAI, a parallel software infrastructure for general AMR applications. Examples of applications to small nanoclusters calculations are presented.
On Some Algebraic and Combinatorial Properties of Dunkl Elements
NASA Astrophysics Data System (ADS)
Kirillov, Anatol N.
2013-06-01
We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the ?-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.
On Some Algebraic and Combinatorial Properties of Dunkl Elements
NASA Astrophysics Data System (ADS)
Kirillov, Anatol N.
2012-11-01
We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the ?-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.
Nahrwold, Sophie Berger, Robert; Clemens-Schöpf-Institute, Technical University Darmstadt, Petersenstr. 22, D-64287 Darmstadt ; Schwerdtfeger, Peter; Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str., D-35032 Marburg
2014-01-14
Density functional theory within the two-component quasi-relativistic zeroth-order regular approximation (ZORA) is used to predict parity violation shifts in {sup 183}W nuclear magnetic resonance shielding tensors of chiral, tetrahedrally bonded tungsten complexes of the form NWXYZ (X, Y, Z = H, F, Cl, Br or I), as well as for the heavier systems NWHAtF and NWH(117)F for comparison. The calculations reveal that sub-mHz accuracy is required to detect such tiny effects in this class of compounds, and that parity violation effects are very sensitive to the choice of ligands.
Kaarour, A. Ouardi, O. Meskine, M.
2015-03-30
The use of tensor models adapted to tetrahedral molecules such CH{sub 4}, SiH{sub 4}, G{sub e}H{sub 4}... that use mathematical tools (group theory, irreducible tensor operators) and the characteristics of symmetrical molecules, gives good results. Starting from an experimental spectrum, we can calculate some parameters of the Hamiltonian and consequently the energy levels. Once the line positions are determined, we calculate the parameters of the dipole moment of these molecules and consequently the rovibrational intensities. Both software STDS and SPVIEW, we determined the parameters of the Hamiltonian and those of the dipole moment.
NASA Astrophysics Data System (ADS)
Carlowicz, Michael
He set out to prove that ocean sediments contain elevated levels of the rare element iridium because of the natural weathering of the continents. Instead, what Ariel Anbar found was new evidence that a meteorite may have had a role in the mass extinctions that marked the end of the Cretaceous era.By studying the geochemical properties of iridium, Anbar, a professor of earth and environmental sciences and chemistry at the University of Rochester, found that the residence time—a measure of the rate at which an element settles out of water into sediments—of iridium in ocean water is 2000 to 20,000 years. That finding suggests that a large deposit of iridium could have lingered in the world's oceans long enough to explain the thickness of the iridium-rich sediment layers at the K-T boundary.
Derivation of a Tappered p-Version Beam Finite Element
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1989-01-01
A tapered p-version beam finite element suitable for dynamic applications is derived. The taper in the element is represented by allowing the area moments of inertia to vary as quartic polynomials along the length of the beam, and the cross-sectional area to vary as a quadratic polynomial. The p-version finite-element characteristics are implemented through a set of polynomial shape functions. The lower-order shape functions are identical to the classical cubic and linear shape functions normally associated with a beam element. The higher-order shape functions are a hierarchical set of polynomials that are integrals of orthogonal polynomials. Explicit expressions for the mass and stiffness matrices are presented for an arbitrary value of p. The element has been verified to be numerically stable using shape functions through 22nd order.
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
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
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
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.
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.
Discrete Element Method Simulation of a Boulder Extraction From an Asteroid
NASA Technical Reports Server (NTRS)
Kulchitsky, Anton K.; Johnson, Jerome B.; Reeves, David M.; Wilkinson, Allen
2014-01-01
The force required to pull 7t and 40t polyhedral boulders from the surface of an asteroid is simulated using the discrete element method considering the effects of microgravity, regolith cohesion and boulder acceleration. The connection between particle surface energy and regolith cohesion is estimated by simulating a cohesion sample tearing test. An optimal constant acceleration is found where the peak net force from inertia and cohesion is a minimum. Peak pulling forces can be further reduced by using linear and quadratic acceleration functions with up to a 40% reduction in force for quadratic acceleration.
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.
Non-Quadratic Gauge Fixing and Ghosts for Gauge Theories on the Hypersphere
F. T. Brandt; D. G. C. McKeon
2011-10-07
It has been suggested that using a gauge fixing Lagrangian that is not quadratic in a gauge fixing condition is most appropriate for gauge theories formulated on a hypersphere. We reexamine the appropriate ghost action that is to be associated with gauge fixing, applying a technique that has been used for ensuring that the propagator for a massless spin-two field is transverse and traceless. It is shown that this non-quadratic gauge fixing Lagrangian leads to two pair of complex Fermionic ghosts and two Bosonic real ghosts.
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.
On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients
Berkovich, Alexander
2012-01-01
In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. We observe that the function that appears in Ramanujan's identities can be obtained from a Hecke action on a certain family of eta products. We establish further Hecke-type relations for these functions involving binary quadratic forms. Our observations enable us to find new identities for the Rogers-Ramanujan functions and also to use such identities in return to find identities involving binary quadratic forms.
Quadratic curvature gravity with second order trace and massive gravity models in three dimensions
NASA Astrophysics Data System (ADS)
Baykal, Ahmet
2012-08-01
The quadratic curvature lagrangians having metric field equations with second order trace are constructed relative to an orthonormal coframe. In n > 4 dimensions, pure quadratic curvature lagrangian having second order trace constructed contains three free parameters in the most general case. The fourth order field equations of some of these models, in arbitrary dimensions, are cast in a particular form using the Schouten tensor. As a consequence, the field equations for the New massive gravity theory are related to those of the Topologically massive gravity. In particular, the conditions under which the latter is "square root" of the former are presented.
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
Nonadiabatic Effects in Ultracold Molecules via Anomalous Linear and Quadratic Zeeman Shifts
B. H. McGuyer; C. B. Osborn; M. McDonald; G. Reinaudi; W. Skomorowski; R. Moszynski; T. Zelevinsky
2013-12-20
Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold $^{88}$Sr$_2$ 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 \\textit{ab initio} model.
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.
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.
A parametric quadratic programming method for dynamic contact problems with friction
NASA Astrophysics Data System (ADS)
Sun, S. M.; Tzou, H. S.; Natori, M. C.
1993-04-01
Based on the parametric variational principle, a general but effective parametric quadratic programming technique satisfying various contact conditions is established for dynamic analysis of contact problems with friction and damping. The discretization with respect to time and space leads to a static Linear Complementary Problem (LCP) for each time step which is solved by a quadratic optimization algorithm such as Lemke algorithm, etc. Thus, the convergence and numerical stability of the solution can be guaranteed. The substructure condensation technique is implemented to handle the unknown contact boundary condition so that the computation effort is considerably reduced. As an application of the method presented, two dynamic contact examples and numerical results are given.
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
NASA Technical Reports Server (NTRS)
Rankin, C. C.
1988-01-01
A consistent linearization is provided for the element-dependent corotational formulation, providing the proper first and second variation of the strain energy. As a result, the warping problem that has plagued flat elements has been overcome, with beneficial effects carried over to linear solutions. True Newton quadratic convergence has been restored to the Structural Analysis of General Shells (STAGS) code for conservative loading using the full corotational implementation. Some implications for general finite element analysis are discussed, including what effect the automatic frame invariance provided by this work might have on the development of new, improved elements.
Development of a finite dynamic element for free vibration analysis of two-dimensional structures
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1978-01-01
The paper develops an efficient free-vibration analysis procedure of two-dimensional structures. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and inertia matrices. A plane rectangular dynamic element is developed in detail. Numerical solution results of free-vibration analysis presented herein clearly indicate that these dynamic elements combined with a suitable quadratic matrix eigenproblem solution technique effect a most economical and efficient solution for such an analysis when compared with the usual finite element method.
A projection hybrid finite volume/element method for low-Mach number flows
NASA Astrophysics Data System (ADS)
Bermúdez, A.; Ferrín, J. L.; Saavedra, L.; Vázquez-Cendón, M. E.
2014-08-01
The purpose of this article is to introduce a projection hybrid finite volume/element method for low-Mach number flows of viscous or inviscid fluids. Starting with a 3D tetrahedral finite element mesh of the computational domain, the equation of the transport-diffusion stage is discretized by a finite volume method associated with a dual mesh where the nodes of the volumes are the barycenters of the faces of the initial tetrahedra. The transport-diffusion stage is explicit. Upwinding of convective terms is done by classical Riemann solvers as the Q-scheme of van Leer or the Rusanov scheme. Concerning the projection stage, the pressure correction is computed by a piecewise linear finite element method associated with the initial tetrahedral mesh. Passing the information from one stage to the other is carefully made in order to get a stable global scheme. Numerical results for several test examples aiming at evaluating the convergence properties of the method are shown.
Doping of indium phosphide with group IV elements
Zakharenkov, L.F.; Samorukov, B.E.; Zykov, A.M.
1985-06-01
This paper studies the doping of single crystals of indium phosphide (InP) with group IV elements using data obtained by measuring the total charge concentration of additives and carriers. Single crystals of indium phosphide were grown by the Czochralski method from liquid melts with a liquid hermetic seal in quartz cubicles. The total impurity concentration was determined by atomic-absorption analysis with + or - 10% error. In order to explain the behavior of germanium and tin in indium phosphide, the authors consider the bond energies of additives in indium phosphide and their tetrahedral radii. The authors conclude that the established higher amphoteric character of germanium with respect to tin is probably explained by the moduli of elasticity of the doped crystal.
Hajir, Farshid
HEURISTICS FOR p-CLASS TOWERS OF IMAGINARY QUADRATIC FIELDS NIGEL BOSTON, MICHAEL R. BUSH have given a heuristic which, for a fixed odd prime p, leads to many interesting predictions about the distribution of p-class groups of imaginary quadratic fields. We extend the Cohen-Lenstra heuristic to a non
Rontogiannis, Athanasios A.
--In this paper, the statistics of quadratic forms in normal random variables (RVs) are studied and their impact--Quadratic forms in normal RVs, OSTBC, MIMO, Nakagami-q (Hoyt) distribution, fading channels, per- formance within the framework of the "Reinforcement Programme of Human Research Man- power" (PENED) and co
Zelevinsky, Tanya
Nonadiabatic Effects in Ultracold Molecules via Anomalous Linear and Quadratic Zeeman Shifts B. H, Germany (Received 16 July 2013; published 9 December 2013) Anomalously large linear and quadratic Zeeman. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises
Ames, Aaron
to achieve flat-ground and up-slope walking on a fully-actuated above-knee prosthesis. CLF based quadratic-actuated above-knee prosthesis for different types of locomotion. This goal will be achieved via a three stepsQuadratic Program based Control of Fully-Actuated Transfemoral Prosthesis for Flat-Ground and Up
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...
Unified Theory of Ghost and Quadratic-Flux-Minimizing Surfaces Robert L. DEWAR, Stuart R. HUDSON1)
Hudson, Stuart
Unified Theory of Ghost and Quadratic-Flux-Minimizing Surfaces Robert L. DEWAR, Stuart R. HUDSON1, Princeton NJ 08543, USA June 22, 2010 A generalized Hamiltonian definition of ghost surfaces (surfaces calculations show uncorrected quadratic-flux- minimizing (QFMin) and Lagrangian ghost surfaces give very
3-dimensional wells and tunnels for finite element grids
Cherry, T.A.; Gable, C.W.; Trease, H.
1996-04-01
Modeling fluid, vapor, and air injection and extraction from wells poses a number of problems. The length scale of well bores is centimeters, the region of high pressure gradient may be tens of meters and the reservoir may be tens of kilometers. Furthermore, accurate representation of the path of a deviated well can be difficult. Incorporating the physics of injection and extraction can be made easier and more accurate with automated grid generation tools that incorporate wells as part of a background mesh that represents the reservoir. GEOMESH is a modeling tool developed for automating finite element grid generation. This tool maintains the geometric integrity of the geologic framework and produces optimal (Delaunay) tetrahedral grids. GEOMESH creates a 3D well as hexagonal segments formed along the path of the well. This well structure is tetrahedralized into a Delaunay mesh and then embedded into a background mesh. The well structure can be radially or vertically refined and each well layer is assigned a material property or can take on the material properties of the surrounding stratigraphy. The resulting embedded well can then be used by unstructured finite element models for gas and fluid flow in the vicinity of wells or tunnels. This 3D well representation allows the study of the free- surface of the well and surrounding stratigraphy. It reduces possible grid orientation effects, and allows better correlation between well sample data and the geologic model. The well grids also allow improved visualization for well and tunnel model analysis. 3D observation of the grids helps qualitative interpretation and can reveal features not apparent in fewer dimensions.
Logistic Growth: Quadratic, No Time Delay, K Constant b = [K -N(0)]/N(0)
Caraco, Thomas
Logistic Growth: Quadratic, No Time Delay, K Constant #12;b = [K - N(0)]/N(0) Logistic Population ~ Individual Growth Rate When Rare : Time Delay Population Reproduction: Responds to Density Time Units/Period Lesson: Time delay in density-dependent population regulation may destabilize population growth
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…
Localized Polaritons and Second-Harmonic Generation in a Resonant Medium with Quadratic Nonlinearity
Skryabin, Dmitry
Localized Polaritons and Second-Harmonic Generation in a Resonant Medium with Quadratic-bright polaritons. We report the specific phase matching condition for efficient 2nd harmonic generation, which involves detuning from the resonance. We also demonstrate that the 2nd harmonic emission by the polaritonic
NASA Astrophysics Data System (ADS)
Varaksin, O. L.; Firstov, V. V.; Shapovalov, A. V.; Shirokov, I. V.
1995-05-01
The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented.
NEURAL NETWORK TRAINING VIA QUADRATIC OPTIMIZATION Michael A. Satton' and PanosJ. Antsaklis2
Antsaklis, Panos
NEURAL NETWORK TRAINING VIA QUADRATIC OPTIMIZATION Michael A. Satton' and PanosJ. Antsaklis2-layer neural network, and extended to the multi-layer neural network. It is proposed here to fuui the weights the neural networks layers, the proposed method is extended to the multi-layer neural network. The described
A Novel Mutual Authentication Scheme Based on Quadratic Residues for RFID Systems
International Association for Cryptologic Research (IACR)
A Novel Mutual Authentication Scheme Based on Quadratic Residues for RFID Systems *Jue-Sam Chou 1] proposed a Yoking-Proofs protocol for RFID systems. The aim is to permit tags to generate a proof which-line and replay attacks. In 2006, Kirk H.M. Wong et al. [3] proposed an authentication scheme on RFID passive tags
Applications of Quadratics : When we model the height of a projectile shot from a
Lega, Joceline
will need one person to do each of the following: a. Launch the catapult. b. Watch the penny and markApplications of Quadratics : When we model the height of a projectile shot from a catapult the catapults to shoot a penny into the air. We will measure the time the penny spends in the air
QUADRATIC JULIA SETS WITH POSITIVE AREA. XAVIER BUFF AND ARNAUD CHERITAT
Buff, Xavier
QUADRATIC JULIA SETS WITH POSITIVE AREA. XAVIER BUFF AND ARNAUD CHÂ´ERITAT Abstract. We prove.7. The proof 44 2. The linearizable case 49 3. The infinitely renormalizable case 51 Appendix A. Parabolic to J(P) the methods of Borel-Lebesgue for the measure of sets. It is known that the area (Lebesgue
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.
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.
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…
A STRUCTURED METHOD FOR THE REAL QUADRATIC EIGENVALUE PROBLEM FOR SPECIFIC GYROSCOPIC SYSTEMS
Rush, Wade
2008-12-15
This study examines a specific numerical approach that computes the eigenvalues (normal modes) of a Quadratic Eigenvalue Problem (QEP) of the form (&lambda^2 & middotI + &lambda · B + C)· x = 0 where B is constrained to a real skew-symmetric matrix...
A Quadratic Regulator-Based Heuristic for Rapidly Exploring State Space Elena Leah Glassman
Tedrake, Russ
A Quadratic Regulator-Based Heuristic for Rapidly Exploring State Space by Elena Leah Glassman S Regulator-Based Heuristic for Rapidly Exploring State Space by Elena Leah Glassman Submitted computational cost. We demonstrate improved exploration of the state spaces of the double integrator and simple
Solving Large Scale Binary Quadratic Problems: Spectral Methods vs. Semidefinite Programming
Lunds Universitet
for solving binary quadratic problems. While spectral relaxation meth- ods have been the workhorse subroutine as the number of decision variables grows making them inappli- cable to large scale problems. Our methods. Thus one is forced to rely on approximate meth- ods which results in sub-optimal solutions. Certain
ERIC Educational Resources Information Center
Han, Kyung T.; Rudner, Lawrence M.
2014-01-01
This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…
Classical and Variational Di#erentiability of BSDEs with Quadratic Growth
Imkeller, Peter
, transportation and tourism. The public awareness of climate hazards such as floods or hurricanes is continually. In this setting we again encounter a BSDE with quadratic nonlinearity, of the type Y t = # + # T t f(s, Y s , Z is rivalled by the number of papers on BSDEs of this type of nonlinearity. For a more complete list
ADMISSIBILITY OF KNEADING SEQUENCES AND STRUCTURE OF HUBBARD TREES FOR QUADRATIC POLYNOMIALS
Bruin, Henk
precisely which sequences correspond to quadratic polynomials. We identify the occurrence of so-called evil they are evil or not) from the kneading sequence. 1. Introduction In complex dynamics, a frequent observation, and that these suffice to describe the Hubbard tree and its dynamics up to a natural equivalence relation. We show
PRIME SIEVES USING BINARY QUADRATIC FORMS A. O. L. ATKIN AND D. J. BERNSTEIN
Bernstein, Daniel
. The idea of the sieve of Eratosthenes is to enumerate values of the reducible binary quadratic form xy in the sieve of Eratosthenes is to enumerate values of xy not divisible by 2, 3, or 5; see section 2 of the sieve of Eratosthenes by letting W grow slowly with N . The same is true of the new method. In section 5
PRIME SIEVES USING BINARY QUADRATIC FORMS A. O. L. ATKIN AND D. J. BERNSTEIN
Bernstein, Daniel
. Strategy. The idea of the sieve of Eratosthenes is to enumerate values of the reducible binary quadratic of Eratosthenes is to enumerate values of xy not divisible by 2, 3, or 5; see section 2 for details. This reduces of Eratosthen* *es by letting W grow slowly with N. The same is true of the new method. In section 5 * *we
ERIC Educational Resources Information Center
Bandele, Samuel Oye; Adekunle, Adeyemi Suraju
2015-01-01
The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…
Gesture Recognition Using Quadratic Curves Qiulei Dong, Yihong Wu, and Zhanyi Hu
Dong, Qiulei
curvilinear integral and matrix computation are involved. Experi- ments on hip-hop dance show that our method for human gesture recog- nition based on quadratic curves. Firstly, face and hands in the images and Pentland [3] presented an HMM-based system for recognizing American Sign Language. Brand and Kettnaker [4
A Quadratic Method for Nonlinear Model Order Reduction Y. Chen J. White
Chen, Yong P.
network showthat the nonlinearapproachis much more accurate than using a linearized approach alone and then describe the quadratic reduction algorithm. Finally, results are presented for a nonlinear resistor network subspace froma k,1th #12;order orthogonalized Krylov subspace. First, the last vec- tor in the k,1th -order
Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals
Arie, Ady
Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals to the highly asymmetric shape of nonlinear crystal in the Fourier space, these noncollinear interactions space propagation of an Airy beam. This beam is generated by a nonlinear wave mixing process
Quadratic Programming based data assimilation with passive drifting sensors for shallow water flows
Quadratic Programming based data assimilation with passive drifting sensors for shallow water flows],[15],[14]); for hydraulic systems, Lagrangian data assimilation of shallow water flows to estimate the bottom topology, communication, and visual- ization, that is capable of performing data assimilation for shallow water flows
Taxonomy of Public Key Schemes based on the problem of Multivariate Quadratic equations
International Association for Cryptologic Research (IACR)
Taxonomy of Public Key Schemes based on the problem of Multivariate Quadratic equations Christopher into a taxonomy of only four basic schemes and some generic modifiers. Moreover, we sug gest new constructions . . . . . . . . . . . . . . . . 26 3.4 Hidden Field Equations: HFE . . . . . . . . . . . . . . . . . . 27 3.5 Taxonomy
Taxonomy of Public Key Schemes based on the problem of Multivariate Quadratic equations
International Association for Cryptologic Research (IACR)
Taxonomy of Public Key Schemes based on the problem of Multivariate Quadratic equations Christopher into a taxonomy of only four basic schemes and some generic modifiers. Moreover, we sug- gest new constructions . . . . . . . . . . . . . . . . 26 3.4 Hidden Field Equations: HFE . . . . . . . . . . . . . . . . . . 27 3.5 Taxonomy
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
OVERCONVERGENT GENERALISED EIGENFORMS OF WEIGHT ONE AND CLASS FIELDS OF REAL QUADRATIC FIELDS
Rotger, VÃctor
OVERCONVERGENT GENERALISED EIGENFORMS OF WEIGHT ONE AND CLASS FIELDS OF REAL QUADRATIC FIELDS HENRI non-classical p-adic mod- ular forms of weight one: the eponymous generalised eigenforms of the title of special cycles arising in the formulae of Hirzebruch-Zagier, Gross-Kohnen-Zagier, and their vast
Linear-Quadratic Optimal Controller 10.3 Optimal Linear Control Systems
Gajic, Zoran
Linear-Quadratic Optimal Controller 10.3 Optimal Linear Control Systems In Chapters 8 and 9 originated in the sixties (Kalman, 1960)--called modern optimal control theory in this book--is a time domain technique. During the sixties and sev- enties, the main contributor to modern optimal control theory
Matrix-Vector Multiplication in Sub-Quadratic Time (Some Preprocessing Required)
Boneh, Dan
Matrix-Vector Multiplication in Sub-Quadratic Time (Some Preprocessing Required) Ryan Williams Abstract We show that any n × n matrix A over any finite semiring can be preprocessed in O(n2+ ) time applications are described. 1 Introduction Matrix-vector multiplication is an absolutely fundamental operation
Quadratic hedging of weather and catastrophe risk by using short term climate predictions
Imkeller, Peter
Quadratic hedging of weather and catastrophe risk by using short term climate predictions Stefan 10099 Berlin Germany February 12, 2008 Abstract The extent to which catastrophic weather events occur into account in any reasonable management of weather related risk. In this paper we first set up a risk model
Fitting timeseries by continuous-time Markov chains: A quadratic programming approach
Van Den Eijnden, Eric
as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm be solved using quadratic programming tech- niques. The technique is illustrated on various toy problems the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator
SPECTRAL DECOMPOSITION OF SELF-ADJOINT QUADRATIC PENCILS AND ITS APPLICATIONS
SPECTRAL DECOMPOSITION OF SELF-ADJOINT QUADRATIC PENCILS AND ITS APPLICATIONS DRAFT AS OF March 28, 2007 MOODY T. CHU AND SHU-FANG XU Abstract. Spectral decomposition is of fundamental importance in many applications. Generally speaking, spectral decomposition provides a canonical representation of a linear
Landau-Zener transition in quadratic nonlinear two-state systems
Ishkhanyan, A. M.
2010-05-15
A comprehensive theory of the Landau-Zener transition in quadratic nonlinear two-state systems is developed. A compact analytic formula involving elementary functions only is derived for the final transition probability. The formula provides a highly accurate approximation for the whole rage of the variation of the Landau-Zener parameter.
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…
Are ghost surfaces and quadratic-flux-minimizing surfaces the same?
Hudson, Stuart
Are ghost surfaces and quadratic-flux-minimizing surfaces the same? Dr. Stuart Hudson CEMM Workshop, - and - are almost identical the "easy method" of constructing the "best surfaces" may be possible! ghost surfaces is solved by chaotic-coordinates. ghost-surfaces for high-order periodic orbits "fill
NASA Astrophysics Data System (ADS)
Beyerlein, Irene J.; Phoenix, S. Leigh
1996-12-01
A new computational technique, called the quadratic influence superposition (QIS) technique, is developed to study the stresses around arbitrary arrays of fiber breaks in a unidirectional composite loaded in simple tension, and consisting of elastic fibers in a matrix, which is either elastic-perfectly plastic or which can debond at the interface leaving residual friction. The method involves extending a recently developed break influence superposition (BIS) technique, where to model the behavior of damaged (yielded or debonded) matrix elements, we use special compensating shear stress profiles and develop the corresponding influence functions. The QIS technique appears to be at least an order of magnitude more efficient than other numerical schemes as the computation time is tied mainly to the amount of damage, and it is more accurate than a simpler version of this technique developed earlier. In illustrative examples, the method determines the Mode I fiber and matrix stress distributions around a "center crack" consisting of up to 31 contiguous fiber breaks. Incremental treatment is needed to establish the extent of the inelastic regions and the results, which achieve excellent agreement with exact shear lag analyses, clearly show that QIS calculated these correctly. Results show that the extent of the matrix damage region increases approximately linearly with applied load and nonlinearly with the number of breaks. The stress concentrations and overload profiles along nearby unbroken fibers are altered as compared to the fully elastic case with magnitudes reduced but length scales increased.
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.
Structural instability of the CoO_{4} tetrahedral chain in SrCoO_{3-?} thin films
Glamazda, A.; Choi, Kwang-yong; Lemmens, P.; Choi, Woo Seok; Jeen, Hyoungjeen; Meyer, Tricia L.; Lee, Ho Nyung
2015-08-31
Raman scattering experiments together with detailed lattice dynamic calculations are performed to elucidate crystallographic and electronic peculiarities of SrCoO_{3-?} films. We observe that the 85 cm^{-1} phonon mode involving the rotation of a CoO_{4} tetrahedron undergoes a hardening by 21 cm^{-1} when the temperature is decreased. In addition, new phonon modes appear at 651.5 and 697.6 cm^{-1} . The latter modes are attributed to the Jahn-Teller activated modes. Upon cooling from room temperature, all phonons exhibit an exponential-like increase of intensity with a characteristic energy of about 103–107 K. We attribute this phenomenon to an instability of the CoO_{4} tetrahedral chain structure, which constitutes a key ingredient to understand the electronic and structural properties of the brownmillerite SrCoO_{2.5}.
Jahns, Jürgen
2015-01-01
Subwavelength apertures in a metallic film act as hollow waveguides. By using a non-quadratic cross-section orientation and shape of the cross-sections locally, one can design polarization shifting elements for complex include heterodyne trans- mission systems, optical displays, interferometers, laser radar systems, etc
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.
NASA Astrophysics Data System (ADS)
Varaksin, O. L.; Firstov, V. V.; Shapovalov, A. V.; Shirokov, I. V.
1995-03-01
The study is continued on noncommutative integration of linear partial differential equations [1] in application to the exact integration of quantum-mechanical equations in a Riemann space. That method gives solutions to the Klein-Gordon equation when the set of noncommutative symmetry operations for that equation forms a quadratic algebra consisting of one second-order operator and of first-order operators forming a Lie algebra. The paper is a continuation of [2], where a single nontrivial example is used to demonstrate noncommutative integration of the Klein-Gordon equation in a Riemann space not permitting variable separation.
Igor G. Vladimirov; Ian R. Petersen
2012-05-15
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic polynomials of the system observables, with the latter satisfying canonical commutation relations. In combination with a cubic system Hamiltonian, this leads to a class of quasilinear quantum stochastic systems which retain algebraic closedness in the evolution of mixed moments of the observables. Although such a system is nonlinear and its quantum state is no longer Gaussian, the dynamics of the moments of any order are amenable to exact analysis, including the computation of their steady-state values. In particular, a generalized criterion is developed for quadratic stability of the quasilinear systems. The results of the paper are applicable to the generation of non-Gaussian quantum states with manageable moments and an optimal design of linear quantum controllers for quasilinear quantum plants.
Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching
Lukas Janssen; Igor F. Herbut
2015-07-03
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 analogue 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.
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.
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.
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.
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.
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.
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 ? ?(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.
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.
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
Fitting timeseries by continuous-time Markov chains: A quadratic programming approach
Crommelin, D.T. . E-mail: crommelin@cims.nyu.edu; Vanden-Eijnden, E. . E-mail: eve2@cims.nyu.edu
2006-09-20
Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows.
Bianchi Cosmological Models in the Minimum Quadratic Poincare Gauge Theory of Gravity
Nguyen Hong Chuong; Nguyen Van Hoang
1993-04-01
Within the framework of the minimum quadratic Poincare gauge theory of gravity in the Riemann-Cartan spacetime the dynamics of homogeneous anisotropic Bianchi types I-IX spinning-fluid cosmological models is investigated. A basic equation set for these models is obtained and analyzed. In particular, exact solutions for the Bianchi type-I spinning-fluid and Bianchi type-V perfect-fluid models are found in analytic form.
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.
Application’s Method of Quadratic Programming for Optimization of Portfolio Selection
NASA Astrophysics Data System (ADS)
Kawamoto, Shigeru; Takamoto, Masanori; Kobayashi, Yasuhiro
Investors or fund-managers face with optimization of portfolio selection, which means that determine the kind and the quantity of investment among several brands. We have developed a method to obtain optimal stock’s portfolio more rapidly from twice to three times than conventional method with efficient universal optimization. The method is characterized by quadratic matrix of utility function and constrained matrices divided into several sub-matrices by focusing on structure of these matrices.
Andrzej Okninski; Boguslaw Radziszewski
2010-10-14
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands appear due to homoclinic structures created from unstable 2 - cycles in a corner-type bifurcation.
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.
Bilinear and quadratic Hamiltonians in two-mode cavity quantum electrodynamics
F. O. Prado; N. G. de Almeida; M. H. Y. Moussa; C. J. Villas-Boas
2006-02-20
In this work we show how to engineer bilinear and quadratic Hamiltonians in cavity quantum electrodynamics (QED) through the interaction of a single driven two-level atom with cavity modes. The validity of the engineered Hamiltonians is numerically analyzed even considering the effects of both dissipative mechanisms, the cavity field and the atom. The present scheme can be used, in both optical and microwave regimes, for quantum state preparation, the implementation of quantum logical operations, and fundamental tests of quantum theory.
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)
Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2014-04-01
A class of nonlinear symmetry operators has been constructed for the many-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation quadratic in independent variables and derivatives. The construction of each symmetry operator includes an interwining operator for the auxiliary linear equations and additional nonlinear algebraic conditions. Symmetry operators for the one-dimensional equation with a constant influence function have been constructed in explicit form and used to obtain a countable set of exact solutions.
Classification of constraints and degrees of freedom for quadratic discrete actions
Höhn, 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 Höhn [“Constraint analysis for variational discrete systems,” J. Math. Phys. 54, 093505 (2013); e-print http://arxiv.org/abs/arXiv:1303.4294 [math-ph
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.
A voxel-based finite element model for the prediction of bladder deformation
Chai Xiangfei; Herk, Marcel van; Hulshof, Maarten C. C. M.; Bel, Arjan
2012-01-15
Purpose: A finite element (FE) bladder model was previously developed to predict bladder deformation caused by bladder filling change. However, two factors prevent a wide application of FE models: (1) the labor required to construct a FE model with high quality mesh and (2) long computation time needed to construct the FE model and solve the FE equations. In this work, we address these issues by constructing a low-resolution voxel-based FE bladder model directly from the binary segmentation images and compare the accuracy and computational efficiency of the voxel-based model used to simulate bladder deformation with those of a classical FE model with a tetrahedral mesh. Methods: For ten healthy volunteers, a series of MRI scans of the pelvic region was recorded at regular intervals of 10 min over 1 h. For this series of scans, the bladder volume gradually increased while rectal volume remained constant. All pelvic structures were defined from a reference image for each volunteer, including bladder wall, small bowel, prostate (male), uterus (female), rectum, pelvic bone, spine, and the rest of the body. Four separate FE models were constructed from these structures: one with a tetrahedral mesh (used in previous study), one with a uniform hexahedral mesh, one with a nonuniform hexahedral mesh, and one with a low-resolution nonuniform hexahedral mesh. Appropriate material properties were assigned to all structures and uniform pressure was applied to the inner bladder wall to simulate bladder deformation from urine inflow. Performance of the hexahedral meshes was evaluated against the performance of the standard tetrahedral mesh by comparing the accuracy of bladder shape prediction and computational efficiency. Results: FE model with a hexahedral mesh can be quickly and automatically constructed. No substantial differences were observed between the simulation results of the tetrahedral mesh and hexahedral meshes (<1% difference in mean dice similarity coefficient to manual contours and <0.02 cm difference in mean standard deviation of residual errors). The average equation solving time (without manual intervention) for the first two types of hexahedral meshes increased to 2.3 h and 2.6 h compared to the 1.1 h needed for the tetrahedral mesh, however, the low-resolution nonuniform hexahedral mesh dramatically decreased the equation solving time to 3 min without reducing accuracy. Conclusions: Voxel-based mesh generation allows fast, automatic, and robust creation of finite element bladder models directly from binary segmentation images without user intervention. Even the low-resolution voxel-based hexahedral mesh yields comparable accuracy in bladder shape prediction and more than 20 times faster in computational speed compared to the tetrahedral mesh. This approach makes it more feasible and accessible to apply FE method to model bladder deformation in adaptive radiotherapy.
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.
The generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2
NASA Astrophysics Data System (ADS)
Yan, Litan; Liu, Junfeng; Chen, Chao
2014-11-01
In this paper, we study the generalized quadratic covariation of f(BH) and BH defined by $ [f(BH),BH](H)t:=\\lim_\\varepsilon\\downarrow 0}(1)/(\\varepsilon2H)\\int 0t{f(BHs+\\varepsilon) -f(BHs)}(BHs+\\varepsilon-BH_s)ds2H in probability, where f is a Borel function and BH is a fractional Brownian motion with Hurst index 0 < H < 1/2. We construct a Banach space {H} of measurable functions such that the generalized quadratic covariation exists in L2(?) and the Bouleau-Yor identity takes the form [f(BH),BH]t(H)=-\\int_ {R}}f(x){L}H(dx,t) provided f\\in {H}, where {L}^{H}(x, t) is the weighted local time of BH. These are also extended to the time-dependent case, and as an application we give the identity between the generalized quadratic covariation and the 4-covariation [g(BH), BH, BH, BH] when H = 1/4.
The Standard Model Has No Quadratic Divergences And Thus No Weak Hierarchy Problem
Lynn, Bryan W
2011-01-01
We show by explicit calculation that, after tadpole renormalization, all 1-loop quadratic ultra-violet divergences in the Standard Model (SM) S-Matrix cancel exactly among themselves: i.e. for each virtual multiplet, with the usual subtlety in the gauge-ghost-Goldstone sector. They are not absorbed into renormalized parameters nor cancelled between virtual bosons and fermions. The parameters of the 1-loop effective Higgs potential remain "natural". No "fine-tuning", even with Planck scale ultra-violet cut-off, is necessary: e.g. for Higgs mass. The 1-loop SM does not suffer a quadratic-divergence-generated Weak Hierarchy Problem (WHP). We extend these results to all-loop-orders in electroweak perturbation theory and to also include all-loop-order QCD perturbative corrections. The resulting all-loop-order SM S-Matrix has no surviving perturbative quadratic divergences. Their exact cancellation among themselves, without absorption into renormalized parameters, is traced directly to spontaneous symmetry breaking...
An efficient finite element method applied to quantum billiard systems
Woo-Sik Son; Sunghwan Rim; Chil-Min Kim
2009-02-25
An efficient finite element method (FEM) for calculating eigenvalues and eigenfunctions of quantum billiard systems is presented. We consider the FEM based on triangular $C_1$ continuity quartic interpolation. Various shapes of quantum billiards including an integrable unit circle are treated. The numerical results show that the applied method provides accurate set of eigenvalues exceeding a thousand levels for any shape of quantum billiards on a personal computer. Comparison with the results from the FEM based on well-known $C_0$ continuity quadratic interpolation proves the efficiency of the method.
Thermoelectric transport properties of diamond-like Cu1-xFe1+xS2 tetrahedral compounds
NASA Astrophysics Data System (ADS)
Li, Yulong; Zhang, Tiansong; Qin, Yuting; Day, Tristan; Jeffrey Snyder, G.; Shi, Xun; Chen, Lidong
2014-11-01
Polycrystalline samples with the composition of Cu1-xFe1+xS2 (x = 0, 0.01, 0.03, 0.05, 0.1) were synthesized by a melting-annealing-sintering process. X-ray powder diffraction reveals all the samples are phase pure. The backscattered electron image and X-ray map indicate that all elements are distributed homogeneously in the matrix. The measurements of Hall coefficient, electrical conductivity, and Seebeck coefficient show that Fe is an effective n-type dopant in CuFeS2. The electron carrier concentration of Cu1-xFe1+xS2 is tuned within a wide range leading to optimized power factors. The lattice phonons are also strongly scattered by the substitution of Fe for Cu, leading to reduced thermal conductivity. We use Debye approximation to model the low temperature lattice thermal conductivity. It is found that the large strain field fluctuation introduced by the disordered Fe ions generates extra strong phonon scatterings for lowered lattice thermal conductivity.
Mott-insulator phases of spin-3/2 fermions in the presence of quadratic Zeeman coupling
Rodriguez, K.; Argueelles, A.; Colome-Tatche, M.; Vekua, T.; Santos, L.
2010-07-30
We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2) x SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Neel order in spin-1/2 gases.
Nussbaum, Roger D.
2001-01-01
)=(z, z+w2 ). The map 9 is one of the simplest possible examples of a nonlinear polynomial map of C2 refer to these as solutions of the quadratic Fibonacci recurrence or the QF recurrence. Some aspects
Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography.
Javaherian, Ashkan; Soleimani, Manuchehr; Moeller, Knut
2015-01-01
This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT. PMID:25501046
NASA Astrophysics Data System (ADS)
D'Amico, María Belén; Calandrini, Guillermo L.
2015-11-01
Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.
Quadratic energy-loss straggling and energy widths of the states of slow ions in an electron gas
Wang, N.
1997-10-01
The energy-loss straggling and energy width of states of slow ions interacting with a homogeneous electron gas are evaluated within a quadratic response theory and the random-phase approximation. These results are compared with corresponding results determined from a fully nonlinear scattering theory approach. The quadratic response theory is shown to be a good approximation for high electron densities and small ion charges. {copyright} {ital 1997} {ital The American Physical Society}
D'Amico, María Belén; Calandrini, Guillermo L
2015-11-01
Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced. PMID:26627573
On a 3-D singularity element for computation of combined mode stress intensities
NASA Technical Reports Server (NTRS)
Atluri, S. N.; Kathiresan, K.
1976-01-01
A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Anderson, W. J.
1983-01-01
Rolling element bearings are a precision, yet simple, machine element of great utility. A brief history of rolling element bearings is reviewed and the type of rolling element bearings, their geometry and kinematics, as well as the materials they are made from and the manufacturing processes they involve are described. Unloaded and unlubricated rolling element bearings, loaded but unlubricated rolling element bearings and loaded and lubricated rolling element bearings are considered. The recognition and understanding of elastohydrodynamic lubrication covered, represents one of the major development in rolling element bearings.
STARS: A general-purpose finite element computer program for analysis of engineering structures
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1984-01-01
STARS (Structural Analysis Routines) is primarily an interactive, graphics-oriented, finite-element computer program for analyzing the static, stability, free vibration, and dynamic responses of damped and undamped structures, including rotating systems. The element library consists of one-dimensional (1-D) line elements, two-dimensional (2-D) triangular and quadrilateral shell elements, and three-dimensional (3-D) tetrahedral and hexahedral solid elements. These elements enable the solution of structural problems that include truss, beam, space frame, plane, plate, shell, and solid structures, or any combination thereof. Zero, finite, and interdependent deflection boundary conditions can be implemented by the program. The associated dynamic response analysis capability provides for initial deformation and velocity inputs, whereas the transient excitation may be either forces or accelerations. An effective in-core or out-of-core solution strategy is automatically employed by the program, depending on the size of the problem. Data input may be at random within a data set, and the program offers certain automatic data-generation features. Input data are formatted as an optimal combination of free and fixed formats. Interactive graphics capabilities enable convenient display of nodal deformations, mode shapes, and element stresses.
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Piris, M; March, N H
2015-10-01
Motivated by previous work involving one of us (N.H.M.) on some 20 stable tetrahedral (t) and octahedral (o) molecules, including XF4 (X = C, Si, Ge), the natural orbital functional PNOF6 is here used to study the free-space halogen cluster t-F4. We consider an extended functional PNOF6(Nc) by coupling Nc orbitals (Nc > 1) to each orbital below the Fermi level, which improves the description of the electron pairs. Similar studies are presented for t-Cl4. The successful calculation on the stable molecule BrF5 (Theor. Chem. Acc. 2013, 132, 1298) has prompted a study of the clusters o-F6 and o-Cl6 too. The size relation with calculated known stable molecules and the experimental data are finally considered. In the case of the o-SF6, the geometry optimization with fixed octahedral symmetry has also been performed at the PNOF6(3) level of theory, leading to an equilibrium distance of 2.95 au in perfect agreement with the experiment. Our results confirm the multireferential character of Z4 and Z6 compounds (Z = H, F, Cl), in contrast with the single-reference character of the XZ4 (X = C, Si, Ge) and YZ6 (Y = S, Se, U) compounds; therefore, despite the clear patterns within a group, it is not possible to extrapolate the results to the case when the atomic number, X or Y, becomes zero. PMID:26393379
Williams, Christopher D; Carbone, Paola
2015-11-01
Radioactive pertechnetate, (99)TcO4 (-), is one of the most problematic ionic species in the context of the clean up and storage of nuclear waste. Molecular simulations can be used to understand the behavior of TcO4 (-) in dilute aqueous solutions, providing reliable potentials are available. This work outlines the development of a new potential model for TcO4 (-) and competing SO4 (2-), optimized using their hydration properties, such as the Gibbs hydration free energy (calculated using Bennett's acceptance ratio method). The findings show that the TcO4 (-) oxyanion has a very low hydration free energy (-202 kJ mol(-1)) compared to other anions (Cl(-), I(-), SO4 (2-)) leading to fast water exchange dynamics and explaining its observed high mobility in the aqueous environment. Its hydrated structure, investigated using ion-water radial distribution functions, shows that it is unique amongst the other anions in that it does not possess well-defined hydration shells. Since contaminants and ubiquitous species in the aqueous environment are often present as tetrahedral oxyanions, it is proposed that the approach could easily be extended to a whole host of other species. PMID:26547171
Yang, Ting; Hao, Yajuan; Abella, Laura; Tang, Qiangqiang; Li, Xiaohong; Wan, Yingbo; Rodríguez-Fortea, Antonio; Poblet, Josep M; Feng, Lai; Chen, Ning
2015-07-27
A new cluster fullerene, Sc2 O@Td (19151)-C76 , has been isolated and characterized by mass spectrometry, UV/Vis/NIR absorption, (45) Sc NMR spectroscopy, cyclic voltammetry, and single-crystal X-ray diffraction. The crystallographic analysis unambiguously assigned the cage structure as Td (19151)-C76 , which is the first tetrahedral fullerene cage characterized by single-crystal X-ray diffraction. This study also demonstrated that the Sc2 O cluster has a much smaller Sc?O?Sc angle than that of Sc2 O@Cs (6)-C82 and the Sc2 O unit is fully ordered inside the Td (19151)-C76 cage. Computational studies further revealed that the cluster motion of the Sc2 O is more restrained in the Td (19151)-C76 cage than that in the Cs (6)-C82 cage. These results suggest that cage size affects not only the shapes but also the cluster motion inside fullerene cages. PMID:26088830
NASA Astrophysics Data System (ADS)
Williams, Christopher D.; Carbone, Paola
2015-11-01
Radioactive pertechnetate, 99TcO4-, is one of the most problematic ionic species in the context of the clean up and storage of nuclear waste. Molecular simulations can be used to understand the behavior of TcO4- in dilute aqueous solutions, providing reliable potentials are available. This work outlines the development of a new potential model for TcO 4- and competing SO42-, optimized using their hydration properties, such as the Gibbs hydration free energy (calculated using Bennett's acceptance ratio method). The findings show that the TcO4- oxyanion has a very low hydration free energy (-202 kJ mol-1) compared to other anions (Cl-, I-, SO42-) leading to fast water exchange dynamics and explaining its observed high mobility in the aqueous environment. Its hydrated structure, investigated using ion-water radial distribution functions, shows that it is unique amongst the other anions in that it does not possess well-defined hydration shells. Since contaminants and ubiquitous species in the aqueous environment are often present as tetrahedral oxyanions, it is proposed that the approach could easily be extended to a whole host of other species.
Xue, Siqi; Pinnavaia, Thomas J.
2010-01-01
The synthesis of saponite in the presence of bis(triethoxysilyl)methane (BTESM) as an organosilicon reagent results in the replacement of up to 33.3 % of the oxygen atoms in the tetrahedral sheet by bridging methylene groups. The methylene-functionalized saponites represent a new form of covalently-bonded organoclay that truly is isomorphic with purely inorganic saponite made under equivalent reaction conditions from sodium silicate as the silicon source. The isoelectronic and isolobal relationship between methylene and bridging oxygen centers is essential for methylene saponite formation. Bridging ethylene groups are not incorporated into the Kagome net of the basal surfaces due to a mismatch in bridging group size. The textural properties of the methylene saponites are similar to those for purely inorganic magnesium saponite made under equivalent synthetic conditions in the absence of BTESM. Layer stacking disorders afford large surface areas (~550 to 650 m2/g), making the methylene saponites attractive candidates for use as adsorbents and functional fillers for polymer composites. PMID:20508733
ERIC Educational Resources Information Center
Ma, T. S.; Wang, C. Y.
1984-01-01
Presents a literature review on methods used to analyze organic elements. Topic areas include methods for: (1) analyzing carbon, hydrogen, and nitrogen; (2) analyzing oxygen, sulfur, and halogens; (3) analyzing other elements; (4) simultaneously determining several elements; and (5) determing trace elements. (JN)
Driving/Braking Force Distribution of Four Wheel Vehicle by Quadratic Programming with Constraints
NASA Astrophysics Data System (ADS)
Ikeda, Yuichi; Suzuki, Ryo; Chida, Yuichi
This paper proposes a yaw rate tracking control method that distributes the driving/ braking force exerted on vehicles at the time of negotiating sharp turns and driving at high speeds. The proposed method employs quadratic programming to distribute the driving/braking force in order to equalize the tire load factor on all wheels and consider the limits of the driving/braking force. The yaw rate tracking performance can be improved even while driving at high speeds and negotiating sharp turns by setting limits for the driving/braking force, differential moment, etc. The effectiveness of our proposed method is proven by a numerical simulation.
A simplified dual neural network for quadratic programming with its KWTA application.
Liu, Shubao; Wang, Jun
2006-11-01
The design, analysis, and application of a new recurrent neural network for quadratic programming, called simplified dual neural network, are discussed. The analysis mainly concentrates on the convergence property and the computational complexity of the neural network. The simplified dual neural network is shown to be globally convergent to the exact optimal solution. The complexity of the neural network architecture is reduced with the number of neurons equal to the number of inequality constraints. Its application to k-winners-take-all (KWTA) operation is discussed to demonstrate how to solve problems with this neural network. PMID:17131664
A sequential quadratic programming algorithm using an incomplete solution of the subproblem
Murray, W.; Prieto, F.J.
1993-05-01
We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set.
Elementary quadratic chaotic flows with a single non-hyperbolic equilibrium
NASA Astrophysics Data System (ADS)
Wei, Zhouchao; Sprott, J. C.; Chen, Huai
2015-10-01
This paper describes a class of third-order explicit autonomous differential equations, called jerk equations, with quadratic nonlinearities that can generate a catalog of nine elementary dissipative chaotic flows with the unusual feature of having a single non-hyperbolic equilibrium. They represent an interesting sub-class of dynamical systems that can exhibit many major features of regular and chaotic motion. The proposed systems are investigated through numerical simulations and theoretical analysis. For these jerk dynamical systems, a certain amount of nonlinearity is sufficient to produce chaos through a sequence of period-doubling bifurcations.
A New Method to Extract Dorsal Hand Vein Pattern using Quadratic Inference Function
Khan, Maleika Heenaye Mamode
2010-01-01
Among all biometric, dorsal hand vein pattern is attracting the attention of researchers, of late. Extensive research is being carried out on various techniques in the hope of finding an efficient one which can be applied on dorsal hand vein pattern to improve its accuracy and matching time. One of the crucial step in biometric is the extraction of features. In this paper, we propose a method based on quadratic inference function to the dorsal hand vein features to extract its features. The biometric system developed was tested on a database of 100 images. The false acceptance rate (FAR), false rejection rate (FRR) and the matching time are being computed.
Ulvila, Ville; Halonen, Lauri; Vainio, Markku
2015-01-01
We present an experimental study of optical frequency comb generation based on cascaded quadratic nonlinearities inside a continuous-wave-pumped optical parametric oscillator. We demonstrate comb states which produce narrow-linewidth intermode beat note signals, and we verify the mode spacing uniformity of the comb at the Hz level. We also show that spectral quality of the comb can be improved by modulating the parametric gain at a frequency that corresponds to the comb mode spacing. We have reached a high average output power of over 4 W in the near-infrared region, at ~2 {\\mu}m.