Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.
Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A
2016-03-21
Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. PMID:26900037
An Improved Linear Tetrahedral Element for Plasticity
Puso, M
2005-04-25
A stabilized, nodally integrated linear tetrahedral is formulated and analyzed. It is well known that linear tetrahedral elements perform poorly in problems with plasticity, nearly incompressible materials, and acute bending. For a variety of reasons, linear tetrahedral elements are preferable to quadratic tetrahedral elements in most nonlinear problems. Whereas, mixed methods work well for linear hexahedral elements, they don't for linear tetrahedrals. On the other hand, automatic mesh generation is typically not feasible for building many 3D hexahedral meshes. A stabilized, nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity, nearly incompressible materials and acute bending. Furthermore, the formulation is analytically and numerically shown to be stable and optimally convergent. The element is demonstrated to perform well in several standard linear and nonlinear benchmarks.
An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations
Key, S.W.; Heinstein, M.W.; Stone, C.M.
1997-12-31
Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four midface nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping and the element`s performance in applications are presented. In particular, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite element and handbuilt meshes.
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.
1999-01-01
This report documents a collection of papers on a family of uniform strain tetrahedral finite elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral Finite Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform strain and enhanced uniform strain formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.
A computational study of nodal-based tetrahedral element behavior.
Gullerud, Arne S.
2010-09-01
This report explores the behavior of nodal-based tetrahedral elements on six sample problems, and compares their solution to that of a corresponding hexahedral mesh. The problems demonstrate that while certain aspects of the solution field for the nodal-based tetrahedrons provide good quality results, the pressure field tends to be of poor quality. Results appear to be strongly affected by the connectivity of the tetrahedral elements. Simulations that rely on the pressure field, such as those which use material models that are dependent on the pressure (e.g. equation-of-state models), can generate erroneous results. Remeshing can also be strongly affected by these issues. The nodal-based test elements as they currently stand need to be used with caution to ensure that their numerical deficiencies do not adversely affect critical values of interest.
Tetrahedral mesh improvement via optimization of the element condition number
FREITAG,LORI A.; KNUPP,PATRICK
2000-05-22
The authors present a new shape measure for tetrahedral elements that is optimal in that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. Using this shape measure, they formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the tetrahedral mesh; the second aims to improve the worst-quality element in the mesh. They review the optimization techniques used with each objective function and presents experimental results that demonstrate the effectiveness of the mesh improvement methods. They show that a combined optimization approach that uses both objective functions obtains the best-quality meshes for several complex geometries.
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.
A suitable low-order, eight-node tetrahedral finite element for solids
Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.
1998-03-01
To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the eight-node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties.
A 3D Frictional Segment-to-Segment Contact Method for Large Deformations and Quadratic Elements
Puso, M; Laursen, T; Solberg, J
2004-04-01
Node-on-segment contact is the most common form of contact used today but has many deficiencies ranging from potential locking to non-smooth behavior with large sliding. Furthermore, node-on-segment approaches are not at all applicable to higher order discretizations (e.g. quadratic elements). In a previous work, [3, 4] we developed a segment-to-segment contact approach for eight node hexahedral elements based on the mortar method that was applicable to large deformation mechanics. The approach proved extremely robust since it eliminated the over-constraint that caused 'locking' and provided smooth force variations in large sliding. Here, we extend this previous approach to treat frictional contact problems. In addition, the method is extended to 3D quadratic tetrahedrals and hexahedrals. The proposed approach is then applied to several challenging frictional contact problems that demonstrate its effectiveness.
NASA Astrophysics Data System (ADS)
Cheng, Jiahao; Shahba, Ahmad; Ghosh, Somnath
2016-05-01
Image-based CPFE modeling involves computer generation of virtual polycrystalline microstructures from experimental data, followed by discretization into finite element meshes. Discretization is commonly accomplished using three-dimensional four-node tetrahedral or TET4 elements, which conform to the complex geometries. It has been commonly observed that TET4 elements suffer from severe volumetric locking when simulating deformation of incompressible or nearly incompressible materials. This paper develops and examines three locking-free stabilized finite element formulations in the context of crystal plasticity finite element analysis. They include a node-based uniform strain (NUS) element, a locally integrated B-bar (LIB) based element and a F-bar patch (FP) based element. All three formulations are based on the partitioning of TET4 element meshes and integrating over patches to obtain favorable incompressibility constraint ratios without adding large degrees of freedom. The results show that NUS formulation introduces unstable spurious energy modes, while the LIB and FP elements stabilize the solutions and are preferred for reliable CPFE analysis. The FP element is found to be computationally efficient over the LIB element.
Uniform Strain Elements for Three-Node Triangular and Four-Node Tetrahedral Meshes
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.; Witkowski, W.R.
1999-03-02
A family of uniform strain elements is presented for three-node triangular and four-node tetrahedral meshes. The elements use the linear interpolation functions of the original mesh, but each element is associated with a single node. As a result, a favorable constraint ratio for the volumetric response is obtained for problems in solid mechanics. The uniform strain elements do not require the introduction of additional degrees of freedom and their performance is shown to be significantly better than that of three-node triangular or four-node tetrahedral elements. In addition, nodes inside the boundary of the mesh are observed to exhibit superconvergent behavior for a set of example problems.
Tetrahedral element shape optimization via the Jacobian determinant and condition number.
Freitag, L. A.; Knupp, P. M.
1999-07-30
We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. We use this shape measure to formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the tetrahedral mesh; the second aims to improve the worst-quality element in the mesh. Because the element condition number is not defined for tetrahedral with negative volume, these objective functions can be used only when the initial mesh is valid. Therefore, we formulate a third objective function using the determinant of the element Jacobian that is suitable for mesh untangling. We review the optimization techniques used with each objective function and present experimental results that demonstrate the effectiveness of the mesh improvement and untangling methods. We show that a combined optimization approach that uses both condition number objective functions obtains the best-quality meshes.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
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
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
Quadratic Finite Element Method for 1D Deterministic Transport
Tolar, Jr., D R; Ferguson, J M
2004-01-06
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.
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
A three-dimensional FE analysis of large deformations for impact loadings using tetrahedral elements
NASA Astrophysics Data System (ADS)
Yoo, Y. H.; Lee, M.
A three-dimensional dynamic program for the anaysis of large deformations in contact-penetration problems is developed using the finite element Lagrangian method with explicit time integration. By incorporating a tetrahedral element, which allows a single-point integration without a special hourglass control scheme, this program can be more effective to the present problem. The position code algorithm is used to search contact surface. Eroding surfaces are also considered. The defense node algorithm was slightly modified for the calculation of contact forces. A study of obliquity effects on metallic plate perforation and ricochet processes in thin plates impacted by a sphere was conducted. It is well simulated that on separation of two parts of the sphere, the portion still within the crater tends to perforate, while the portion in contact with the plate surface ricochets. This deformation pattern is observed in experiments, especially at high obliquities. A long rod that impacts an oblique steel plate at high impact velocity was also simulated in order to study the dynamics of the rod caused by the three dimensional asymmetric contact. The agreement between simulated and experimental results is quite good. Fracture phenomena occuring at high obliquity deserves further investigations.
Hollaus, K; Magele, C; Merwa, R; Scharfetter, H
2004-02-01
Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed. PMID:15005313
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.
Solving the transport equation with quadratic finite elements: Theory and applications
Ferguson, J.M.
1997-12-31
At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.
Parallel Anisotropic Tetrahedral Adaptation
NASA Technical Reports Server (NTRS)
Park, Michael A.; Darmofal, David L.
2008-01-01
An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domain-decomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.
NASA Astrophysics Data System (ADS)
Mulder, W. A.; Shamasundar, R.
2016-07-01
We consider isotropic elastic wave propagation with continuous mass-lumped finite elements on tetrahedra with explicit time stepping. These elements require higher-order polynomials in their interior to preserve accuracy after mass lumping and are only known up to degree 3. Global assembly of the symmetric stiffness matrix is a natural approach but requires large memory. Local assembly on the fly, in the form of matrix-vector products per element at each time step, has a much smaller memory footprint. With dedicated expressions for local assembly, our code ran about 1.3 times faster for degree 2 and 1.9 times for degree 3 on a simple homogeneous test problem, using 24 cores. This is similar to the acoustic case. For a more realistic problem, the gain in efficiency was a factor 2.5 for degree 2 and 3 for degree 3. For the lowest degree, the linear element, the expressions for both the global and local assembly can be further simplified. In that case, global assembly is more efficient than local assembly. Among the three degrees, the element of degree 3 is the most efficient in terms of accuracy at a given cost.
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…
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.
1971-01-01
Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.
Optimization of tetrahedral meshes
Briere De L`Isle, E.; George, P.L.
1995-12-31
Finite element computations are all the more exact if we start from {open_quotes}good{close_quotes} elements. We are interested in meshes where the elements are tetrahedra and we shall develop utilities allowing us to improve the quality of these meshes.
Parallel tetrahedral mesh refinement with MOAB.
Thompson, David C.; Pebay, Philippe Pierre
2008-12-01
In this report, we present the novel functionality of parallel tetrahedral mesh refinement which we have implemented in MOAB. This report details work done to implement parallel, edge-based, tetrahedral refinement into MOAB. The theoretical basis for this work is contained in [PT04, PT05, TP06] while information on design, performance, and operation specific to MOAB are contained herein. As MOAB is intended mainly for use in pre-processing and simulation (as opposed to the post-processing bent of previous papers), the primary use case is different: rather than refining elements with non-linear basis functions, the goal is to increase the number of degrees of freedom in some region in order to more accurately represent the solution to some system of equations that cannot be solved analytically. Also, MOAB has a unique mesh representation which impacts the algorithm. This introduction contains a brief review of streaming edge-based tetrahedral refinement. The remainder of the report is broken into three sections: design and implementation, performance, and conclusions. Appendix A contains instructions for end users (simulation authors) on how to employ the refiner.
Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees
Bronson, Jonathan; Levine, Joshua A.; Whitaker, Ross
2014-01-01
We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach. PMID:24356365
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…
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
Li, Jun; Li, Xi; Zhai, Hua Jin; Wang, Lai S.
2003-02-07
Photoelectron spectroscopy revealed that a 20 atom gold cluster has an extremely large energy gap, which is even greater than that of C60, and an electron affinity comparable with that of C60. This observation suggests that the Au20 cluster must be extremely stable and chemically inert. Using relativistic density functional calculations, we found that Au20 possesses a remarkable tetrahedral structure, which is a fragment of the bulk face-centered cubic lattice of gold with a small structural relaxation. Au20 is thus a true cluster molecule, while at the same time it is exactly part of the bulk, but with very different properties. The tetrahedral Au20 may possess interesting catalytic properties and may be synthesized in bulk quantity or assembled on non-interacting surfaces.
A tetrahedral entropy for water.
Kumar, Pradeep; Buldyrev, Sergey V; Stanley, H Eugene
2009-12-29
We introduce the space-dependent correlation function C (Q)(r) and time-dependent autocorrelation function C (Q)(t) of the local tetrahedral order parameter Q identical with Q(r,t). By using computer simulations of 512 waterlike particles interacting through the transferable interaction potential with five points (TIP5 potential), we investigate C (Q)(r) in a broad region of the phase diagram. We find that at low temperatures C (Q)(t) exhibits a two-step time-dependent decay similar to the self-intermediate scattering function and that the corresponding correlation time tau(Q) displays a dynamic cross-over from non-Arrhenius behavior for T > T (W) to Arrhenius behavior for T < T (W), where T (W) denotes the Widom temperature where the correlation length has a maximum as T is decreased along a constant-pressure path. We define a tetrahedral entropy S (Q) associated with the local tetrahedral order of water molecules and find that it produces a major contribution to the specific heat maximum at the Widom line. Finally, we show that tau(Q) can be extracted from S (Q) by using an analog of the Adam-Gibbs relation. PMID:20018692
Quadratic eigenvalue problems.
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
Henchman, Richard H; Cockram, Stuart J
2013-01-01
The case for liquid water having non-tetrahedral as well as tetrahedral coordination is put forward. Given the dependence of structure on the hydrogen bond definition, a recent conceptual breakthrough has been the topological hydrogen bond definition which overcomes the shortcomings of traditional cut-off-based hydrogen bond definitions. It identifies the hydrogen bonds in water's first coordination shell using assumed transition states as boundaries instead of fixed cut-offs. Here, the topological definition is applied to liquid water to characterise the distances, angles and energies of the hydrogen bonds for the different types of coordinations found. These coordinations include bent, trigonal, tetrahedral, trigonal bipyramidal, and octahedral structures, as well as bifurcated hydrogens, bifurcated oxygens and cyclic dimers, and larger polygons. All species are shown to have properties consistent with their classification, justifying their assignments, and supporting the structure of water as a continuous, single phase mixture. However, a detailed analysis to assess the existence of the assumed transition states reveals the remarkable finding that hydrogen bond switching via a bifurcated hydrogen under certain circumstances is a barrierless process. The likelihood of a switch depends on both the acceptor numbers and on the proximity of a donor to its acceptor. Specifically, a donor in an acceptor's outermost subshell switches uphill to an acceptor of the same or higher coordination to the starting acceptor, downhill to an acceptor of lower coordination by two or more, or sits bifurcated between two acceptors if the new acceptor has a coordination lower by only one. Which it is depends intimately on the donor molecule's oscillations and on other hydrogen bond switches that control the nearby acceptors' coordinations. Finally, a search is conducted for long-range structure in water in terms of asymmetry in the distribution of the donor-acceptor bias but none is
NASA Astrophysics Data System (ADS)
Withers, Christopher S.; Nadarajah, Saralees
2012-06-01
We show that there are exactly four quadratic polynomials, Q(x) = x 2 + ax + b, such that
Resolvability and the Tetrahedral Configuration of Carbon.
ERIC Educational Resources Information Center
Kauffman, George B.
1983-01-01
Discusses evidence for the tetrahedral configuration of the carbon atom, indicating that three symmetrical configurations are theoretically possible for coordination number four. Includes table indicating that resolvability of compounds of type CR'R"R"'R"" is a necessary but not sufficient condition for proving tetrahedral configuration. (JN)
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…
Sequentially deployable maneuverable tetrahedral beam
NASA Technical Reports Server (NTRS)
Mikulas, M. M., Jr.; Crawford, R. F. (Inventor)
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.
Sequentially deployable maneuverable tetrahedral beam
NASA Astrophysics Data System (ADS)
Mikulas, M. M., Jr.; Crawford, R. F.
1985-12-01
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.
Au40: A large tetrahedral magic cluster
NASA Astrophysics Data System (ADS)
Jiang, De-En; Walter, Michael
2011-11-01
40 is a magic number for tetrahedral symmetry predicted in both nuclear physics and the electronic jellium model. We show that Au40 could be such a a magic cluster from density functional theory-based basin hopping for global minimization. The putative global minimum found for Au40 has a twisted pyramid structure, reminiscent of the famous tetrahedral Au20, and a sizable HOMO-LUMO gap of 0.69 eV, indicating its molecular nature. Analysis of the electronic states reveals that the gap is related to shell closings of the metallic electrons in a tetrahedrally distorted effective potential.
Au40: A Large Tetrahedral Magic Cluster
Jiang, Deen; Walter, Michael
2011-01-01
40 is a magic number for tetrahedral symmetry predicted in both nuclear physics and the electronic jellium model. We show that Au{sub 40} could be such a magic cluster from density functional theory-based basin hopping for global minimization. The putative global minimum found for Au{sub 40} has a twisted pyramid structure, reminiscent of the famous tetrahedral Au{sub 20}, and a sizable HOMO-LUMO gap of 0.69 eV, indicating its molecular nature. Analysis of the electronic states reveals that the gap is related to shell closings of the metallic electrons in a tetrahedrally distorted effective potential.
NASA Technical Reports Server (NTRS)
Kim, Sang-Wook
1988-01-01
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.
The Mystical "Quadratic Formula."
ERIC Educational Resources Information Center
March, Robert H.
1993-01-01
Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)
ERIC Educational Resources Information Center
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Details of tetrahedral anisotropic mesh adaptation
NASA Astrophysics Data System (ADS)
Jensen, Kristian Ejlebjerg; Gorman, Gerard
2016-04-01
We have implemented tetrahedral anisotropic mesh adaptation using the local operations of coarsening, swapping, refinement and smoothing in MATLAB without the use of any for- N loops, i.e. the script is fully vectorised. In the process of doing so, we have made three observations related to details of the implementation: 1. restricting refinement to a single edge split per element not only simplifies the code, it also improves mesh quality, 2. face to edge swapping is unnecessary, and 3. optimising for the Vassilevski functional tends to give a little higher value for the mean condition number functional than optimising for the condition number functional directly. These observations have been made for a uniform and a radial shock metric field, both starting from a structured mesh in a cube. Finally, we compare two coarsening techniques and demonstrate the importance of applying smoothing in the mesh adaptation loop. The results pertain to a unit cube geometry, but we also show the effect of corners and edges by applying the implementation in a spherical geometry.
MMS Spacecraft Transition to Tetrahedral Flying Formation
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...
Tetrahedrality and hydrogen bonds in water
NASA Astrophysics Data System (ADS)
Székely, Eszter; Varga, Imre K.; Baranyai, András
2016-06-01
We carried out extensive calculations of liquid water at different temperatures and pressures using the BK3 model suggested recently [P. T. Kiss and A. Baranyai, J. Chem. Phys. 138, 204507 (2013)]. In particular, we were interested in undercooled regions to observe the propensity of water to form tetrahedral coordination of closest neighbors around a central molecule. We compared the found tetrahedral order with the number of hydrogen bonds and with the partial pair correlation functions unfolded as distributions of the closest, the second closest, etc. neighbors. We found that contrary to the number of hydrogen bonds, tetrahedrality changes substantially with state variables. Not only the number of tetrahedral arrangements increases with lowering the pressure, the density, and the temperature but the domain size of connecting tetrahedral structures as well. The difference in tetrahedrality is very pronounced between the two sides of the Widom line and even more so between the low density amorphous (LDA) and high density amorphous (HDA) phases. We observed that in liquid water and in HDA, the 5th water molecule, contrary to ice and LDA, is positioned between the first and the second coordination shell. We found no convincing evidence of structural heterogeneity or regions referring to structural transition.
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.
A finite element computational method for high Reynolds number laminar flows
NASA Technical Reports Server (NTRS)
Kim, Sang-Wook
1987-01-01
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.
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.
NASA Astrophysics Data System (ADS)
Colin, M.; Di Menza, L.; Saut, J. C.
2016-03-01
In this paper, we investigate the properties of solitonic structures arising in quadratic media. First, we recall the derivation of systems governing the interaction process for waves propagating in such media and we check the local and global well-posedness of the corresponding Cauchy problem. Then, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or non-elliptic systems and we address the problem of orbital stability. Finally, some numerical experiments are carried out in order to compute localized states for several regimes and to study dynamic stability as well as long-time asymptotics.
The NASA Tetrahedral Unstructured Software System (TETRUSS)
NASA Technical Reports Server (NTRS)
Frink, Neal T.; Pirzadeh, Shahyar Z.; Parikh, Paresh C.; Pandya, Mohagna J.; Bhat, M. K.
2000-01-01
The NASA Tetrahedral Unstructured Software System (TetrUSS) was developed during the 1990's to provide a rapid aerodynamic analysis and design capability to applied aerodynamicists. The system is comprised of loosely integrated, user-friendly software that enables the application of advanced Euler and Navier-Stokes tetrahedral finite volume technology to complex aerodynamic problems. TetrUSS has matured well because of the generous feedback from many willing users representing a broad cross-section of background and skill levels. This paper presents an overview of the current capabilities of the TetrUSS system along with some representative results from selected applications.
Evidence for tetrahedral symmetry in (16)O.
Bijker, R; Iachello, F
2014-04-18
We derive the rotation-vibration spectrum of a 4α configuration with tetrahedral symmetry Td and show evidence for the occurrence of this symmetry in the low-lying spectrum of (16)O. All vibrational states with A, E, and F symmetry appear to have been observed as well as the rotational bands with LP=0+, 3-, 4+, 6+ on the A states and part of the rotational bands built on the E, F states. We derive analytic expressions for the form factors and B(EL) values of the ground-state rotational band and show that the measured values support the tetrahedral symmetry of this band. PMID:24785032
Quadratic spatial soliton interactions
NASA Astrophysics Data System (ADS)
Jankovic, Ladislav
Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30
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.
Quadratic soliton self-reflection at a quadratically nonlinear interface
NASA Astrophysics Data System (ADS)
Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai
2003-11-01
The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.
On a combined adaptive tetrahedral tracing and edge diffraction model
NASA Astrophysics Data System (ADS)
Hart, Carl R.
A major challenge in architectural acoustics is the unification of diffraction models and geometric acoustics. For example, geometric acoustics is insufficient to quantify the scattering characteristics of acoustic diffusors. Typically the time-independent boundary element method (BEM) is the method of choice. In contrast, time-domain computations are of interest for characterizing both the spatial and temporal scattering characteristics of acoustic diffusors. Hence, a method is sought that predicts acoustic scattering in the time-domain. A prediction method, which combines an advanced image source method and an edge diffraction model, is investigated for the prediction of time-domain scattering. Adaptive tetrahedral tracing is an advanced image source method that generates image sources through an adaptive process. Propagating tetrahedral beams adapt to ensonified geometry mapping the geometric sound field in space and along boundaries. The edge diffraction model interfaces with the adaptive tetrahedral tracing process by the transfer of edge geometry and visibility information. Scattering is quantified as the contribution of secondary sources along a single or multiple interacting edges. Accounting for a finite number of diffraction permutations approximates the scattered sound field. Superposition of the geometric and scattered sound fields results in a synthesized impulse response between a source and a receiver. Evaluation of the prediction technique involves numerical verification and numerical validation. Numerical verification is based upon a comparison with analytic and numerical (BEM) solutions for scattering geometries. Good agreement is shown for the selected scattering geometries. Numerical validation is based upon experimentally determined scattered impulse responses of acoustic diffusors. Experimental data suggests that the predictive model is appropriate for high-frequency predictions. For the experimental determination of the scattered impulse
Students' Understanding of Quadratic Equations
ERIC Educational Resources Information Center
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
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 γ- γ 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 γ- γ 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
NASA Astrophysics Data System (ADS)
Khoreshok, A. A.; Mametyev, L. E.; Borisov, A. Yu; Vorobyev, A. V.
2016-04-01
This paper presents the results of modeling of the stressed state of structural elements of the paired fastening points of the two disc tools to the tetrahedral prisms of the working bodies of the roadheaders of selective action when cutting work faces of heterogeneous structure. The advantages of cooperative mode rotation to separate two disc tools on each of the tetrahedral prisms placed between the axial cutting crowns.
Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality
Bronson, Jonathan R.; Levine, Joshua A.; Whitaker, Ross T.
2013-01-01
Summary We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity. PMID:25309969
Kinetically Trapped Tetrahedral Cages via Alkyne Metathesis.
Lee, Semin; Yang, Anna; Moneypenny, Timothy P; Moore, Jeffrey S
2016-02-24
In dynamic covalent synthesis, kinetic traps are perceived as disadvantageous, hindering the system from reaching its thermodynamic equilibrium. Here we present the near-quantitative preparation of tetrahedral cages from simple tritopic precursors using alkyne metathesis. While the cages are the presumed thermodynamic sink, we experimentally demonstrate that the products no longer exchange their vertices once they have formed. The example reported here illustrates that kinetically trapped products may facilitate high yields of complex products from dynamic covalent synthesis. PMID:26854552
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
Enhanced temperature uniformity by tetrahedral laser heating
Schroers, Jan; Bossuyt, Sven; Rhim, Won-Kyu; Li Jianzhong; Zhou Zhenhua; Johnson, William L.
2004-11-01
Temperature profile on a spherical sample that is heated by laser beams in various geometries while processed in vacuum is analyzed. Sample heating by one or four laser beams was considered. An analytical expression was derived for directional sample heating cases. It suggests an enhanced temperature uniformity over the samples when heated with four diffuse laser beams arranged in a tetrahedral geometry. This was experimentally verified by heating a spherical stainless steel sample by laser beams. Both the calculated and experimentally determined temperature variations over the sample suggest that use of diffuse four beams arranged in tetrahedral geometry would be effective in reducing temperature variation to within 1 K. The enhancement in the temperature uniformity for four diffuse beams arranged in a tetrahedral geometry by a factor of 50 over a single focused beam is promising to accurately measure of thermophysical properties. This drastic improvement in temperature uniformity might even enable atomic diffusion measurements in the undercooled liquid states of the bulk glass forming alloys since Marangoni and gravity driven convection will be substantially reduced.
Methods for prismatic/tetrahedral grid generation and adaptation
NASA Astrophysics Data System (ADS)
Kallinderis, Y.
1995-10-01
The present work involves generation of hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is a method for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A High Speed Civil Transport (HSCT) type of aircraft geometry is considered. The generated hybrid grid required only 170 K tetrahedra instead of an estimated two million had a tetrahedral mesh been used in the prisms region as well. A solution adaptive scheme for viscous computations on hybrid grids is also presented. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples 3-D, isotropic division of tetrahedra and 2-D, directional division of prisms.
Boundary Recovery For Delaunay Tetrahedral Meshes Using Local Topological Transformations
Ghadyani, Hamid; Sullivan, John; Wu, Ziji
2009-01-01
Numerous high-quality, volume mesh-generation systems exist. However, no strategy can address all geometry situations without some element qualities being compromised. Many 3D mesh generation algorithms are based on Delaunay tetrahedralization which frequently fails to preserve the input boundary surface topology. For biomedical applications, this surface preservation can be critical as they usually contain multiple material regions of interest coherently connected. In this paper we present an algorithm as a post-processing method that optimizes local regions of compromised element quality and recovers the original boundary surface facets (triangles) regardless of the original mesh generation strategy. The algorithm carves out a small sub-volume in the vicinity of the missing boundary facet or compromised element, creating a cavity. If the task is to recover a surface boundary facet, a natural exit hole in the cavity will be present. This hole is patched with the missing boundary surface face first followed by other patches to seal the cavity. If the task was to improve a compromised region, then the cavity is already sealed. Every triangular facet of the cavity shell is classified as an active face and can be connected to another shell node creating a tetrahedron. In the process the base of the tetrahedron is removed from the active face list and potentially 3 new active faces are created. This methodology is the underpinnings of our last resort method. Each active face can be viewed as the trunk of a tree. An exhaustive breath and depth search will identify all possible tetrahedral combinations to uniquely fill the cavity. We have streamlined this recursive process reducing the time complexity by orders of magnitude. The original surfaces boundaries (internal and external) are fully restored and the quality of compromised regions improved. PMID:20305743
Small Power Technology for Tetrahedral Rovers
NASA Astrophysics Data System (ADS)
Clark, P. E.; Floyd, S. R.; Butler, C. D.; Flom, Y.
2006-01-01
The Small Power Technology (SPOT) being studied at GSFC has the potential to be an efficient and compact radioisotope based electrical power system. Such a system would provide power for innovative tetrahedral robotic arms and walkers to support the lunar exploration initiative within the next decade. Presently, NASA has designated two flight qualified Radioisotope Power Supplies (RPS): the Multi-Mission RTG (MMRTG) which uses thermocouple technology and the more efficient but more massive Stirling RTG (SRTG) which uses a mechanical heat (Stirling) engine technology. With SPOT, thermal output from a radioisotope source is converted to electrical power using a combination of shape memory material and piezoelectric crystals. The SPOT combined energy conversion technologies are potentially more efficient than thermocouples and do not require moving parts, thus keeping efficiency high with an excellent mass to power ratio. Applications of particular interest are highly modular, addressable, reconfigurable arrays of tetrahedral structural components designed to be arms or rovers with high mobility in rough terrain. Such prototypes are currently being built at GSFC. Missions requiring long-lived operation in unilluminated environments preclude the use of solar cells as the main power source and must rely on the use of RPS technology. The design concept calls for a small motor and battery assembly for each strut, and thus a distributed power system. We estimate, based on performance of our current tetrahedral prototypes and power scaling for small motors, that such devices require tens of watts of power output per kilogram of power supply. For these reasons, SPOT is a good candidate for the ART (addressable Reconfigurable Technology) baseline power system.
Extreme Mobility: Next Generation Tetrahedral Rovers
NASA Astrophysics Data System (ADS)
Clark, P. E.; Curtis, S. A.; Rilee, M. L.; Cheung, C. Y.; Wesenberg, R.; Brown, G.; Cooperrider, C.
2007-01-01
This paper describes the development and testing of a patented rover concept called Tetrahedral Explorer Technologies (TET), designed to provide extreme mobility and plug-and-play utility through reconfigurable addressable architecture. Here, we present the results of preliminary lab and field tests of Prototype III. Reconfigurable architecture is essential in exploration because reaching features of the great potential interest will require crossing a wide range of terrains largely inaccessible to permanently appendaged vehicles. One surface might be relatively flat and navigable, while another could be rough, variably sloping, broken, or dominated by unconsolidated debris. To be totally functional, structures must form pseudo-appendages varying in size, rate, and manner of deployment (gait) and moving at a speed approaching that of a human in rugged terrain. TET architecture is based on the tetrahedron, the basic space-filling shape, as building block. Tetrahedra are interconnected, their apices acting as nodes from which struts reversibly deploy. The tetrahedral framework acts as a simple skeletal muscular structure. Two simple robotic walker prototypes have already been developed from a single reconfigurable tetrahedron capable of tumbling. This paper presents the results of our attempts to simulate motions, improve the hardware, and develop gaits for a more evolved 12Tetrahedral Walker (Prototype 3) which high degrees of freedom locomotion commandable through a user friendly interface. Our rover is an early level mission concept, realized as an electromechanical system at present, which would allow autonomous in situ exploration of lunar sites when we return to the Moon. Such a rover could carry into inaccessible terrain an in situ analysis payload designed to provide not only details of composition of traversed terrain, but the identification of sites with resources useful for permanent bases, including water and high Ti glass.
Dark Matter from Binary Tetrahedral Flavor Symmetry
NASA Astrophysics Data System (ADS)
Eby, David; Frampton, Paul
2012-03-01
Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.
A quadratic analog-to-digital converter
NASA Technical Reports Server (NTRS)
Harrison, D. C.; Staples, M. H.
1980-01-01
An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.
Students' understanding of quadratic equations
NASA Astrophysics Data System (ADS)
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
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.
Phase diagram of a truncated tetrahedral model.
Krcmar, Roman; Gendiar, Andrej; Nishino, Tomotoshi
2016-08-01
Phase diagram of a discrete counterpart of the classical Heisenberg model, the truncated tetrahedral model, is analyzed on the square lattice, when the interaction is ferromagnetic. Each spin is represented by a unit vector that can point to one of the 12 vertices of the truncated tetrahedron, which is a continuous interpolation between the tetrahedron and the octahedron. Phase diagram of the model is determined by means of the statistical analog of the entanglement entropy, which is numerically calculated by the corner transfer matrix renormalization group method. The obtained phase diagram consists of four different phases, which are separated by five transition lines. In the parameter region, where the octahedral anisotropy is dominant, a weak first-order phase transition is observed. PMID:27627273
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.
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
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.
More About the Tetrahedral Unstructured Software System
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.; Frink, Neal T.; Hunter, Craig A.; Parikh, Paresh C.; Pizadeh, Shalyar Z.; Samareh, Jamshid A.; Bhat, Maharaj K.; Pandya, Mohagna J.; Grismer, Matthew J.
2006-01-01
TetrUSS is a comprehensive suite of computational fluid dynamics (CFD) programs that won the Software of the Year award in 1996 and has found increasing use in government, academia, and industry for solving realistic flow problems (especially in aerodynamics and aeroelastics of aircraft having complex shapes). TetrUSS includes not only programs for solving basic equations of flow but also programs that afford capabilities for efficient generation and utilization of computational grids and for graphical representation of computed flows (see figure). The 2004 version of the Tetrahedral Unstructured Software System (TetrUSS), which is one of two software systems reported in "NASA s 2004 Software of the Year," NASA Tech Briefs, Vol. 28, No. 10 (October 2004), page 18, has been improved greatly since 1996. These improvements include (1) capabilities to simulate viscous flow by solving the Navier-Stokes equations on unstructured grids, (2) portability to personal computers from diverse manufacturers, (3) advanced models of turbulence, (4) a parallel-processing version of one of the unstructured-grid Navier-Stokes-equation-solving programs, and (5) advanced programs for generating unstructured grids.
Streaming Compression of Tetrahedral Volume Meshes
Isenburg, M; Lindstrom, P; Gumhold, S; Shewchuk, J
2005-11-21
Geometry processing algorithms have traditionally assumed that the input data is entirely in main memory and available for random access. This assumption does not scale to large data sets, as exhausting the physical memory typically leads to IO-inefficient thrashing. Recent works advocate processing geometry in a 'streaming' manner, where computation and output begin as soon as possible. Streaming is suitable for tasks that require only local neighbor information and batch process an entire data set. We describe a streaming compression scheme for tetrahedral volume meshes that encodes vertices and tetrahedra in the order they are written. To keep the memory footprint low, the compressor is informed when vertices are referenced for the last time (i.e. are finalized). The compression achieved depends on how coherent the input order is and how many tetrahedra are buffered for local reordering. For reasonably coherent orderings and a buffer of 10,000 tetrahedra, we achieve compression rates that are only 25 to 40 percent above the state-of-the-art, while requiring drastically less memory resources and less than half the processing time.
Quadratic expressions by means of `summing all the matchsticks'
NASA Astrophysics Data System (ADS)
Faaiz Gierdien, M.
2012-09-01
This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such 'matchstick' problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are linear and not quadratic. It will be shown that a pedagogy of 'summing all the matchsticks' is central to the emergence of quadratic expressions. This pedagogy involves generational and transformational activities which are considered as some of the main activities of algebra. Key elements to these activities are processes such as recognizing and extending patterns, and specializing and generalizing particular functional relationships. Implications of these processes in terms of algebraic thinking are considered.
Orthogonality preserving infinite dimensional quadratic stochastic operators
Akın, Hasan; Mukhamedov, Farrukh
2015-09-18
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Preliminary design of a large tetrahedral truss/hexagonal heatshield panel aerobrake
NASA Technical Reports Server (NTRS)
Dorsey, John T.; Mikulas, Martin M., Jr.
1989-01-01
An aerobrake structural concept is introduced which consists of two primary components: (1) a lightweight erectable tetrahedral support truss; and (2) sandwich hexagonal heatshield panels which, when attached to the truss, form a continuous impermeable aerobraking surface. Generic finite element models and a general analysis procedure to design tetrahedral truss/hexagonal heatshield panel aerobrakes is developed, and values of the aerobrake design parameters which minimize mass and packaging volume for a 120-foot-diameter aerobrake are determined. Sensitivity of the aerobrake design to variations in design parameters is also assessed. The results show that a 120-foot-diameter aerobrake is viable using the concept presented (i.e., the aerobrake mass is less than or equal to 15 percent of the payload spacecraft mass). Minimizing the aerobrake mass (by increasing the number of rings in the support truss) however, leads to aerobrakes with the highest part count.
Adaptive hybrid prismatic-tetrahedral grids for viscous flows
NASA Astrophysics Data System (ADS)
Kallinderis, Yannis; Khawaja, Aly; McMorris, Harlan
1995-03-01
The paper presents generation of adaptive hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is an Automatic Receding Method (ARM) for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples division of tetrahedra, as well as 2-D directional division of prisms.
Adaptive hybrid prismatic-tetrahedral grids for viscous flows
NASA Technical Reports Server (NTRS)
Kallinderis, Yannis; Khawaja, Aly; Mcmorris, Harlan
1995-01-01
The paper presents generation of adaptive hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is an Automatic Receding Method (ARM) for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples division of tetrahedra, as well as 2-D directional division of prisms.
Dynamic Modulation of DNA Hybridization Using Allosteric DNA Tetrahedral Nanostructures.
Song, Ping; Li, Min; Shen, Juwen; Pei, Hao; Chao, Jie; Su, Shao; Aldalbahi, Ali; Wang, Lihua; Shi, Jiye; Song, Shiping; Wang, Lianhui; Fan, Chunhai; Zuo, Xiaolei
2016-08-16
The fixed dynamic range of traditional biosensors limits their utility in several real applications. For example, viral load monitoring requires the dynamic range spans several orders of magnitude; whereas, monitoring of drugs requires extremely narrow dynamic range. To overcome this limitation, here, we devised tunable biosensing interface using allosteric DNA tetrahedral bioprobes to tune the dynamic range of DNA biosensors. Our strategy takes the advantage of the readily and flexible structure design and predictable geometric reconfiguration of DNA nanotechnology. We reconfigured the DNA tetrahedral bioprobes by inserting the effector sequence into the DNA tetrahedron, through which, the binding affinity of DNA tetrahedral bioprobes can be tuned. As a result, the detection limit of DNA biosensors can be programmably regulated. The dynamic range of DNA biosensors can be tuned (narrowed or extended) for up to 100-fold. Using the regulation of binding affinity, we realized the capture and release of biomolecules by tuning the binding behavior of DNA tetrahedral bioprobes. PMID:27435955
A boundary recovery algorithm for Delaunay tetrahedral meshing
Sharov, D.; Nakahashi, K.
1996-12-31
A method for automatic generation of unstructured grids comprised of tetrahedra is discussed. Delaunay approach for tetrahedral grid generation is used. Particular attention is given to the boundary constraining problem. A simple and robust algorithm for the boundary constraining by successive use of boundary edge swapping, tetrahedral edge swapping and direct subdivision of tetrahedra is used. Small modifications allow to apply the method for viscous grid generation as well. Grid examples demonstrate efficiency of the method.
Coherent states for quadratic Hamiltonians
NASA Astrophysics Data System (ADS)
Contreras-Astorga, Alonso; Fernández C, David J.; Velázquez, Mercedes
2011-01-01
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
Geometrical and Graphical Solutions of Quadratic Equations.
ERIC Educational Resources Information Center
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Single-photon quadratic optomechanics
Liao, Jie-Qiao; Nori, Franco
2014-01-01
We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon. PMID:25200128
THE GENERATION OF TETRAHEDRAL MESH MODELS FOR NEUROANATOMICAL MRI
Lederman, Carl; Joshi, Anand; Dinov, Ivo; Vese, Luminita; Toga, Arthur; Van Horn, John Darrell
2010-01-01
In this article, we describe a detailed method for automatically generating tetrahedral meshes from 3D images having multiple region labels. An adaptively sized tetrahedral mesh modeling approach is described that is capable of producing meshes conforming precisely to the voxelized regions in the image. Efficient tetrahedral construction is performed minimizing an energy function containing three terms: a smoothing term to remove the voxelization, a fidelity term to maintain continuity with the image data, and a novel elasticity term to prevent the tetrahedra from becoming flattened or inverted as the mesh deforms while allowing the voxelization to be removed entirely. The meshing algorithm is applied to structural MR image data that has been automatically segmented into 56 neuroanatomical sub-divisions as well as on two other examples. The resulting tetrahedral representation has several desirable properties such as tetrahedra with dihedral angles away from 0 and 180 degrees, smoothness, and a high resolution. Tetrahedral modeling via the approach described here has applications in modeling brain structure in normal as well as diseased brain in human and non-human data and facilitates examination of 3D object deformations resulting from neurological illness (e.g. Alzheimer’s Disease), development, and/or aging. PMID:21073968
A comparison of tetrahedral mesh improvement techniques
Freitag, L.A.; Ollivier-Gooch, C.
1996-12-01
Automatic mesh generation and adaptive refinement methods for complex three-dimensional domains have proven to be very successful tools for the efficient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more difficult to compute. Fortunately, the shape of the elements can be improved through several mechanisms, including face-swapping techniques that change local connectivity and optimization-based mesh smoothing methods that adjust grid point location. The authors consider several criteria for each of these two methods and compare the quality of several meshes obtained by using different combinations of swapping and smoothing. Computational experiments show that swapping is critical to the improvement of general mesh quality and that optimization-based smoothing is highly effective in eliminating very small and very large angles. The highest quality meshes are obtained by using a combination of swapping and smoothing techniques.
Binary Quadratic Forms: A Historical View
ERIC Educational Resources Information Center
Khosravani, Azar N.; Beintema, Mark B.
2006-01-01
We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…
An Unexpected Influence on a Quadratic
ERIC Educational Resources Information Center
Davis, Jon D.
2013-01-01
Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…
Factorising a Quadratic Expression with Geometric Insights
ERIC Educational Resources Information Center
Joarder, Anwar H.
2015-01-01
An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…
Molecular origin of auxetic behavior in tetrahedral framework silicates.
Alderson, Andrew; Evans, Kenneth E
2002-11-25
Recent analytical models for the Poisson's ratios (nu(ij)) of tetrahedral frameworks are applied to alpha-cristobalite and alpha-quartz for the first time. Rotation and dilation of the SiO4 tetrahedral subunits are considered. Each mechanism leads to negative nu(31) values, whereas negative and positive values are possible when they act concurrently. The concurrent model is in excellent agreement with experiment and explains the dichotomy between negative and positive nu(31) values in alpha-cristobalite and alpha-quartz, respectively. The predicted strain-dependent trends confirm those from molecular modeling. PMID:12485081
The response of cranial biomechanical finite element models to variations in mesh density.
Bright, Jen A; Rayfield, Emily J
2011-04-01
Finite element (FE) models provide discrete solutions to continuous problems. Therefore, to arrive at the correct solution, it is vital to ensure that FE models contain a sufficient number of elements to fully resolve all the detail encountered in a continuum structure. Mesh convergence testing is the process of comparing successively finer meshes to identify the point of diminishing returns; where increasing resolution has marginal effects on results and further detail would become costly and unnecessary. Historically, convergence has not been considered in most CT-based biomechanical reconstructions involving complex geometries like the skull, as generating such models has been prohibitively time-consuming. To assess how mesh convergence influences results, 18 increasingly refined CT-based models of a domestic pig skull were compared to identify the point of convergence for strain and displacement, using both linear and quadratic tetrahedral elements. Not all regions of the skull converged at the same rate, and unexpectedly, areas of high strain converged faster than low-strain regions. Linear models were slightly stiffer than their quadratic counterparts, but did not converge less rapidly. As expected, insufficiently dense models underestimated strain and displacement, and failed to resolve strain "hot-spots" notable in contour plots. In addition to quantitative differences, visual assessments of such plots often inform conclusions drawn in many comparative studies, highlighting that mesh convergence should be performed on all finite element models before further analysis takes place. PMID:21370496
NASA Astrophysics Data System (ADS)
Louboutin, Stephane
1992-07-01
Starting from the analytic class number formula involving its L-function, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class number tables. Then, using class field theory, we will construct a periodic character &chi , defined on the ring of integers of a field K that is a quadratic extension of a principal imaginary quadratic field k, such that the zeta function of K is the product of the zeta function of k and of the L-function L(s,χ) . We will then determine an integral representation of this L-function that enables us to calculate the class number of K numerically, as soon as its regulator is known. It will also provide us with an upper bound for these class numbers, showing that Hua's bound for the class numbers of imaginary and real quadratic fields is not the best that one could expect. We give statistical results concerning the class numbers of the first 50000 quadratic extensions of {Q}(i) with prime relative discriminant (and with K/Q a non-Galois quartic extension). Our analytic calculation improves the algebraic calculation used by Lakein in the same way as the analytic calculation of the class numbers of real quadratic fields made by Williams and Broere improved the algebraic calculation consisting in counting the number of cycles of reduced ideals. Finally, we give upper bounds for class numbers of K that is a quadratic extension of an imaginary quadratic field k which is no longer assumed to be of class number one.
Selective refinement queries for volume visualization of unstructured tetrahedral meshes.
Cignoni, Paolo; De Floriani, Leila; Magillo, Paola; Puppo, Enrico; Scopigno, Roberto
2004-01-01
In this paper, we address the problem of the efficient visualization of large irregular volume data sets by exploiting a multiresolution model based on tetrahedral meshes. Multiresolution models, also called Level-Of-Detail (LOD) models, allow encoding the whole data set at a virtually continuous range of different resolutions. We have identified a set of queries for extracting meshes at variable resolution from a multiresolution model, based on field values, domain location, or opacity of the transfer function. Such queries allow trading off between resolution and speed in visualization. We define a new compact data structure for encoding a multiresolution tetrahedral mesh built through edge collapses to support selective refinement efficiently and show that such a structure has a storage cost from 3 to 5.5 times lower than standard data structures used for tetrahedral meshes. The data structures and variable resolution queries have been implemented together with state-of-the art visualization techniques in a system for the interactive visualization of three-dimensional scalar fields defined on tetrahedral meshes. Experimental results show that selective refinement queries can support interactive visualization of large data sets. PMID:15382696
Hinge specification for a square-faceted tetrahedral truss
NASA Technical Reports Server (NTRS)
Adams, L. R.
1984-01-01
A square-faceted tetrahedral truss is geometrically analyzed. Expressions are developed for single degree of freedom hinges which allow packaging of the structure into a configuration in which all members are parallel and closely packed in a square pattern. Deployment is sequential, thus providing control over the structure during deployment.
Tetrahedral Models of Learning: Application to College Reading.
ERIC Educational Resources Information Center
Nist, Sherrie L.
J. D. Bransford's tetrahedral model of learning considers four variables: (1) learning activities, (2) characteristics of the learner, (3) criterial tasks, and (4) the nature of the materials. Bransford's model provides a research-based theoretical framework that can be used to teach, model, and have students apply a variety of study strategies to…
Quadratic boundedness of uncertain nonlinear dynamic systems
NASA Astrophysics Data System (ADS)
Brockman, Mark Lawrence
Physical systems are often perturbed by unknown external disturbances or contain important system parameters which are difficult to model exactly. However, engineers are expected to design systems which perform well even in the presence of uncertainties. For example, an airplane designer can never know the precise direction or magnitude of wind gusts, or the exact mass distribution inside the aircraft, but passengers expect to arrive on time after a smooth ride. This thesis will first present the concept of quadratic boundedness of an uncertain nonlinear dynamic system, and then develop analysis techniques and control design methods for systems containing unknown disturbances and parameters. For a class of nonlinear systems, conditions for quadratic boundedness are given, and the relationship between quadratic boundedness and quadratic stability is explored. An important consequence of quadratic boundedness is the ability to calculate an upper bound on the system gain of an uncertain nonlinear system. For nominally linear systems, necessary and sufficient conditions for quadratic boundedness are given. The innovative use of linear matrix inequalities in an iterative algorithm provides a means to analyze the quadratic boundedness properties of systems containing parameter uncertainties. The analysis results establish a framework for the development of design methods which integrate performance specifications into the control design process for all the types of systems considered. Numerous examples illustrate the major results of the thesis.
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.
Seven Wonders of the Ancient and Modern Quadratic World.
ERIC Educational Resources Information Center
Taylor, Sharon E.; Mittag, Kathleen Cage
2001-01-01
Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)
Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes
NASA Technical Reports Server (NTRS)
Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.
2015-01-01
Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the
Quadratic Stochastic Operators with Countable State Space
NASA Astrophysics Data System (ADS)
Ganikhodjaev, Nasir
2016-03-01
In this paper, we provide the classes of Poisson and Geometric quadratic stochastic operators with countable state space, study the dynamics of these operators and discuss their application to economics.
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.)
Quantum integrability of quadratic Killing tensors
Duval, C.; Valent, G.
2005-05-01
Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a 'minimal' quantization scheme, quantum integrability is ensured for a large class of classic examples.
Weight of quadratic forms and graph states
NASA Astrophysics Data System (ADS)
Cosentino, Alessandro; Severini, Simone
2009-11-01
We prove a connection between Schmidt rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.
Quadratic mutual information for dimensionality reduction and classification
NASA Astrophysics Data System (ADS)
Gray, David M.; Principe, José C.
2010-04-01
A research area based on the application of information theory to machine learning has attracted considerable interest in the last few years. This research area has been coined information-theoretic learning within the community. In this paper we apply elements of information-theoretic learning to the problem of automatic target recognition (ATR). A number of researchers have previously shown the benefits of designing classifiers based on maximizing the mutual information between the class data and the class labels. Following prior research in information-theoretic learning, in the current results we show that quadratic mutual information, derived using a special case of the more general Renyi's entropy, can be used for classifier design. In this implementation, a simple subspace projection classifier is formulated to find the optimal projection weights such that the quadratic mutual information between the class data and the class labels is maximized. This subspace projection accomplishes a dimensionality reduction of the raw data set wherein information about the class membership is retained while irrelevant information is discarded. A subspace projection based on this criterion preserves as much class discriminability as possible within the subspace. For this paper, laser radar images are used to demonstrate the results. Classification performance against this data set is compared for a gradient descent MLP classifier and a quadratic mutual information MLP classifier.
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.
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.
Transition Strength Ratios in the Tetrahedral Candidate ^156Dy
NASA Astrophysics Data System (ADS)
Hartley, D. J.; Riedinger, L. L.; Curien, D.; Dudek, J.; Gall, B.; Allmond, J. M.; Beausang, C. W.; Carpenter, M. P.; Chiara, C. J.; Janssens, R. V. F.; Kondev, F. G.; Lauritsen, T.; McCutchan, E. A.; Stefanescu, I.; Zhu, S.; Garrett, P. E.; Kulp, W. D.; Wood, J. L.; Mazurek, K.; Riley, M. A.; Wang, X.; Schunck, N.; Yu, C.-H.; Sharpey-Schafer, J.; Simpson, J.
2009-10-01
A new symmetry has been recently proposed where nuclei may stabilize in a tetrahedral (pyramid) shape. One of the consequences of this symmetry is that the transition strength, B(E2), of the inband transitions should approach zero in the ideal case. Thus, one signal of this exotic shape would be a rotational band where the inband E2 transitions are extremely weak or nonexistent. Such bands exist in many of the lowest negative-parity bands in the N 90 nuclei, which is also a predicted ``magic" region for tetrahedral symmetry. A Gammasphere experiment was performed to measure the B(E2)/B(E1) ratios of such a negative-parity band in ^156Dy. The results (which are consistent with the theory) will be presented, as well as a discussion of the proposed follow-up experiment to directly measure the B(E2) rates.
Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2012-01-01
Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522
Coarse-grained theory of a realistic tetrahedral liquid model
NASA Astrophysics Data System (ADS)
Procaccia, I.; Regev, I.
2012-02-01
Tetrahedral liquids such as water and silica-melt show unusual thermodynamic behavior such as a density maximum and an increase in specific heat when cooled to low temperatures. Previous work had shown that Monte Carlo and mean-field solutions of a lattice model can exhibit these anomalous properties with or without a phase transition, depending on the values of the different terms in the Hamiltonian. Here we use a somewhat different approach, where we start from a very popular empirical model of tetrahedral liquids —the Stillinger-Weber model— and construct a coarse-grained theory which directly quantifies the local structure of the liquid as a function of volume and temperature. We compare the theory to molecular-dynamics simulations and show that the theory can rationalize the simulation results and the anomalous behavior.
Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation.
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2012-12-01
Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing "bad" triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522
Optimal channels for channelized quadratic estimators.
Kupinski, Meredith K; Clarkson, Eric
2016-06-01
We present a new method for computing optimized channels for estimation tasks that is feasible for high-dimensional image data. Maximum-likelihood (ML) parameter estimates are challenging to compute from high-dimensional likelihoods. The dimensionality reduction from M measurements to L channels is a critical advantage of channelized quadratic estimators (CQEs), since estimating likelihood moments from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. The channelized likelihood is then used to form ML estimates of the parameter(s). In this work we choose an imaging example in which the second-order statistics of the image data depend upon the parameter of interest: the correlation length. Correlation lengths are used to approximate background textures in many imaging applications, and in these cases an estimate of the correlation length is useful for pre-whitening. In a simulation study we compare the estimation performance, as measured by the root-mean-squared error (RMSE), of correlation length estimates from CQE and power spectral density (PSD) distribution fitting. To abide by the assumptions of the PSD method we simulate an ergodic, isotropic, stationary, and zero-mean random process. These assumptions are not part of the CQE formalism. The CQE method assumes a Gaussian channelized likelihood that can be a valid for non-Gaussian image data, since the channel outputs are formed from weighted sums of the image elements. We have shown that, for three or more channels, the RMSE of CQE estimates of correlation length is lower than conventional PSD estimates. We also show that computing CQE by using a standard nonlinear optimization method produces channels that yield RMSE within 2% of the analytic optimum. CQE estimates of anisotropic correlation length estimation are reported to demonstrate this technique on a two-parameter estimation problem. PMID:27409452
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.
ATTILA: A three-dimensional, unstructured tetrahedral mesh discrete ordinates transport code
Wareing, T.A.; McGhee, J.M.; Morel, J.E.
1996-12-31
Many applications of radiation transport require the accurate modeling of complex three-dimensional geometries. Historically, Monte Carlo codes have been used for such applications. Existing deterministic transport codes were not applied to such problems because of the difficulties of modeling complex three-dimensional geometries with rectangular meshes. The authors have developed a three-dimensional discrete ordinates (S{sub n}) code, ATTILA, which uses linear-discontinuous finite element spatial differencing in conjunction with diffusion-synthetic acceleration (DSA) on an unstructured tetrahedral mesh. This tetrahedral mesh capability enables the authors to efficiently model complex three-dimensional geometries. One interesting and challenging application of neutron and/or gamma-ray transport is nuclear well-logging applications. Nuclear well-logging problems usually involve a complex geometry with fixed sources and one or more detectors. Detector responses must generally be accurate to within {approx}1%. The combination of complex three-dimensional geometries and high accuracy requirements makes it difficult to perform logging problems with traditional S{sub n} differencing schemes and rectangular meshes. Hence, it is not surprising that deterministic S{sub n} codes have seen limited use in nuclear well-logging applications. The geometric modeling capabilities and the advanced spatial differencing of ATTILA give it a significant advantage, relative to traditional S{sub n} codes, for performing nuclear well-logging calculations.
Schwarz and multilevel methods for quadratic spline collocation
Christara, C.C.; Smith, B.
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
The Factorability of Quadratics: Motivation for More Techniques
ERIC Educational Resources Information Center
Bosse, Michael J.; Nandakumar, N. R.
2005-01-01
Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…
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
Limit cycles near hyperbolas in quadratic systems
NASA Astrophysics Data System (ADS)
Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume
In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics DI2a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability.
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624
Quadratic forms of projective spaces over rings
NASA Astrophysics Data System (ADS)
Levchuk, V. M.; Starikova, O. A.
2006-06-01
In the passage from fields to rings of coefficients quadratic forms with invertible matrices lose their decisive role. It turns out that if all quadratic forms over a ring are diagonalizable, then in effect this is always a local principal ideal ring R with 2\\in R^*. The problem of the construction of a `normal' diagonal form of a quadratic form over a ring R faces obstacles in the case of indices \\vert R^*:R^{*2}\\vert greater than 1. In the case of index 2 this problem has a solution given in Theorem 2.1 for 1+R^{*2}\\subseteq R^{*2} (an extension of the law of inertia for real quadratic forms) and in Theorem 2.2 for 1+R^2 containing an invertible non-square. Under the same conditions on a ring R with nilpotent maximal ideal the number of classes of projectively congruent quadratic forms of the projective space associated with a free R-module of rank n is explicitly calculated (Proposition 3.2). Up to projectivities, the list of forms is presented for the projective plane over R and also (Theorem 3.3) over the local ring F\\lbrack\\lbrack x,y\\rbrack\\rbrack/\\langle x^{2},xy,y^{2}\\rangle with non-principal maximal ideal, where F=2F is a field with an invertible non-square in 1+F^{2} and \\vert F^{*}:F^{*2}\\vert=2. In the latter case the number of classes of non-diagonalizable quadratic forms of rank 0 depends on one's choice of the field F and is not even always finite; all the other forms make up 21 classes.
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.
Heredity in one-dimensional quadratic maps
NASA Astrophysics Data System (ADS)
Romera, M.; Pastor, G.; Alvarez, G.; Montoya, F.
1998-12-01
In an iterative process, as is the case of a one-dimensional quadratic map, heredity has never been mentioned. In this paper we show that the pattern of a superstable orbit of a one-dimensional quadratic map can be expressed as the sum of the gene of the chaotic band where the pattern is to be found, and the ancestral path that joins all its ancestors. The ancestral path holds all the needed genetic information to calculate the descendants of the pattern. The ancestral path and successive descendant generations of the pattern constitute the family tree of the pattern, which is important to study and understand the orbit's ordering.
Quadratic-Like Dynamics of Cubic Polynomials
NASA Astrophysics Data System (ADS)
Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen
2016-02-01
A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.
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 λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
On orthogonality preserving quadratic stochastic operators
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA
NASA Technical Reports Server (NTRS)
Djomehri, M. Jahed; Erickson, Larry L.
1994-01-01
A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.
NASA Astrophysics Data System (ADS)
Yang, Xiaofeng; James, Ashley J.
2006-05-01
In volume of fluid methods for interfacial flow simulations, one essential process is the so-called interface reconstruction, in which an approximate interface is reconstructed from a given discrete volume fraction field. In [J. Comput. Phys. 164 (2000) 228-237], Scardovelli and Zaleski presented analytical relations connecting linear interfaces and volume fractions in rectangular grids. Here, we present analytical relations connecting linear interfaces and volume fractions in triangular and tetrahedral grids. For computing the volume of fluid in an arbitrary polygonal or polyhedral fluid element, we also cite some of the most efficient formulas for polygon area and polyhedron volume computations. Simple test cases show that this analytic method of interface reconstruction is about 18 times faster than an iterative method in two dimensions, and four to six times faster in three dimensions. The results can be in general applied to other fields as well.
Platelet adhesion on phosphorus-incorporated tetrahedral amorphous carbon films
NASA Astrophysics Data System (ADS)
Liu, Aiping; Zhu, Jiaqi; Liu, Meng; Dai, Zhifei; Han, Xiao; Han, Jiecai
2008-11-01
The haemocompatibility of phosphorus-incorporated tetrahedral amorphous carbon (ta-C:P) films, synthesized by filtered cathodic vacuum arc technique with PH 3 as the dopant source, was assessed by in vitro platelet adhesion tests. Results based on scanning electron microscopy and contact angle measurements reveal that phosphorus incorporation improves the wettability and blood compatibility of ta-C film. Our studies may provide a novel approach for the design and synthesis of doped ta-C films to repel platelet adhesion and reduce thrombosis risk.
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.
Integration of the Quadratic Function and Generalization
ERIC Educational Resources Information Center
Mitsuma, Kunio
2011-01-01
We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…
Curious Consequences of a Miscopied Quadratic
ERIC Educational Resources Information Center
Poet, Jeffrey L.; Vestal, Donald L., Jr.
2005-01-01
The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.
Fourier analysis of quadratic phase interferograms
NASA Astrophysics Data System (ADS)
Muñoz-Maciel, Jesús; Mora-González, Miguel; Casillas-Rodríguez, Francisco J.; Peña-Lecona, Francisco G.
2015-06-01
A phase demodulation method from a single interferogram with a quadratic phase term is developed. The fringe pattern being analysed may contain circular, elliptic or astigmatic fringes. The Fourier transform of such interferograms is seen to be also a sine or a cosine of a second order polynomial in both the real and imaginary parts. In this work we take a discrete Fourier transform of the fringe patterns and then we take separate inverse discrete transforms of the real and imaginary parts of the frequency spectrum. This results in two new interferograms corresponding to the sine and cosine of the quadratic term of the phase modulated by the sine and cosine of the linear term. The linear term of these interferograms may be recovered with similar procedures of fringe analysis from open fringe interferograms. Once the linear term is retrieved the quadratic phase of the interferogram being analysed can also be calculated. The present approach is also being investigated for interferograms with nearly circularly symmetry given that the phase contains some tilt. The described procedure of Fourier analysis from quadratic phase interferograms of nearly symmetric interferograms could be used instead of complex and time consuming algorithms for phase recovery from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.
Quadratic minima and modular forms II
NASA Astrophysics Data System (ADS)
Brent, Barry
We give upper bounds on the size of the gap between a non-zero constant term and the next non-zero Fourier coefficient of an entire level two modular form. We give upper bounds for the minimum positive integer represented by a level two even positive-definite quadratic form. These bounds extend partial results in part I.
Robust linear quadratic designs with respect to parameter uncertainty
NASA Technical Reports Server (NTRS)
Douglas, Joel; Athans, Michael
1992-01-01
The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.
Evaluation of a Kinematically-Driven Finite Element Footstrike Model.
Hannah, Iain; Harland, Andy; Price, Dan; Schlarb, Heiko; Lucas, Tim
2016-06-01
A dynamic finite element model of a shod running footstrike was developed and driven with 6 degree of freedom foot segment kinematics determined from a motion capture running trial. Quadratic tetrahedral elements were used to mesh the footwear components with material models determined from appropriate mechanical tests. Model outputs were compared with experimental high-speed video (HSV) footage, vertical ground reaction force (GRF), and center of pressure (COP) excursion to determine whether such an approach is appropriate for the development of athletic footwear. Although unquantified, good visual agreement to the HSV footage was observed but significant discrepancies were found between the model and experimental GRF and COP readings (9% and 61% of model readings outside of the mean experimental reading ± 2 standard deviations, respectively). Model output was also found to be highly sensitive to input kinematics with a 120% increase in maximum GRF observed when translating the force platform 2 mm vertically. While representing an alternative approach to existing dynamic finite element footstrike models, loading highly representative of an experimental trial was not found to be achievable when employing exclusively kinematic boundary conditions. This significantly limits the usefulness of employing such an approach in the footwear development process. PMID:26671721
NASA Technical Reports Server (NTRS)
Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung
2016-01-01
Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-12-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-01-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
Characterization of a Quadratic Function in Rn
ERIC Educational Resources Information Center
Xu, Conway
2010-01-01
It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.
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.
An alternative method on quadratic programming problems
NASA Astrophysics Data System (ADS)
Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.
2015-05-01
In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.
Extended Decentralized Linear-Quadratic-Gaussian Control
NASA Technical Reports Server (NTRS)
Carpenter, J. Russell
2000-01-01
A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.
Optimal Approximation of Quadratic Interval Functions
NASA Technical Reports Server (NTRS)
Koshelev, Misha; Taillibert, Patrick
1997-01-01
Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.
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.
Graphical Solution of the Monic Quadratic Equation with Complex Coefficients
ERIC Educational Resources Information Center
Laine, A. D.
2015-01-01
There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…
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...
Photoconductive Detection of Tetrahedrally Coordinated Hydrogen in ZnO
NASA Astrophysics Data System (ADS)
Koch, S. G.; Lavrov, E. V.; Weber, J.
2012-04-01
In this Letter we apply an innovative experimental approach, which allows us to improve the sensitivity of detecting local vibrational modes (LVMs) even in highly absorbing spectral regions. This photoconductive technique allowed us to confirm a recent suggestion of a new multicenter bond for hydrogen in ZnO [A. Janotti and C. G. Van de Walle, Nature Mater.NMAACR1476-1122 6, 44 (2007)10.1038/nmat1795]. The two LVMs of the hydrogen substituting oxygen in ZnO are identified at 742 and 792cm-1. The modes belong to a nondegenerated A1 and a twofold degenerated E representations of the C3v point group. The tetrahedral coordination of the hydrogen atom is the result of a newly detected multicenter bond for defects in solids.
Search for Tetrahedral Symmetry in Nuclei:. a Short Overview
NASA Astrophysics Data System (ADS)
Curien, D.; Dudek, J.; Molique, H.; Sengele, L.; Góźdź, A.; Mazurek, K.
Following a series of experiments launched by the TetraNuc collaboration to possibly demonstrate the existence of high-rank symmetries in subatomic physics, the first experimental results on the Rare Earth region appear in publications. Meanwhile an important progress has been made on the theory side strongly suggesting that the original criterion of the static tetrahedral symmetry in the form of vanishing quadrupole moments may need to be revised to include explicitly the vibrational motion. The Actinide region seems of particular interest because of the extra stability provided by the octahedral symmetry. In this article a summary of the current experimental efforts on both the Rare-Earth and Actinide regions is given. Finally the ELMA project addressing the experimental search for the symmetries in the Actinides is briefly discussed.
Optimization of Time-Dependent Particle Tracing Using Tetrahedral Decomposition
NASA Technical Reports Server (NTRS)
Kenwright, David; Lane, David
1995-01-01
An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation and step-size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations or expensive matrix inversions. Integration accuracy is maintained using an adaptive step-size control scheme which is regulated by the path line curvature. The problem of cell-searching, point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells yet produces almost identical particle trajectories.
Why Is the Tetrahedral Bond Angle 109 Degrees? The Tetrahedron-in-a-Cube
ERIC Educational Resources Information Center
Lim, Kieran F.
2012-01-01
The common question of why the tetrahedral angle is 109.471 degrees can be answered using a tetrahedron-in-a-cube, along with some Year 10 level mathematics. The tetrahedron-in-a-cube can also be used to demonstrate the non-polarity of tetrahedral molecules, the relationship between different types of lattice structures, and to demonstrate that…
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.
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.
Polyamorphism in tetrahedral substances: Similarities between silicon and ice.
Garcez, K M S; Antonelli, A
2015-07-21
Tetrahedral substances, such as silicon, water, germanium, and silica, share various unusual phase behaviors. Among them, the so-called polyamorphism, i.e., the existence of more than one amorphous form, has been intensively investigated in the last three decades. In this work, we study the metastable relations between amorphous states of silicon in a wide range of pressures, using Monte Carlo simulations. Our results indicate that the two amorphous forms of silicon at high pressures, the high density amorphous (HDA) and the very high density amorphous (VHDA), can be decompressed from high pressure (∼20 GPa) down to the tensile regime, where both convert into the same low density amorphous. Such behavior is also observed in ice. While at high pressure (∼20 GPa), HDA is less stable than VHDA, at the pressure of 10 GPa both forms exhibit similar stability. On the other hand, at much lower pressure (∼5 GPa), HDA and VHDA are no longer the most stable forms, and, upon isobaric annealing, an even less dense form of amorphous silicon emerges, the expanded high density amorphous, again in close similarity to what occurs in ice. PMID:26203030
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.
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.
Slow dynamics in a primitive tetrahedral network model.
De Michele, Cristiano; Tartaglia, Piero; Sciortino, Francesco
2006-11-28
We report extensive Monte Carlo and event-driven molecular dynamics simulations of the fluid and liquid phase of a primitive model for silica recently introduced by Ford et al. [J. Chem. Phys. 121, 8415 (2004)]. We evaluate the isodiffusivity lines in the temperature-density plane to provide an indication of the shape of the glass transition line. Except for large densities, arrest is driven by the onset of the tetrahedral bonding pattern and the resulting dynamics is strong in Angell's classification scheme [J. Non-Cryst. Solids 131-133, 13 (1991)]. We compare structural and dynamic properties with corresponding results of two recently studied primitive models of network forming liquids-a primitive model for water and an angular-constraint-free model of four-coordinated particles-to pin down the role of the geometric constraints associated with bonding. Eventually we discuss the similarities between "glass" formation in network forming liquids and "gel" formation in colloidal dispersions of patchy particles. PMID:17144726
Glutamate detection by amino functionalized tetrahedral amorphous carbon surfaces.
Kaivosoja, Emilia; Tujunen, Noora; Jokinen, Ville; Protopopova, Vera; Heinilehto, Santtu; Koskinen, Jari; Laurila, Tomi
2015-08-15
In this paper, a novel amperometric glutamate biosensor with glutamate oxidase (GlOx) immobilized directly on NH2 functionalized, platinum doped tetrahedral amorphous carbon (ta-C) film, has been successfully developed. First, we demonstrate that direct GlOx immobilization is more effective on amino-groups than on carboxyl- or hydroxyl-groups. Second, we show that anodizing and plasma treatments increase the amount of nitrogen and the proportion of protonated amino groups relative to amino groups on the aminosilane coating, which subsequently results in an increased amount of active GlOx on the surface. This effect, however, is found to be unstable due to unstable electrostatic interactions between GlOx and NH3(+). We demonstrate the detection of glutamate in the concentration range of 10µM-1mM using the NH2 functionalized Pt doped ta-C surface. The biosensor showed high sensitivity (2.9nA μM(-1)cm(-2)), low detection limit (10μM) and good storage stability. The electrode response to glutamate was linear in the concentrations ranging from 10µM to 500µM. In conclusion, the study shows that GlOx immobilization is most effective on aminosilane treated ta-C surface without any pre-treatments and the fabricated sensor structure is able to detect glutamate in the micromolar range. PMID:25966399
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.
Galactic chemical evolution and nucleocosmochronology - Analytic quadratic models
NASA Technical Reports Server (NTRS)
Clayton, D. D.
1985-01-01
Quadratic models of the chemical evolution of the Galaxy for a star formation rate proportional to the square of the gas mass are studied. The search for analytic solutions to the gas mass and star mass for time-dependent rates of gaseous infall onto the disk is examined. The quadratic models are compared to models having linear star formation rates. The mass, metallicity, number of stars, and U-235/U-238 isotopic ratio for the models which are subjected to the same infall rate, the same initial disk mass, and the same final gas fraction are compared. The results of the comparison indicate that: (1) the average dwarf age is greater in the quadratic model, (2) the metallicity grows initially faster in the quadratic model, (3) the quadratic model has a smaller percentage of low-Z dwarfs, and (4) the U-235/U-238 isotopic ratio indicates a younger quadratic model.
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.
Quadratic relations in continuous and discrete Painlevé equations
NASA Astrophysics Data System (ADS)
Ramani, A.; Grammaticos, B.; Tamizhmani, T.
2000-04-01
The quadratic relations between the solutions of a Painlevé equation and that of a different one, or the same one with a different set of parameters, are investigated in the continuous and discrete cases. We show that the quadratic relations existing for the continuous PII , PIII , PV and PVI have analogues as well as consequences in the discrete case. Moreover, the discrete Painlevé equations have quadratic relations of their own without any reference to the continuous case.
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.
Quadratic dynamical decoupling with nonuniform error suppression
Quiroz, Gregory; Lidar, Daniel A.
2011-10-15
We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.
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.
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.
Lu Yongming; Lan Yaqian; Xu Yanhong; Su Zhongmin; Li Shunli; Zang Hongying; Xu Guangjuan
2009-11-15
To investigate the relationship between topological types and molecular building blocks (MBBs), we have designed and synthesized a series of three-dimensional (3D) interpenetrating metal-organic frameworks based on different polygons or polyhedra under hydrothermal conditions, namely [Cd(bpib){sub 0.5}(L{sup 1})] (1), [Cd(bpib){sub 0.5}(L{sup 2})].H{sub 2}O (2), [Cd(bpib){sub 0.5}(L{sup 3})] (3) and [Cd(bib){sub 0.5}(L{sup 1})] (4), where bpib=1,4-bis(2-(pyridin-2-yl)-1H-imidazol-1-yl)butane, bib=1,4-bis(1H-imidazol-1-yl)butane, H{sub 2}L{sup 1}=4-(4-carboxybenzyloxy)benzoic acid, H{sub 2}L{sup 2}=4,4'-(ethane-1,2-diylbis(oxy))dibenzoic acid and H{sub 2}L{sup 3}=4,4'-(1,4-phenylenebis(methylene))bis(oxy)dibenzoic acid, respectively. Their structures have been determined by single crystal X-ray diffraction analyses and further characterized by elemental analyses, IR spectra, and thermogravimetric (TG) analyses. Compounds 1-3 display alpha-Po topological nets with different degrees of interpenetration based on the similar octahedral [Cd{sub 2}(-COO){sub 4}] building blocks. Compound 4 is a six-fold interpenetrating diamondoid net based on tetrahedral MBBs. By careful inspection of these structures, we find that various carboxylic ligands and N-donor ligands with different coordination modes and conformations, and metal centers with different geometries are important for the formation of the different MBBs. It is believed that different topological types lie on different MBBs with various polygons or polyhedra. Such as four- and six-connected topologies are formed by tetrahedral and octahedral building blocks. In addition, with the increase of carboxylic ligands' length, the degrees of interpenetration have been changed in the alpha-Po topological nets. And the luminescent properties of these compounds have been investigated in detail. - Graphical abstract: A series of three-dimensional interpenetrating metal-organic frameworks based on different polygons or polyhedra
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.
Tetrahedrality and structural order for hydrophobic interactions in a coarse-grained water model
NASA Astrophysics Data System (ADS)
Chaimovich, Aviel; Shell, M. Scott
2014-02-01
The hydrophobic interaction manifests two separate regimes in terms of size: Small nonpolar bodies exhibit a weak oscillatory force (versus distance) while large nonpolar surfaces exhibit a strong monotonic one. This crossover in hydrophobic behavior is typically explained in terms of water's tetrahedral structure: Its tetrahedrality is enhanced near small solutes and diminished near large planar ones. Here, we demonstrate that water's tetrahedral correlations signal this switch even in a highly simplified, isotropic, "core-softened" water model. For this task, we introduce measures of tetrahedrality based on the angular distribution of water's nearest neighbors. On a quantitative basis, the coarse-grained model of course is only approximate: (1) While greater than simple Lennard-Jones liquids, its bulk tetrahedrality remains lower than that of fully atomic models; and (2) the decay length of the large-scale hydrophobic interaction is less than has been found in experiments. Even so, the qualitative behavior of the model is surprisingly rich and exhibits numerous waterlike hydrophobic behaviors, despite its simplicity. We offer several arguments for the manner in which it should be able to (at least partially) reproduce tetrahedral correlations underlying these effects.
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…
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.)
Effects of Classroom Instruction on Students' Understanding of Quadratic Equations
ERIC Educational Resources Information Center
Vaiyavutjamai, Pongchawee; Clements, M. A.
2006-01-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…
Geometric quadratic stochastic operator on countable infinite set
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-02-03
In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.
Visualising the Roots of Quadratic Equations with Complex Coefficients
ERIC Educational Resources Information Center
Bardell, Nicholas S.
2014-01-01
This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…
Quadratic divergences and quantum gravitational contributions to gauge coupling constants
NASA Astrophysics Data System (ADS)
Toms, David J.
2011-10-01
The calculation of quadratic divergences in Einstein-Maxwell theory with a possible cosmological constant is considered. We describe a method of calculation, using the background-field method, that is sensitive to quadratic divergences, is respectful of gauge invariance, and is independent of gauge conditions. A standard renormalization group analysis is applied to the result where it is shown that the quadratic divergences do lead to asymptotic freedom as found in the original paper of Robinson and Wilczek. The role and nature of these quadratic divergences is critically evaluated in light of recent criticism. Within the context of the background-field method, it is shown that it is possible to define the charge in a physically motivated way in which the quadratic divergences do not play a role. This latter view is studied in more depth in a toy model described in an appendix.
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.
Polychromatic solitons in a quadratic medium.
Towers, I N; Malomed, B A
2002-10-01
We introduce the simplest model to describe parametric interactions in a quadratically nonlinear optical medium with the fundamental harmonic containing two components with (slightly) different carrier frequencies [which is a direct analog of wavelength-division multiplexed models, well known in media with cubic nonlinearity]. The model takes a closed form with three different second-harmonic components, and it is formulated in the spatial domain. We demonstrate that the model supports both polychromatic solitons (PCSs), with all the components present in them, and two types of mutually orthogonal simple solitons, both types being stable in a broad parametric region. An essential peculiarity of PCS is that its power is much smaller than that of a simple (usual) soliton (taken at the same values of control parameters), which may be an advantage for experimental generation of PCSs. Collisions between the orthogonal simple solitons are simulated in detail, leading to the conclusion that the collisions are strongly inelastic, converting the simple solitons into polychromatic ones, and generating one or two additional PCSs. A collision velocity at which the inelastic effects are strongest is identified, and it is demonstrated that the collision may be used as a basis to design a simple all-optical XOR logic gate. PMID:12443362
A Quadratic Closure for Compressible Turbulence
Futterman, J A
2008-09-16
We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.
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
Equation for disentangling time-ordered exponentials with arbitrary quadratic generators
Budanov, V.G.
1987-12-01
In many quantum-mechanical constructions, it is necessary to disentangle an operator-valued time-ordered exponential with time-dependent generators quadratic in the creation and annihilation operators. By disentangling, one understands the finding of the matrix elements of the time-ordered exponential or, in a more general formulation. The solution of the problem can also be reduced to calculation of a matrix time-ordered exponential that solves the corresponding classical problem. However, in either case the evolution equations in their usual form do not enable one to take into account explicitly the symmetry of the system. In this paper the methods of Weyl analysis are used to find an ordinary differential equation on a matrix Lie algebra that is invariant with respect to the adjoint action of the dynamical symmetry group of a quadratic Hamiltonian and replaces the operator evolution equation for the Green's function.
Sternick, Marcelo Back; Dallacosta, Darlan; Bento, Daniela Águida; do Reis, Marcelo Lemos
2015-01-01
Objective: To analyze the rigidity of a platform-type external fixator assembly, according to different numbers of pins on each clamp. Methods: Computer simulation on a large-sized Cromus dynamic external fixator (Baumer SA) was performed using a finite element method, in accordance with the standard ASTM F1541. The models were generated with approximately 450,000 quadratic tetrahedral elements. Assemblies with two, three and four Schanz pins of 5.5 mm in diameter in each clamp were compared. Every model was subjected to a maximum force of 200 N, divided into 10 sub-steps. For the components, the behavior of the material was assumed to be linear, elastic, isotropic and homogeneous. For each model, the rigidity of the assembly and the Von Mises stress distribution were evaluated. Results: The rigidity of the system was 307.6 N/mm for two pins, 369.0 N/mm for three and 437.9 N/mm for four. Conclusion: The results showed that four Schanz pins in each clamp promoted rigidity that was 19% greater than in the configuration with three pins and 42% greater than with two pins. Higher tension occurred in configurations with fewer pins. In the models analyzed, the maximum tension occurred on the surface of the pin, close to the fixation area. PMID:27047879
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
Phase recovery based on quadratic programming
NASA Astrophysics Data System (ADS)
Zhang, Quan Bing; Ge, Xiao Juan; Cheng, Ya Dong; Ni, Na
2014-11-01
Most of the information of optical wavefront is encoded in the phase which includes more details of the object. Conventional optical measuring apparatus is relatively easy to record the intensity of light, but can not measure the phase of light directly. Thus it is important to recovery the phase from the intensity measurements of the object. In recent years, the methods based on quadratic programming such as PhaseLift and PhaseCut can recover the phase of general signal exactly for overdetermined system. To retrieve the phase of sparse signal, the Compressive Phase Retrieval (CPR) algorithm combines the l1-minimization in Compressive Sensing (CS) with low-rank matrix completion problem in PhaseLift, but the result is unsatisfied. This paper focus on the recovery of the phase of sparse signal and propose a new method called the Compressive Phase Cut Retrieval (CPCR) by combining the CPR algorithm with the PhaseCut algorithm. To ensure the sparsity of the recovered signal, we use CPR method to solve a semi-definite programming problem firstly. Then apply linear transformation to the recovered signal, and set the phase of the result as the initial value of the PhaseCut problem. We use TFOCS (a library of Matlab-files) to implement the proposed CPCR algorithm in order to improve the recovered results of the CPR algorithm. Experimental results show that the proposed method can improve the accuracy of the CPR algorithm, and overcome the shortcoming of the PhaseCut method that it can not recover the sparse signal effectively.
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.
Ngo, Phong D; Mansoorabadi, Steven O; Frey, Perry A
2016-08-01
Peptide boronic acids and peptidyl trifluoromethyl ketones (TFKs) inhibit serine proteases by forming monoanionic, tetrahedral adducts to serine in the active sites. Investigators regard these adducts as analogs of monoanionic, tetrahedral intermediates. Density functional theory (DFT) calculations and fractional charge analysis show that tetrahedral adducts of model peptidyl TFKs are structurally and electrostatically very similar to corresponding tetrahedral intermediates. In contrast, the DFT calculations show the structures and electrostatic properties of analogous peptide boronate adducts to be significantly different. The peptide boronates display highly electrostatically positive boron, with correspondingly negative ligands in the tetrahedra. In addition, the computed boron-oxygen and boron-carbon bond lengths in peptide boronates (which are identical or very similar to the corresponding bonds in a peptide boronate adduct of α-lytic protease determined by X-ray crystallography at subangstrom resolution) are significantly longer than the corresponding bond lengths in model tetrahedral intermediates. Since protease-peptidyl TFKs incorporate low-barrier hydrogen bonds (LBHBs) between an active site histidine and aspartate, while the protease-peptide boronates do not, these data complement the spectroscopic and chemical evidence for the participation of LBHBs in catalysis by serine proteases. Moreover, while the potency of these classes of inhibitors can be correlated to the structures of the peptide moieties, the present results indicate that the strength of their bonds to serine contribute significantly to their inhibitory properties. PMID:27387593
Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
NASA Astrophysics Data System (ADS)
Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko; Paramekanti, Arun
2016-04-01
Motivated by cold atom experiments on Chern insulators, we study the honeycomb lattice Haldane-Hubbard Mott insulator of spin-1 /2 fermions using exact diagonalization and density matrix renormalization group methods. We show that this model exhibits various chiral magnetic orders including a wide regime of triple-Q tetrahedral order. Incorporating third-neighbor hopping frustrates and ultimately melts this tetrahedral spin crystal. From analyzing the low energy spectrum, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid (CSL) with gapped semion excitations. We formulate and study the Chern-Simons-Higgs field theory of the exotic CSL-to-tetrahedral spin crystallization transition.
Self-equilibrium and stability of regular truncated tetrahedral tensegrity structures
NASA Astrophysics Data System (ADS)
Zhang, J. Y.; Ohsaki, M.
2012-10-01
This paper presents analytical conditions of self-equilibrium and super-stability for the regular truncated tetrahedral tensegrity structures, nodes of which have one-to-one correspondence to the tetrahedral group. These conditions are presented in terms of force densities, by investigating the block-diagonalized force density matrix. The block-diagonalized force density matrix, with independent sub-matrices lying on its leading diagonal, is derived by making use of the tetrahedral symmetry via group representation theory. The condition for self-equilibrium is found by enforcing the force density matrix to have the necessary number of nullities, which is four for three-dimensional structures. The condition for super-stability is further presented by guaranteeing positive semi-definiteness of the force density matrix.
Observation of all-in type tetrahedral displacements in nonmagnetic pyrochlore niobates
NASA Astrophysics Data System (ADS)
Torigoe, S.; Ishimoto, Y.; Aoishi, Y.; Murakawa, H.; Matsumura, D.; Yoshii, K.; Yoneda, Y.; Nishihata, Y.; Kodama, K.; Tomiyasu, K.; Ikeda, K.; Nakao, H.; Nogami, Y.; Ikeda, N.; Otomo, T.; Hanasaki, N.
2016-02-01
We observed all-in type Nb tetrahedral displacement in nonmagnetic pyrochlore niobates A2Nb2O7 (A =Nd0.5Ca0.5 and Y0.5Ca0.5 ) through the analysis of the neutron pair distribution function and the extended x-ray absorption function spectroscopy. The all-in type Nb tetrahedral displacement, which has the character of a charge singlet state, is driven by the formation of the bonding orbital. The diffuse scattering in the x-ray diffraction, which has the resonant component in the Nb L3 edge, indicates that the all-in type Nb tetrahedral displacement has the periodicity with its short-range correlation.
LETTER TO THE EDITOR: A new approach to modelling tetrahedral amorphous carbon
NASA Astrophysics Data System (ADS)
Walters, J. K.; Gilkes, K. W. R.; Wicks, J. D.; Newport, R. J.
1997-08-01
We have generated a new model for the structure of tetrahedral amorphous carbon using a modified reverse Monte Carlo modelling method. The novel feature of this approach is the definition of three different types of carbon atom, corresponding to tetrahedral, planar and linear bonding conformations. The particular strengths of the method are the large model size (3000 atoms), that all the possible arrangements of 0953-8984/9/34/001/img7 and 0953-8984/9/34/001/img8 bonds are allowed, and that no interatomic potential is required. For the first time we have determined the distribution of 0953-8984/9/34/001/img8 bonded sites within the predominantly disordered tetrahedral structure, and we find that they form polymer-like chains and small clusters which connect the 0953-8984/9/34/001/img7 bonded regions.
Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid.
Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko; Paramekanti, Arun
2016-04-01
Motivated by cold atom experiments on Chern insulators, we study the honeycomb lattice Haldane-Hubbard Mott insulator of spin-1/2 fermions using exact diagonalization and density matrix renormalization group methods. We show that this model exhibits various chiral magnetic orders including a wide regime of triple-Q tetrahedral order. Incorporating third-neighbor hopping frustrates and ultimately melts this tetrahedral spin crystal. From analyzing the low energy spectrum, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid (CSL) with gapped semion excitations. We formulate and study the Chern-Simons-Higgs field theory of the exotic CSL-to-tetrahedral spin crystallization transition. PMID:27082001
Tetrahedral-mesh-based computational human phantom for fast Monte Carlo dose calculations
NASA Astrophysics Data System (ADS)
Yeom, Yeon Soo; Jeong, Jong Hwi; Han, Min Cheol; Kim, Chan Hyeong
2014-06-01
Although polygonal-surface computational human phantoms can address several critical limitations of conventional voxel phantoms, their Monte Carlo simulation speeds are much slower than those of voxel phantoms. In this study, we sought to overcome this problem by developing a new type of computational human phantom, a tetrahedral mesh phantom, by converting a polygonal surface phantom to a tetrahedral mesh geometry. The constructed phantom was implemented in the Geant4 Monte Carlo code to calculate organ doses as well as to measure computation speed, the values were then compared with those for the original polygonal surface phantom. It was found that using the tetrahedral mesh phantom significantly improved the computation speed by factors of between 150 and 832 considering all of the particles and simulated energies other than the low-energy neutrons (0.01 and 1 MeV), for which the improvement was less significant (17.2 and 8.8 times, respectively).
Direct Orthogonal Distance to Quadratic Surfaces in 3D.
Lott, Gus K
2014-09-01
Discovering the orthogonal distance to a quadratic surface is a classic geometric task in vision, modeling, and robotics. I describe a simple, efficient, and stable direct solution for the orthogonal distance (foot-point) to an arbitrary quadratic surface from a general finite 3D point. The problem is expressed as the intersection of three quadratic surfaces, two of which are derived from the requirement of orthogonality of two non-coincident planes with the tangent plane to the quadric. A sixth order single-variable polynomial is directly generated in one coordinate of the surface point. The method detects intersection points at infinity and operates smoothly across all real quadratic surface classes. The method also geometrically detects continuums of orthogonal points (i.e., from the exact center of a sphere). I discuss algorithm performance, compare it to a state-of-the-art estimator, demonstrate the algorithm on synthetic data, and describe extension to arbitrary dimension. PMID:26352239
On a 'Mysterious' Case of a Quadratic Hamiltonian
NASA Astrophysics Data System (ADS)
Sakovich, Sergei
2006-07-01
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 Painlevé test for integrability.
Quadratic function approaching method for magnetotelluric soundingdata inversion
Liangjun, Yan; Wenbao, Hu; Zhang, Keni
2004-04-05
The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.
AdS waves as exact solutions to quadratic gravity
Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin
2011-04-15
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.
Dynamic mesh adaption for triangular and tetrahedral grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger
1993-01-01
The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.
Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
NASA Astrophysics Data System (ADS)
Hickey, Ciaran; Cincio, Lukasz; Papic, Zlatko; Paramekanti, Arun
Motivated by recent experimental realizations of artificial gauge fields in ultracold atoms, we study the honeycomb lattice Haldane-Hubbard Mott insulator of spin- 1 / 2 fermions using exact diagonalization and density matrix renormalization group methods. We show that this model exhibits various chiral magnetic orders including a wide regime of triple-Q tetrahedral order. Incorporating third-neighbor hopping frustrates and ultimately melts this tetrahedral spin crystal. From analyzing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid with gapped semion excitations.
NASA Astrophysics Data System (ADS)
Lábár, János L.
1999-07-01
It is shown in this letter that, in contrast to the accepted belief in the literature, it is possible to determine if a minority component is located on the dodecahedral, octahedral, or tetrahedral sites in a garnet single crystal. This prediction of ours is based on dynamical Bloch-wave calculations and proved experimentally with x-ray measurements in a transmission electron microscope. The previous literature seemed to agree on the assumption that the dodecahedral and tetrahedral sites are indistinguishable from each other.
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.
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.
Refining quadrilateral and brick element meshes
Schneiders, R.; Debye, J.
1995-12-31
We consider the problem of refining unstructured quadrilateral and brick element meshes. We present an algorithm which is a generalization of an algorithm developed by Cheng et. al. for structured quadrilateral element meshes. The problem is solved for the two-dimensional case. Concerning three dimensions we present a solution for some special cases and a general solution that introduces tetrahedral and pyramidal transition elements.
Lattice thermal expansion for normal tetrahedral compound semiconductors
Omar, M.S. . E-mail: dr_m_s_omar@yahoo.com
2007-02-15
The cubic root of the deviation of the lattice thermal expansion from that of the expected value of diamond for group IV semiconductors, binary compounds of III-V and II-VI, as well as several ternary compounds from groups I-III-VI{sub 2}, II-IV-V{sub 2} and I-IV{sub 2}V{sub 3} semiconductors versus their bonding length are given straight lines. Their slopes were found to be 0.0256, 0.0210, 0.0170, 0.0259, 0.0196, and 0.02840 for the groups above, respectively. Depending on the valence electrons of the elements forming these groups, a formula was found to correlate all the values of the slopes mentioned above to that of group IV. This new formula which depends on the melting point and the bonding length as well as the number of valence electrons for the elements forming the compounds, will gives best calculated values for lattice thermal expansion for all compounds forming the groups mentioned above. An empirical relation is also found between the mean ionicity of the compounds forming the groups and their slopes mentioned above and that gave the mean ionicity for the compound CuGe{sub 2}P{sub 3} in the range of 0.442.
A transient, quadratic nodal method for triangular-Z geometry
DeLorey, T.F.
1993-06-01
Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.
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.
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.
Regioselective placement of alkanethiolate domains on tetrahedral and octahedral gold nanocrystals.
Wang, Yifeng; Zeiri, Offer; Meshi, Louisa; Stellacci, Francesco; Weinstock, Ira A
2012-10-01
Electrostatically stabilized monolayer shells of metal-oxide cluster anions (polyoxometalates, or POMs) on the surfaces of ca. 8 nm tetrahedral and octahedral gold nanocrystals regioselectively direct water-soluble alkanethiolate ligands to the corners and edges of the gold polyhedra. PMID:22918232
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.
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…
Pothoczki, Szilvia; Temleitner, László; Pusztai, László
2010-04-28
The method of Rey [Rey, J. Chem. Phys. 126, 164506 (2007)] for describing how molecules orient toward each other in systems with perfect tetrahedral molecules is extended to the case of distorted tetrahedral molecules of c(2v) symmetry by means of introducing 28 subgroups. Additionally, the original analysis developed for perfect tetrahedral molecules, based on six groups, is adapted for molecules with imperfect tetrahedral shape. Deriving orientational correlation functions have been complemented with detailed analyses of dipole-dipole correlations. This way, (up to now) the most complete structure determination can be carried out for such molecular systems. In the present work, these calculations have been applied for particle configurations resulting from reverse Monte Carlo computer modeling. These particle arrangements are fully consistent with structure factors from neutron and x-ray diffraction measurements. Here we present a complex structural study for methylene halide (chloride, bromide, and iodide) molecular liquids, as possibly the best representative examples. It has been found that the most frequent orientations of molecules are of the 2:2 type over the entire distance range in these liquids. Focusing on the short range orientation, neighboring molecules turn toward each other with there "H,Y"-"H,Y" (Y: Cl, Br, I) edges, apart from CH(2)Cl(2) where the H,H-H,Cl arrangement is the most frequent. In general, the structure of methylene chloride appears to be different from the structure of the other two liquids. PMID:20441292
Nikitin, A. V.; Rey, M.; Tyuterev, Vl. G.
2015-03-07
A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB{sub 4} molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q){sup −2} type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH{sub 4} molecule is demonstrated.
NASA Astrophysics Data System (ADS)
Nikitin, A. V.; Rey, M.; Tyuterev, Vl. G.
2015-03-01
A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB4 molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q)-2 type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH4 molecule is demonstrated.
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.
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 σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.
On Volterra quadratic stochastic operators with continual state space
NASA Astrophysics Data System (ADS)
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-05-01
Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (V λ )(A ) = ∫X ∫X P (x ,y ,A )d λ (x )d λ (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 n →∞ Vn(λ ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
NASA Astrophysics Data System (ADS)
Fernández, Francisco M.
2016-06-01
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.
A Note on the Linearly and Quadratically Weighted Kappa Coefficients.
Li, Pingke
2016-09-01
The linearly and quadratically weighted kappa coefficients are popular statistics in measuring inter-rater agreement on an ordinal scale. It has been recently demonstrated that the linearly weighted kappa is a weighted average of the kappa coefficients of the embedded 2 by 2 agreement matrices, while the quadratically weighted kappa is insensitive to the agreement matrices that are row or column reflection symmetric. A rank-one matrix decomposition approach to the weighting schemes is presented in this note such that these phenomena can be demonstrated in a concise manner. PMID:27246436
Analysis of integral controls in linear quadratic regulator design
NASA Technical Reports Server (NTRS)
Slater, G. L.
1979-01-01
The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.
Gorodylova, Nataliia; Kosinová, Veronika; Šulcová, Petra; Bělina, Petr; Vlček, 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
Finding Optimal Gains In Linear-Quadratic Control Problems
NASA Technical Reports Server (NTRS)
Milman, Mark H.; Scheid, Robert E., Jr.
1990-01-01
Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.
Radar Rainfall Estimation using a Quadratic Z-R equation
NASA Astrophysics Data System (ADS)
Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan
2016-04-01
The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.
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.
Quadratic invariants for discrete clusters of weakly interacting waves
NASA Astrophysics Data System (ADS)
Harper, Katie L.; Bustamante, Miguel D.; Nazarenko, Sergey V.
2013-06-01
We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix {A} with entries 1, -1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N - M* ⩾ N - M, where M* is the number of linearly independent rows in {A}. Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney-Hasegawa-Mima wave model, and by showing a classification of small (up to three-triad) clusters.
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.
A Version of Quadratic Regression with Interpretable Parameters.
ERIC Educational Resources Information Center
Cudeck, Robert; du Toit, Stephen H. C.
2002-01-01
Suggests an alternative form of the quadratic model that has the same expectation function of the original model but has the useful feature that its parameters are interpretable. Provides examples of a simple regression problem and a nonlinear mixed-effects model. (SLD)
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…
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.
Quadratic Expressions by Means of "Summing All the Matchsticks"
ERIC Educational Resources Information Center
Gierdien, M. Faaiz
2012-01-01
This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such "matchstick" problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are…
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…
Selfsimilarity in a Class of Quadratic-Quasiperiodic Chains
NASA Astrophysics Data System (ADS)
Kaneko, Masanobu; Odagaki, Takashi
1993-04-01
We prove that quasiperiodic chains associated with a class of quadratic irrational numbers have an inflation symmetry and can be generated from a regular chain by a hyperinflation. We devise the explicit method to find the hyperinflation symmetry and discuss the properties of such a class of quasiperiodic sequences.
Unravelling Student Challenges with Quadratics: A Cognitive Approach
ERIC Educational Resources Information Center
Kotsopoulos, Donna
2007-01-01
The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…
A quadratic weight selection algorithm. [for optimal flight control
NASA Technical Reports Server (NTRS)
Broussard, J. R.
1981-01-01
A new numerical algorithm is presented which determines a positive semi-definite state weighting matrix in the linear-quadratic optimal control design problem. The algorithm chooses the weighting matrix by placing closed-loop eigenvalues and eigenvectors near desired locations using optimal feedback gains. A simplified flight control design example is used to illustrate the algorithms capabilities.
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)
Formation of pyramid elements for hexahedra to tetrahedra transitions
OWEN,STEVEN J.; SAIGAL,SUNIL
2000-02-24
New algorithms are proposed for the modification of a mixed hexahedra-tetrahedra element mesh to maintain compatibility by the insertion of pyramid elements. Several methods for generation of the pyramids are presented involving local tetrahedral transformations and/or node insertion near the hex/tet interface. Local smoothing and topological operations improve the quality of the transition region. Results show superior performance of the resulting elements in a commercial finite element code over non-conforming interface conditions.
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.
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.
Flexibility of C3h -Symmetrical Linkers in Tris-oligonucleotide-Based Tetrahedral Scaffolds.
Panagiotidis, Christos; Kath-Schorr, Stephanie; von Kiedrowski, Günter
2016-02-01
Flexibility of tris-oligonucleotides is determined by the length of their connecting hydrocarbon chains. Tris-oligonucleotides are branched DNA building blocks with three oligonucleotide arms attached to a C3h -symmetrical linker core at these chains. Four tris-oligonucleotides hybridise into a tetrahedral nanocage by sequence-determined self-assembly. The influence of methylene, ethylene and propylene chains was studied by synthesising sets of tris-oligonucleotides and analysing the relative stability of the hybridisation products against digestion by mung bean nuclease by using gel electrophoresis. Linkers with ethylene chains showed sufficient flexibility, whereas methylene-chain linkers were too rigid. Tris-oligonucleotides based on the latter still formed tetrahedral scaffolds in intermixing experiments with linkers of higher flexibility. Thus, a new generation of versatile isocyanurate-based linkers was established. PMID:26593127
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme
Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; Nguyen, Manh Cuong; Wang, Cai -Zhuang; Lin, Zijing; Zhu, Zi -Zhong; Ho, Kai -Ming
2015-10-26
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A2MSiO4 with A = Li or Na and M = Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. In addition, these structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been muchmore » less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs.« less
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
Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; Nguyen, Manh Cuong; Wang, Cai -Zhuang; Lin, Zijing; Zhu, Zi -Zhong; Ho, Kai -Ming
2015-10-26
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A_{2}MSiO_{4} with A = Li or Na and M = Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. In addition, these structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs.
Theory of Andreev reflection spectroscopy for tetrahedral and non-unitary superconductors
NASA Astrophysics Data System (ADS)
Bohloul, S.; Curnoe, S. H.
2016-02-01
A general formula for point contact conductance from a normal metal tip into a superconductor is derived using the Blonder-Tinkham-Klapwijk theory of Andreev reflection, with special emphasis on non-unitary superconductors. The results of a comprehensive set of conductance spectrum calculations are presented: all symmetry-allowed gap functions for superconductors with tetrahedral symmetry, such as PrOs4Sb12, are considered, including several non-unitary cases.
A first collision source method for ATTILA, an unstructured tetrahedral mesh discrete ordinates code
Wareing, T.A.; Morel, J.E.; Parsons, D.K.
1998-12-01
A semi-analytic first collision source method is developed for the transport code, ATTILA, a three-dimensional, unstructured tetrahedral mesh, discrete-ordinates code. This first collision source method is intended to mitigate ray effects due to point sources. The method is third-order accurate, which is the same order of accuracy as the linear-discontinuous spatial differencing scheme used in ATTILA. Numerical results are provided to demonstrate the accuracy and efficiency of the first collision source method.
Wareing, T.A.; Parsons, D.K.; Pautz, S.
1997-12-31
Recently, a new state-of-the-art discrete-ordinates code, ATTILA, was developed. ATTILA provides the capabilities to solve geometrically complex 3-D transport problems by using an unstructured tetrahedral mesh. In this paper we describe the application of ATTILA to a 3-D reactor pressure vessel dosimetry problem. We provide numerical results from ATTILA and the Monte Carlo code, MCNP. The results demonstrate the effectiveness and efficiency of ATTILA for such calculations.
Theory of Andreev reflection spectroscopy for tetrahedral and non-unitary superconductors.
Bohloul, S; Curnoe, S H
2016-02-01
A general formula for point contact conductance from a normal metal tip into a superconductor is derived using the Blonder-Tinkham-Klapwijk theory of Andreev reflection, with special emphasis on non-unitary superconductors. The results of a comprehensive set of conductance spectrum calculations are presented: all symmetry-allowed gap functions for superconductors with tetrahedral symmetry, such as PrOs4Sb12, are considered, including several non-unitary cases. PMID:26750247
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 Astrophysics Data System (ADS)
Frink, N. T.; Pirzadeh, S. Z.
1999-09-01
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 USA 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
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
2013-01-01
Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper presents a parallel algorithm for solving the eikonal equation on fully unstructured tetrahedral meshes. The method is appropriate for the type of fine-grained parallelism found on modern massively-SIMD architectures such as graphics processors and takes into account the particular constraints and capabilities of these computing platforms. This work builds on previous work for solving these equations on triangle meshes; in this paper we adapt and extend previous two-dimensional strategies to accommodate three-dimensional, unstructured, tetrahedralized domains. These new developments include a local update strategy with data compaction for tetrahedral meshes that provides solutions on both serial and parallel architectures, with a generalization to inhomogeneous, anisotropic speed functions. We also propose two new update schemes, specialized to mitigate the natural data increase observed when moving to three dimensions, and the data structures necessary for efficiently mapping data to parallel SIMD processors in a way that maintains computational density. Finally, we present descriptions of the implementations for a single CPU, as well as multicore CPUs with shared memory and SIMD architectures, with comparative results against state-of-the-art eikonal solvers. PMID:25221418
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.
Zhang, X. M.; Xu, G. Z.; Liu, E. K.; Wang, W. H. Wu, G. H.; Liu, Z. Y.
2015-01-28
Based on first-principles calculations, we investigate the influence of tetrahedral covalent-hybridization between main-group and transition-metal atoms on the topological band structures of binary HgTe and ternary half-Heusler compounds, respectively. Results show that, for the binary HgTe, when its zinc-blend structure is artificially changed to rock-salt one, the tetrahedral covalent-hybridization will be removed and correspondingly the topologically insulating band character lost. While for the ternary half-Heusler system, the strength of covalent-hybridization can be tuned by varying both chemical compositions and atomic arrangements, and the competition between tetrahedral and octahedral covalent-hybridization has been discussed in details. As a result, we found that a proper strength of tetrahedral covalent-hybridization is probably in favor to realizing the topologically insulating state with band inversion occurring at the Γ point of the Brillouin zone.
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.
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.
Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Kim, Seonghoon; Sohn, Jason W
2015-02-21
In the present study, to achieve accurate 4D Monte Carlo dose calculation in radiation therapy, we devised a new approach that combines (1) modeling of the patient body using tetrahedral-mesh geometry based on the patient's 4D CT data, (2) continuous movement/deformation of the tetrahedral patient model by interpolation of deformation vector fields acquired through deformable image registration, and (3) direct transportation of radiation particles during the movement and deformation of the tetrahedral patient model. The results of our feasibility study show that it is certainly possible to construct 4D patient models (= phantoms) with sufficient accuracy using the tetrahedral-mesh geometry and to directly transport radiation particles during continuous movement and deformation of the tetrahedral patient model. This new approach not only produces more accurate dose distribution in the patient but also replaces the current practice of using multiple 3D voxel phantoms and combining multiple dose distributions after Monte Carlo simulations. For routine clinical application of our new approach, the use of fast automatic segmentation algorithms is a must. In order to achieve, simultaneously, both dose accuracy and computation speed, the number of tetrahedrons for the lungs should be optimized. Although the current computation speed of our new 4D Monte Carlo simulation approach is slow (i.e. ~40 times slower than that of the conventional dose accumulation approach), this problem is resolvable by developing, in Geant4, a dedicated navigation class optimized for particle transportation in tetrahedral-mesh geometry. PMID:25615567
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 ...
Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Adamian, A.
1988-01-01
An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.
An analysis of spectral envelope-reduction via quadratic assignment problems
NASA Technical Reports Server (NTRS)
George, Alan; Pothen, Alex
1994-01-01
A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper, we provide an analysis of the spectral envelope reduction algorithm. We described related 1- and 2-sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work involved in an envelope Cholesky factorization scheme. We formulate the latter two problems as quadratic assignment problems, and then study the 2-sum problem in more detail. We obtain lower bounds on the 2-sum by considering a projected quadratic assignment problem, and then show that finding a permutation matrix closest to an orthogonal matrix attaining one of the lower bounds justifies the spectral envelope reduction algorithm. The lower bound on the 2-sum is seen to be tight for reasonably 'uniform' finite element meshes. We also obtain asymptotically tight lower bounds for the envelope size for certain classes of meshes.
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 = λv2, 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, λ ∈ 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)].
Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators
NASA Astrophysics Data System (ADS)
Marquette, Ian
2011-06-01
We present a generalized Kaluza-Klein monopole system. We solve this quantum superintegrable system on a Euclidean Taub Nut manifold using the separation of variables of the corresponding Schrödinger equation in spherical and parabolic coordinates. We present the integrals of motion of this system, the quadratic algebra generated by these integrals, the realization in terms of a deformed oscillator algebra using the Daskaloyannis construction and the energy spectrum. The structure constants and the Casimir operator are functions not only of the Hamiltonian but also of other two integrals commuting with all generators of the quadratic algebra and forming an Abelian subalgebra. We present another algebraic derivation of the energy spectrum of this system using the factorization method and ladder operators.
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}_{∞ }.
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.
Discrete quadratic solitons with competing second-harmonic components
Setzpfandt, Frank; Pertsch, Thomas; Sukhorukov, Andrey A.
2011-11-15
We describe families of discrete solitons in quadratic waveguide arrays supported by competing cascaded nonlinear interactions between one fundamental and two second-harmonic modes. We characterize the existence, stability, and excitation dynamics of these solitons and show that their features may resemble those of solitons in saturable media. Our results also demonstrate that a power threshold may appear for soliton formation, leading to a suppression of beam self-focusing which explains recent experimental observations.
Construction of Lagrangian Local Symmetries for General Quadratic Theory
NASA Astrophysics Data System (ADS)
Deriglazov, A. A.
We propose a procedure which allows one to construct local symmetry generators of general quadratic Lagrangian theory. Manifest recurrence relations for generators in terms of the so-called structure matrices of the Dirac formalism are obtained. The procedure fulfill in terms of initial variables of the theory, and does not imply either separation of constraints on first and second class subsets or any other choice of basis for constraints.
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.
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.
Measurement of quadratic electrogyration effect in castor oil
NASA Astrophysics Data System (ADS)
Izdebski, Marek; Ledzion, Rafał; Górski, Piotr
2015-07-01
This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.
Pak, Chongin; Kamali, Saeed; Pham, Joyce; Lee, Kathleen; Greenfield, Joshua T.; Kovnir, Kirill
2014-01-01
Fragments of the superconducting FeSe layer, FeSe2 tetrahedral chains, were stabilized in the crystal structure of a new mixed-valent compound Fe3Se4(en)2 (en = ethylenediamine) synthesized from elemental Fe and Se. The FeSe2 chains are separated from each other by means of Fe(en)2 linkers. Mössbauer spectroscopy and magnetometry reveal strong magnetic interactions within the FeSe2 chains which result in antiferromagnetic ordering below 170 K. According to DFT calculations, anisotropic transport and magnetic properties are expected for Fe3Se4(en)2. This compound offers a unique way to manipulate the properties of the Fe-Se infinite fragments by varying the topology and charge of the Fe-amino linkers. PMID:24299423
Tetrahedral site ordering in synthetic gallium albite: A 29Si MAS NMR study
NASA Astrophysics Data System (ADS)
Sherriff, Barbara L.; Fleet, Michael E.; Burns, Peter C.
1991-09-01
The ordering of Si in the tetrahedral sites of gallium albite (NaGaSi 3O 8) has been studied by MAS NMR and Rietveld structure refinement of X-ray powder diffraction data. Low structural state (ordered) material was annealed at about 800°C under a load pressure of 1 kbar, and by Rietveld refinement has tetrahedral-site occupancies for Si of T1O = 0.24(3), T1m = 0.89(2), T2O = 0.98(2), and T2m = 0.89(2), respectively. Corresponding Si occupancies for high structural state (disordered) material are 0.71(2), 0.78(1), 0.76(2), and 0.74(2), respectively. The 29Si MAS NMR spectra of low gallium albite is equivalent to the three-peak spectrum of natural (Amelia) albite, with resonances at -89.6, -96.4, and -104.2 ppm but with relative peak areas of 0.79:1.0:0.77. The tetrahedral-site occupancies derived from the MAS NMR spectrum are in good agreement with those obtained by Rietveld refinement and, in particular, indicate that the -96.4 ppm peak must correspond to Si in T2O. This is the first independent assignment of the 29Si peak at -96 ppm in the spectrum of ordered albite to the T2O site. A peak at -96 ppm is also resolved in the spectrum of high gallium albite. The systematic differences in peak position between the 29Si MAS NMR spectra of low gallium albite and those of Amelia albite cannot be explained simply by the direct replacement of Al by Ga, without a change in angle at the bridging oxygen atoms.
On the fragment ion angular distributions arising from the tetrahedral molecule CH3I
NASA Astrophysics Data System (ADS)
Graham, P.; Ledingham, K. W. D.; Singhai, R. P.; Hankin, S. M.; McCanny, T.; Fang, X.; Kosmidis, C.; Tzallas, P.; Taday, P. F.; Langley, A. J.
2001-10-01
The mass spectra for both horizontal and vertical polarizations and the angular distributions of fragment ions arising from Coulomb explosion of tetrahedral methyl iodide (CH3I) ions, obtained at a laser intensity of 1016 W cm-2 are presented. All fragment ion distributions are peaked along the direction corresponding to collinearity of the laser electric field with the time-of-flight mass spectrometer axis. The In + ion (n≤7) angular distributions from the dissociation of the parent ions are all of similar widths, which would imply a geometric, as opposed to dynamic, alignment. Additionally, the lower-charged I ions have an isotropic component that decreases as the charge state increases. Measurements of the CHm+ (m≤3), Cp + (p≤4) and H+ ion distributions show that these are also maximal along the polarization direction. Furthermore, there is also a CH22+ ion peak present in the CHm group, which has a distribution similar to those measured for the other ions. This mass peak is the prominent multi-charged ion in this group. As the CH3I molecule is initially tetrahedral, these results suggest that the molecular structure undergoes a change such that the H-C and C-I bonds tend to lie along the field. Several authors have described work which first aligned CH3I molecules with a nanosecond laser and then photodissociated with a femtosecond laser, to produce fragment ion distributions. This is the first time that the angular distributions from a tetrahedral molecule have been presented using femtosecond laser pulses only and in the case of CH3I, for fragments other than CH3+ and I+. The fragment energetics from the single CH3I molecule have been compared with those from recent work dealing with the Coulomb explosion of CH3I clusters.
Dietschreit, Johannes C B; Diestler, Dennis J; Knapp, Ernst W
2016-05-10
To speed up the generation of an ensemble of poly(ethylene oxide) (PEO) polymer chains in solution, a tetrahedral lattice model possessing the appropriate bond angles is used. The distance between noncovalently bonded atoms is maintained at realistic values by generating chains with an enhanced degree of self-avoidance by a very efficient Monte Carlo (MC) algorithm. Potential energy parameters characterizing this lattice model are adjusted so as to mimic realistic PEO polymer chains in water simulated by molecular dynamics (MD), which serves as a benchmark. The MD data show that PEO chains have a fractal dimension of about two, in contrast to self-avoiding walk lattice models, which exhibit the fractal dimension of 1.7. The potential energy accounts for a mild hydrophobic effect (HYEF) of PEO and for a proper setting of the distribution between trans and gauche conformers. The potential energy parameters are determined by matching the Flory radius, the radius of gyration, and the fraction of trans torsion angles in the chain. A gratifying result is the excellent agreement of the pair distribution function and the angular correlation for the lattice model with the benchmark distribution. The lattice model allows for the precise computation of the torsional entropy of the chain. The generation of polymer conformations of the adjusted lattice model is at least 2 orders of magnitude more efficient than MD simulations of the PEO chain in explicit water. This method of generating chain conformations on a tetrahedral lattice can also be applied to other types of polymers with appropriate adjustment of the potential energy function. The efficient MC algorithm for generating chain conformations on a tetrahedral lattice is available for download at https://github.com/Roulattice/Roulattice . PMID:27045228
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.
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.
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.
Tian, Jian; Motkuri, Radha K.; Thallapally, Praveen K.; McGrail, B. Peter
2010-10-19
Solvothermal assembly of a semi-rigid tetrahedral carboxylate ligand tetrakis[4-(carboxyphenyl)oxamethyl]methane acid (H4X) with Cd(II) ion in different solvent systems yields three novel metal-organic framework isomers (1-3) based on different secondary building units (SBUs). Although all three frameworks have the same dia (diamondoid) topology, complex 1 and 3 are chiral and complex 2 is achiral. One of the networks, 3 shows cross-linked three-fold interpenetration of the single dia net and exhibits permanent porosities, as confirmed by BET and selective CO2 adsorption.
Zhu, Hai; Chi, Quan; Zhao, Yanxi; Li, Chunya; Tang, Heqing; Li, Jinlin; Huang, Tao; Liu, Hanfan
2012-11-15
Graphical abstract: By using CO as a reducing agent, uniform and well-defined concave tetrahedral Pd nanocrystals were successfully synthesized. CO flow rate was the most essential for the formation of the concave tetrahedral nanostructures. The morphologies and sizes of the final products can be well controlled by adjusting the flow rate of CO. Highlights: ► By using CO as a reducing agent, concave tetrahedral Pd nanocrystals were obtained. ► CO flow rate is critical to the formation of concave tetrahedral Pd nanocrystals. ► The selective adsorption of CO on (1 1 0) facets is essential to concave Pd tetrahedra. -- Abstract: CO reducing strategy to control the morphologies of palladium nanocrystals was investigated. By using CO as a reducing agent, uniform and well-defined concave tetrahedral Pd nanocrystals with a mean size of about 55 ± 2 nm were readily synthesized with Pd(acac){sub 2} as a precursor and PVP as a stabilizer. The structures of the as-prepared Pd nanocrystals were characterized by transmission electron microscopy (TEM), X-ray powder diffraction (XRD), ultraviolet–visible (UV–vis) absorption spectroscopy and electrochemical measurements. The results demonstrated that CO was the most essential for the formation of the concave tetrahedral Pd nanostructures. The morphologies and sizes of the final products can be well controlled by adjusting the flow rate of CO. The most appropriate CO flow rate, temperature and time for the formation of the ideal concave tetrahedral Pd nanocrystals was 0.033 mL s{sup −1}, 100 °C and 3 h, respectively.
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.
Identifying Vortex-Core-Line using a tetrahedral satellite configuration: Field Topology Approach
NASA Astrophysics Data System (ADS)
Jiang, Yao; Lembege, Bertrand; Nishikawa, Ken-ichi; Cai, DongSheng; Hasegawa, Hiroshi
2016-04-01
Identifying vortices are the key to understanding the turbulence in plasma shear layers. Here, the term 'vortex' or 'vortex core' is associated with a region of Galilean invariance [Jeong and Hussain, 1995]. Unfortunately, no single precise definition of a vortex is currently universally accepted, despite the fact that many space plasma authors claim that many observations have detected "vortices" (as Kelvin-Helmholtz vortices at/around the magnetopause). By using the four satellite velocity data, and Taylor series, we expand the velocity data around the satellites, calculate its first order tensor, and linearly approximate the field. We can identify the vortex structures by using various vortex identification criteria as follows: (i) The first criterion is Q-criterion that defines vortices as regions in which the vorticity energy prevails other energies; (ii) the second criterion is the lambda2-criterion that is related to the minus of the Hessian matrix of the pressure related term; and (iii) the third criterion requires the existence of vortex-core-lines that is the Galilean invariance inside the four satellite tetrahedral region. Using these methods, we can identify and analyze more precisely the 3D vortex using tetrahedral satellite configuration.
NASA Astrophysics Data System (ADS)
Neyrinck, Mark C.
2016-07-01
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 obey simple laws, reminiscent of angular-momentum conservation. The model may be most useful in understanding spin correlations between neighbouring galaxies joined by filaments; these correlations would give intrinsic alignments between galaxies, essential to understand for accurate cosmological weak-lensing measurements.
Hong Luo; Yidong Xia; Robert Nourgaliev; Chunpei Cai
2011-06-01
A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.
NASA Astrophysics Data System (ADS)
Neyrinck, Mark C.
2016-04-01
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 obey simple laws, reminiscent of angular-momentum conservation. The model may be most useful in understanding spin correlations between neighbouring galaxies joined by filaments; these correlations would give intrinsic alignments between galaxies, essential to understand for accurate cosmological weak-lensing measurements.
A New Poisson Solver PIC Simulations on Arbitrary Unstructured Tetrahedral Meshes
NASA Astrophysics Data System (ADS)
Averkin, Sergey; Gatsonis, Nikolaos
2015-11-01
A new node-based algorithm is developed for the solution of Poisson's equation in PIC simulations on arbitrary unstructured tetrahedral meshes. The algorithm is derived by applying the integral form of the Gauss law to the indirect dual mesh constructed by connecting the centroids of edges to the centroids of faces and centroids of faces with the centroids of tetrahedral cells for each tetrahedron. The potential variation is assumed linear inside every cell and allows to estimate the potential gradient in each cell from the nodal values. The obtained sparse linear system is solved with the GMRES solver combined with the ILU(0) preconditioner. The new algorithm is verified with the simulation of the current collection by cylindrical Langmuire probes in the collisionless regime for a wide range of probe to Debye length ratios. The computed electron and ion number density variations as well as electric potential and collected currents compare well with the simulation results of Laframboise. AFOSR-FA9550-14-1-0366 Computational Mathematics Program.
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.
Analysis of electroperforated materials using the quadrat counts method
NASA Astrophysics Data System (ADS)
Miranda, E.; Garzón, C.; Martínez-Cisneros, C.; Alonso, J.; García-García, J.
2011-06-01
The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.
Reaction Wheel Control Design Using Linear Quadratic Controller
NASA Astrophysics Data System (ADS)
Nubli Muhamad, Nur; Susanto, Erwin; Syihabuddin, Budi; Prasetya Dwi Wibawa, Ig.
2016-01-01
This paper studies the design of active attitude control system of a nanosatellite in a single axis. In this paper, we consider dc motor based reaction wheel as an actuator, because of its pointing accuracy. However, the power consumption of the dc motor is often relatively large and needed to be optimized. Linear quadratic controller is supposed to have an ability to minimize power consumption and able to enhance the system performance. To show the advantage of this method, simulation result of attitude response, state trajectory, and trajectory of DC motor voltage are presented.
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.
Frontogenesis driven by horizontally quadratic distributions of density
NASA Technical Reports Server (NTRS)
Jacqmin, David
1991-01-01
Attention is given to the quadratic density distribution in a channel, which has been established by Simpson and Linden to be the simplest case of the horizontally nonlinear distribution of fluid density required for the production of frontogenesis. The porous-media and Boussinesq flow models are examined, and their evolution equations are reduced to one-dimensional systems. While both the porous-media and the inviscid/nondiffusive Boussinesq systems exhibit classic frontogenesis behavior, the viscous Boussinesq system exhibits a more complex behavior: boundary-layer effects force frontogenesis away from the lower boundary, and at late times the steepest density gradients are close to mid-channel.
Nios II hardware acceleration of the epsilon quadratic sieve algorithm
NASA Astrophysics Data System (ADS)
Meyer-Bäse, Uwe; Botella, Guillermo; Castillo, Encarnacion; García, Antonio
2010-04-01
The quadratic sieve (QS) algorithm is one of the most powerful algorithms to factor large composite primes used to break RSA cryptographic systems. The hardware structure of the QS algorithm seems to be a good fit for FPGA acceleration. Our new ɛ-QS algorithm further simplifies the hardware architecture making it an even better candidate for C2H acceleration. This paper shows our design results in FPGA resource and performance when implementing very long arithmetic on the Nios microprocessor platform with C2H acceleration for different libraries (GMP, LIP, FLINT, NRMP) and QS architecture choices for factoring 32-2048 bit RSA numbers.
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.
Quadratic integrand double-hybrid made spin-component-scaled
NASA Astrophysics Data System (ADS)
Brémond, Éric; Savarese, Marika; Sancho-García, Juan C.; Pérez-Jiménez, Ángel J.; Adamo, Carlo
2016-03-01
We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.
On a quadratic transformation due to Kummer and its generalizations
NASA Astrophysics Data System (ADS)
Shekhawat, Nidhi; Rathie, Arjun K.; Prakash, Om
2016-05-01
The aim of this paper is to obtain explicit expressions of (1-x ) -a2F1[a ,b 2 b +j ; -2/x 1 -x ] for j = 0, ±1,…, ±9. For j = 0, we have a well-known quadratic transformations formula of Kummer. The results are obtained by using the known hypergeometric identities available in the literature. Several known results obtained earlier by Kim, et al. follow special cases of our main findings. The results derived in this paper are simple, interesting and potentially useful in the applicable sciences.
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;
Multivariable quadratic synthesis of an advanced turbofan engine controller
NASA Technical Reports Server (NTRS)
Dehoff, R. L.; Hall, W. E., Jr.
1978-01-01
A digital controller for an advanced turbofan engine utilizing multivariate feedback is described. The theoretical background of locally linearized control synthesis is reviewed briefly. The application of linear quadratic regulator techniques to the practical control problem is presented. The design procedure has been applied to the F100 turbofan engine, and details of the structure of this system are explained. Selected results from simulations of the engine and controller are utilized to illustrate the operation of the system. It is shown that the general multivariable design procedure will produce practical and implementable controllers for modern, high-performance turbine engines.
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.
NASA Astrophysics Data System (ADS)
Tavelli, Maurizio; Dumbser, Michael
2016-08-01
unstructured meshes allows to discretize even complex physical domains with very coarse grids in both, space and time. The proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3D test problems and by comparing the obtained numerical results with available exact analytical solutions, or with other numerical or experimental reference data. To the knowledge of the authors, this is the first time that a space-time discontinuous Galerkin finite element method is presented for the three-dimensional incompressible Navier-Stokes equations on staggered unstructured tetrahedral grids.
Zhang, Xin; Zhang, Xu; Johnson, Jacob A; Chen, Yu-Sheng; Zhang, Jian
2016-07-13
Two non-interpenetrated zirconium metal-organic frameworks (Zr-MOFs), NPF-200 and NPF-201, were synthesized via the assembly of elongated tetrahedral linkers with Zr6 and Zr8 clusters. They represent the first examples of MOFs to have the β-UH3-like, 4,12,12T1 topology. Upon activation, NPF-200 exhibits the largest BET surface area (5463 m(2) g(-1)) and void volume (81.6%) among all MOFs formed from tetrahedral ligands. Composed of negative-charged boron-centered tetrahedral linkers, NPF-201 is an anionic Zr-MOF which selectively uptakes photoactive [Ru(bpy)3](2+) for heterogeneous photo-oxidation of thioanisole. PMID:27341503
NASA Technical Reports Server (NTRS)
Motiwalla, S. K.
1973-01-01
Using the first and the second derivative of flutter velocity with respect to the parameters, the velocity hypersurface is made quadratic. This greatly simplifies the numerical procedure developed for determining the values of the design parameters such that a specified flutter velocity constraint is satisfied and the total structural mass is near a relative minimum. A search procedure is presented utilizing two gradient search methods and a gradient projection method. The procedure is applied to the design of a box beam, using finite-element representation. The results indicate that the procedure developed yields substantial design improvement satisfying the specified constraint and does converge to near a local optimum.
Advances in 3D electromagnetic finite element modeling
Nelson, E.M.
1997-08-01
Numerous advances in electromagnetic finite element analysis (FEA) have been made in recent years. The maturity of frequency domain and eigenmode calculations, and the growth of time domain applications is briefly reviewed. A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will also be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis is also discussed.
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.
An Instability Index Theory for Quadratic Pencils and Applications
NASA Astrophysics Data System (ADS)
Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd
2014-04-01
Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.
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.
Sequential quadratic programming method for determining the minimum energy path.
Burger, Steven K; Yang, Weitao
2007-10-28
A new method, referred to as the sequential quadratic programming method, is presented for determining minimum energy paths. The method is based on minimizing the points representing the path in the subspace perpendicular to the tangent of the path while using a penalty term to prevent kinks from forming. Rather than taking one full step, the minimization is divided into a number of sequential steps on an approximate quadratic surface. The resulting method can efficiently determine the reaction mechanism, from which transition state can be easily identified and refined with other methods. To improve the resolution of the path close to the transition state, points are clustered close to this region with a reparametrization scheme. The usefulness of the algorithm is demonstrated for the Muller-Brown potential, amide hydrolysis, and an 89 atom cluster taken from the active site of 4-oxalocrotonate tautomerase for the reaction which catalyzes 2-oxo-4-hexenedioate to the intermediate 2-hydroxy-2,4-hexadienedioate. PMID:17979319
Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing
NASA Technical Reports Server (NTRS)
Choi, Benjamin B.
2002-01-01
Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.
Hidden and Nonstandard Bifurcation Diagram of an Alternate Quadratic System
NASA Astrophysics Data System (ADS)
Pastor, G.; Romera, M.; Danca, M.-F.; Martin, A.; Orue, A. B.; Montoya, F.; Encinas, L. Hernández
Alternate quadratic systems A : xn+1 = 1 - axn2,if n is even 1 - a∗xn2,if n is odd andB : xn+1 = 1 - a∗xn2,if n is even 1 - axn2, if n is odd, where a and a∗ are different parameters, seem to be interval maps in a range of the parameter values. However, after a careful graphical analysis of their bifurcation diagrams we conclude that this is true only for system B, but not for system A. In system A we find a hidden and nonstandard bifurcation diagram (“hidden” because it is not visible at normal resolution and “nonstandard” because the bifurcation diagram is empty for some ranges of the parameter values). The different behavior of the underlying critical polynomial in the range of parameter values in both alternate quadratic systems explains why the hidden and nonstandard bifurcation diagram is present in system A and not in system B. The analysis of the Lyapunov exponent also shows both the existence and the different behavior of the hidden bifurcation diagram of system A.
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.
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.
Liu, Fanxin; Tang, Chaojun; Zhan, Peng; Chen, Zhuo; Ma, Hongtao; Wang, Zhenlin
2014-01-01
We have demonstrated the plasmonic characteristics of an ultrathin tetrahedral amorphous carbon (ta-C) film coated with Ag nanoparticles. The simulation result shows that, under resonant and non-resonant excitations, the strongest plasmonic electric field of 1 nm ta-C coated Ag nanoparticle is not trapped within the ta-C layer but is released to its outside surface, while leaving the weaker electric field inside ta-C layer. Moreover, this outside plasmonic field shows higher intensity than that of uncoated Ag nanoparticle, which is closely dependent on the excitation wavelength and size of Ag particles. These observations are supported by the SERS measurements. We expect that the ability for ultrathin ta-C coated Ag nanoparticles as the SERS substrates to detect low concentrations of target biomolecules opens the door to the applications where it can be used as a detection tool for integrated, on-chip devices. PMID:24675437
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.
Ryltsev, R E; Chtchelkatchev, N M
2013-11-01
The local order units of dense simple liquid are typically three-dimensional (close packed) clusters: hcp, fcc, and icosahedrons. We show that the fluid demonstrates the superstable tetrahedral local order up to temperatures several orders of magnitude higher than the melting temperature and down to critical density. While the solid-like local order (hcp, fcc) disappears in the fluid at much lower temperatures and far above critical density. We conclude that the supercritical fluid shows the temperature (density)-driven two-stage "melting" of the three-dimensional local order. We also find that the structure relaxation times in the supercritical fluid are much larger than ones estimated for weakly interactive gas even far above the melting line. PMID:24329208
Tetrahedral Amorphous Carbon (ta-C) Ultra Thin Films for Slider Overcoat Application
NASA Astrophysics Data System (ADS)
Shi, X.; Hu, Y. H.; Hu, L.
Tetrahedral Amorphous Carbon (ta-C) thin film by using Filtered Cathodic Vacuum Arc (FCVA) technique has proven to be wear-resistive and corrosion resistant for a wide range of electrical, optical, and mechanical applications. Many investigations have shown that the ta-C film prepared by the FCVA technique can provide a superior ultra thin overcoat for the sliders and media compared to ECR-CVD and IBD coating technology. The ta-C film excels in terms of the film density, hardness, surface roughness and corrosion resistance. Nanofilm Technology International (NTI) has successfully developed and commercialized the FCVA coating system (FS series) for the slider overcoat application, which provides a good quality film with a high hardness (~50 GPa), low stress (2~3 GPa), low macro-particle density (~1/cm2 for particles > 0.3 μm), good uniformity (< 4%$ in 8 inch coating area) and high production repeatability (< 5%).
X-ray topography of a natural twinned diamond of unusual pseudo-tetrahedral morphology
NASA Astrophysics Data System (ADS)
Fritsch, Emmanuel; Moore, Moreton; Rondeau, Benjamin; Waggett, Richard G.
2005-06-01
The internal morphology of a natural twinned diamond was investigated using X-ray section topography. The diamond consisted of two crystals joined along a {1 1 1} plane whose remote ends were triangular {1 1 1} faces with sizes approximately 4 mm on the edge. A coating of fibrous growth obscured the morphology of the good quality diamond inside. Although the coat displayed re-entrant surfaces near the twin plane along three edges of the crystal, X-ray topography showed the inner crystal to protrude outwards along these same edges. The good quality inner core displayed the classical "spinel law" twinned octahedral morphology whereas the fibrous rim showed a typical sphalerite-like twinned tetrahedral morphology. A possible growth mechanism which could account for this is discussed.
Gas-phase acidities of tetrahedral oxyacids from ab initio electronic structure theory
Rustad, J.R.; Dixon, D.A.; Kubicki, J.D.; Felmy, A.R.
2000-05-04
Density functional calculations have been performed on several protonation states of the oxyacids of Si, P, V, As, Cr, and S. Structures and vibrational frequencies are in good agreement with experimental values where these are available. A reasonably well-defined correlation between the calculated gas-phase acidities and the measured pK{sub a} in aqueous solution has been found. The pK{sub a}/gas-phase acidity slopes are consistent with those derived from previous molecular mechanics calculations on ferric hydrolysis and the first two acidity constants for orthosilicic acid. The successive deprotonation of other H{sub n}TO{sub 4} species, for a given tetrahedral anion T are roughly consistent with this slope, but not to the extent that there is a universal correlation among all species.
Epitaxially stabilized iridium spinel oxide without cations in the tetrahedral site
NASA Astrophysics Data System (ADS)
Kuriyama, Hiromichi; Matsuno, Jobu; Niitaka, Seiji; Uchida, Masaya; Hashizume, Daisuke; Nakao, Aiko; Sugimoto, Kunihisa; Ohsumi, Hiroyuki; Takata, Masaki; Takagi, Hidenori
2010-05-01
Single-crystalline thin film of an iridium dioxide polymorph Ir2O4 has been fabricated by the pulsed laser deposition of LixIr2O4 precursor and the subsequent Li-deintercalation using soft chemistry. Ir2O4 crystallizes in a spinel (AB2O4) without A cations in the tetrahedral site, which is isostructural to λ-MnO2. Ir ions form a pyrochlore sublattice, which is known to give rise to a strong geometrical frustration. This Ir spinel was found to be a narrow gap insulator, in remarkable contrast to the metallic ground state of rutile-type IrO2. We argue that an interplay of a strong spin-orbit coupling and a Coulomb repulsion gives rise to an insulating ground state as in a layered perovskite Sr2IrO4.
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.
Rays of Small Integer Solutions of Homogeneous Ternary Quadratic Equations
NASA Astrophysics Data System (ADS)
Mishra, Sudhakara
1991-02-01
We have dealt with the general ternary quadratic equation: ax2 + by^ {2} + cz2 + dxy + exz + fyz = 0 with integer coefficients. After giving a matrix-reduction formula for a quadratic equation in any number of variables, of which the reduction of the above ternary equation is an easy consequence, we have devoted our attention to the reduced equation: ax^ {2} + by2 + cz^{2 } = 0. We have devised an algorithm for reducing Dirichlet's possibly larger solutions to this prescribed range of Holzer's. Then we have generalized Holzer's theorem to the case of the ternary equation: ax^{2 } + by2 + cz2 + dxy + exz + fyz = 0, giving in this context a new range called the CM-range, of which the Holzer's range is a particular case when d = e = f = 0. We have described an algorithm for getting a solution of the general ternary within this CM-range. After that we have devised an algorithm for getting all the solutions of the Legendre's equation ax 2 + by2 + cz^ {2} = 0 within the Holzer's range--and have shown that if we regard this Legendre's equation as a double cone, these solutions within the Holzer's range lie along some definite rays, here called the CM-rays, which are completely determined by the prime factors of the coefficients a, b and c. After giving an algorithm for detecting these CM-rays of the reduced equation: ax^2 + by^2 + cz^2 = 0, we have shown how one can produce some similar rays of solutions of the above general ternary quadratic equation: ax2 + by2 + cz2 + dxy + exz + fyz = 0. Note that apart from the method of exhausting all the possibilities, so far there has been no precisely stated algorithm to find the minimum solutions of the above ternary equations. Towards the end, observing in the context of our main result an inequality involving two functions, namely C and PCM from doubz_sp{*} {3} to doubz_+, and simultaneously presenting some tables of these positive CM-rays or PCM-rays lying in the positive octant, we have concluded this work with a number of
On the connection of the quadratic Lienard equation with an equation for the elliptic functions
NASA Astrophysics Data System (ADS)
Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I.
2015-07-01
The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential equation has been discussed. Here we show that the whole family of quadratic Lienard equations can be transformed into an equation for the elliptic functions. We demonstrate that this connection can be useful for finding explicit forms of general solutions of the quadratic Lienard equation. We provide several examples of application of our approach.
Cosmology for quadratic gravity in generalized Weyl geometry
NASA Astrophysics Data System (ADS)
Beltrán Jiménez, Jose; Heisenberg, Lavinia; Koivisto, Tomi S.
2016-04-01
A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.
Absence of the Gribov ambiguity in a quadratic gauge
NASA Astrophysics Data System (ADS)
Raval, Haresh
2016-05-01
The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold S^3, when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge.
Wind turbine power tracking using an improved multimodel quadratic approach.
Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier
2010-07-01
In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. PMID:20434153
Developed Adomian method for quadratic Kaluza-Klein relativity
NASA Astrophysics Data System (ADS)
Azreg-Aïnou, Mustapha
2010-01-01
We develop and modify the Adomian decomposition method (ADecM) to work for a new type of nonlinear matrix differential equations (MDE's) which arise in general relativity (GR) and possibly in other applications. The approach consists in modifying both the ADecM linear operator with highest order derivative and ADecM polynomials. We specialize in the case of a 4 × 4 nonlinear MDE along with a scalar one describing stationary cylindrically symmetric metrics in quadratic five-dimensional GR, derive some of their properties using ADecM and construct the most general unique power series solutions. However, because of the constraint imposed on the MDE by the scalar one, the series solutions terminate in closed forms exhausting all possible solutions.
Quadratic Forms for the Fermionic Unitary Gas Model
NASA Astrophysics Data System (ADS)
Finco, Domenico; Teta, Alessandro
2012-04-01
We consider a quantum system in dimension three composed by a group of N identical fermions, with mass 1/2, interacting via zero-range interaction with a group of M identical fermions of a different type, with mass m/2. Exploiting a renormalization procedure, we construct the corresponding quadratic form and define the so-called Skornyakov-Ter-Martirosyan extension Hα, which is the natural candidate as a possible Hamiltonian of the system. It is shown that if the form is unbounded from below then Hα is not a self-adjoint and bounded from below operator, and this in particular suggests that the so-called Thomas effect could occur. In the special case N = 2, M = 1 we prove that this is in fact the case when a suitable condition on the parameter m is satisfied.
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.
Recognition of Graphs with Convex Quadratic Stability Number
NASA Astrophysics Data System (ADS)
Pacheco, Maria F.; Cardoso, Domingos M.
2009-09-01
A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.
Motion corrected intracranial MRA using PROPELLER with RF quadratic encoding.
Zwart, Nicholas R; Pipe, James G
2009-06-01
A new motion corrected Time-of-Flight MRA technique named Variable Pitch PROPELLER is presented. This technique employs the PROPELLER acquisition and reconstruction scheme for in-plane bulk motion correction. A non- Fourier through-plane encoding mechanism called quadratic encoding boosts SNR, relative to conventional 2D MRA, in lieu of traditional 3D encoding. Partial Fourier encoding is applied in the slice direction for a further reduction in scan time. This work details the construction and optimization of this technique. VPPROP MRAs are compared with a clinical MOTSA protocol. Initial results show promising robustness to bulk motion effects. The comparisons with MOTSA provide insight as to the additions required to create a comparable scan. PMID:19353668
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-12
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
NASA Astrophysics Data System (ADS)
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-01
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.
Dark state in a nonlinear optomechanical system with quadratic coupling
NASA Astrophysics Data System (ADS)
Huang, Yue-Xin; Zhou, Xiang-Fa; Guo, Guang-Can; Zhang, Yong-Sheng
We consider a hybrid system consisting of a cavity optomechanical device with nonlinear quadratic radiation pressure coupled to an atomic ensemble. By considering the collective excitation, we show that this system supports nontrivial, nonlinear dark states. The coupling strength can be tuned via the lasers that ensure the population transfer adiabatically between the mechanical modes and the collective atomic excitations in a controlled way. In addition, we show how to detect the dark-state resonance by calculating the single-photon spectrum of the output fields and the transmission of the probe beam based on two-phonon optomechanically induced transparency. Possible application and extension of the dark states are also discussed. Supported by the National Fundamental Research Program of China (Grants No. 2011CB921200 and No. 2011CBA00200), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB01030200), and NSFC (Grants No. 61275122 and 11474266).
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)
Sensitivity Analysis of Parameters in Linear-Quadratic Radiobiologic Modeling
Fowler, Jack F.
2009-04-01
Purpose: Radiobiologic modeling is increasingly used to estimate the effects of altered treatment plans, especially for dose escalation. The present article shows how much the linear-quadratic (LQ) (calculated biologically equivalent dose [BED] varies when individual parameters of the LQ formula are varied by {+-}20% and by 1%. Methods: Equivalent total doses (EQD2 = normalized total doses (NTD) in 2-Gy fractions for tumor control, acute mucosal reactions, and late complications were calculated using the linear- quadratic formula with overall time: BED = nd (1 + d/ [{alpha}/{beta}]) - log{sub e}2 (T - Tk) / {alpha}Tp, where BED is BED = total dose x relative effectiveness (RE = nd (1 + d/ [{alpha}/{beta}]). Each of the five biologic parameters in turn was altered by {+-}10%, and the altered EQD2s tabulated; the difference was finally divided by 20. EQD2 or NTD is obtained by dividing BED by the RE for 2-Gy fractions, using the appropriate {alpha}/{beta} ratio. Results: Variations in tumor and acute mucosal EQD ranged from 0.1% to 0.45% per 1% change in each parameter for conventional schedules, the largest variation being caused by overall time. Variations in 'late' EQD were 0.4% to 0.6% per 1% change in the only biologic parameter, the {alpha}/{beta} ratio. For stereotactic body radiotherapy schedules, variations were larger, up to 0.6 to 0.9 for tumor and 1.6% to 1.9% for late, per 1% change in parameter. Conclusions: Robustness occurs similar to that of equivalent uniform dose (EUD), for the same reasons. Total dose, dose per fraction, and dose-rate cause their major effects, as well known.
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.
Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity
Golubkov, A A; Makarov, Vladimir A
2011-11-30
We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.
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.
EVA assembly of large space structure element
NASA Technical Reports Server (NTRS)
Bement, L. J.; Bush, H. G.; Heard, W. L., Jr.; Stokes, J. W., Jr.
1981-01-01
The results of a test program to assess the potential of manned extravehicular activity (EVA) assembly of erectable space trusses are described. Seventeen tests were conducted in which six "space-weight" columns were assembled into a regular tetrahedral cell by a team of two "space"-suited test subjects. This cell represents the fundamental "element" of a tetrahedral truss structure. The tests were conducted under simulated zero-gravity conditions. Both manual and simulated remote manipulator system modes were evaluated. Articulation limits of the pressure suit and zero gravity could be accommodated by work stations with foot restraints. The results of this study have confirmed that astronaut EVA assembly of large, erectable space structures is well within man's capabilities.
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.
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…
PPN Metric and PPN torsion in the quadratic poincaré gauge theory of gravity
NASA Astrophysics Data System (ADS)
Gladchenko, M. S.; Ponomariov, V. N.; Zhytnikov, V. V.
1990-05-01
The post-newtonian approximation of the quadratic Poincaré gauge theory of gravity is studied. As a result of this investigation the modified PPN metric and PPN torsion is obtained. Post-newtonian equations of motion for different test bodies are analyzed and some restrictions on the parameters of the quadratic lagrangian are found.
The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system
NASA Astrophysics Data System (ADS)
Li, Chengzhi; Llibre, Jaume
2009-12-01
We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka-Volterra differential system \\dot x=y+\\case{3}{2}(x^2-y^2) , \\dot y=-x(1-y) , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.
AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS
NASA Technical Reports Server (NTRS)
Lehtinen, B.
1994-01-01
AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user
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.
Pascucci, V
2004-02-18
This paper presents a simple approach for rendering isosurfaces of a scalar field. Using the vertex programming capability of commodity graphics cards, we transfer the cost of computing an isosurface from the Central Processing Unit (CPU), running the main application, to the Graphics Processing Unit (GPU), rendering the images. We consider a tetrahedral decomposition of the domain and draw one quadrangle (quad) primitive per tetrahedron. A vertex program transforms the quad into the piece of isosurface within the tetrahedron (see Figure 2). In this way, the main application is only devoted to streaming the vertices of the tetrahedra from main memory to the graphics card. For adaptively refined rectilinear grids, the optimization of this streaming process leads to the definition of a new 3D space-filling curve, which generalizes the 2D Sierpinski curve used for efficient rendering of triangulated terrains. We maintain the simplicity of the scheme when constructing view-dependent adaptive refinements of the domain mesh. In particular, we guarantee the absence of T-junctions by satisfying local bounds in our nested error basis. The expensive stage of fixing cracks in the mesh is completely avoided. We discuss practical tradeoffs in the distribution of the workload between the application and the graphics hardware. With current GPU's it is convenient to perform certain computations on the main CPU. Beyond the performance considerations that will change with the new generations of GPU's this approach has the major advantage of avoiding completely the storage in memory of the isosurface vertices and triangles.
A tetrahedral coordination of Zinc during transmembrane transport by P-type Zn2+-ATPases
Raimunda, Daniel; Subramanian, Poorna; Stemmler, Timothy; Argüello, José M.
2012-01-01
Zn2+ is an essential transition metal required in trace amounts by all living organisms. However, metal excess is cytotoxic and leads to cell damage. Cells rely on transmembrane transporters, with the assistance of other proteins, to establish and maintain Zn2+ homeostasis. Metal coordination during transport is key to specific transport and unidirectional translocation without the backward release of free metal. The coordination details of Zn2+ at the transmembrane metal binding site responsible for transport have now been established. Escherichia coli ZntA is a well-characterized Zn2+-ATPase responsible for intracellular Zn2+ efflux. A truncated form of the protein lacking regulatory metal sites and retaining the transport site was constructed. Metrical parameters of the metal-ligand coordination geometry for the zinc bound isolated form were characterized using x-ray absorption spectroscopy (XAS). Our data support a nearest neighbor ligand environment of (O/N)2S2 that is compatible with the proposed invariant metal coordinating residues present in the transmembrane region. This ligand identification and the calculated bond lengths support a tetrahedral coordination geometry for Zn2+ bound to the TM-MBS of P-type ATPase transporters. PMID:22387457
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.
AEM investigation of tetrahedrally coordinated Ti{sup 4+} in nickel-titanate spinel
Anderson, I.M. |; Bentley, J.; Carter, C.B.
1994-12-31
Stoichiometry and site distribution of metastable nickel-titanate spinel was studied with AEM. Results of EDXS and EELS agree that the metastable spinel is nonstoichiometric and titanium-deficient relative to its hypothetical endmember composition, ``Ni{sub 2}TiO{sub 4}``. The titanium deficiency has been determined by EELS to be {Delta} = 0.025 {plus_minus} 0.005. Channeling-enhanced microanalysis and ELNES studies indicate that the Ti{sup 4+} and Ni{sup 2+} cations are in tetrahedral and octahedral coordination, respectively, so that the metastable spinel has the normal cation distribution: Ti{sub l-{Delta}}[Ni{sub 2(1+{Delta})}]O{sub 4}. This is consistent with neutron powder-diffraction studies and SiO{sub 2}-solubility measurements of similar equilibrated and quenched spinel-containing specimens. Metastable nickel-titanate spinel therefore contrasts with stable stoichiometric spinels which tend to the inverse cation distribution, Me[MeTi]O{sub 4}.
NASA Astrophysics Data System (ADS)
Liu, Aiping; Zhu, Jiaqi; Han, Jiecai; Wu, Huaping; Jia, Zechun
2007-09-01
We investigate the growth process and structural properties of phosphorus incorporated tetrahedral amorphous carbon (ta-C:P) films which are deposited at different substrate biases by filtered cathodic vacuum arc technique with PH 3 as the dopant source. The films are characterized by X-ray photoelectron spectroscopy (XPS), atomic force microscopy, Raman spectroscopy, residual stress measurement, UV/VIS/NIR absorption spectroscopy and temperature-dependent conductivity measurement. The atomic fraction of phosphorus in the films as a function of substrate bias is obtained by XPS analysis. The optimum bias for phosphorus incorporation is about -80 V. Raman spectra show that the amorphous structures of all samples with atomic-scaled smooth surface are not remarkably changed when PH 3 is implanted, but some small graphitic crystallites are formed. Moreover, phosphorus impurities and higher-energetic impinging ions are favorable for the clustering of sp 2 sites dispersed in sp 3 skeleton and increase the level of structural ordering for ta-C:P films, which further releases the compressive stress and enhances the conductivity of the films. Our analysis establishes an interrelationship between microstructure, stress state, electrical properties, and substrate bias, which helps to understand the deposition mechanism of ta-C:P films.
NASA Astrophysics Data System (ADS)
Ding, Xue-Hua; Wang, Shi; Li, Yong-Hua; Huang, Wei
2015-01-01
The systematic research has been done into structural variations of supramolecular architectures by the self assembly of two pyridine-based potential anion receptors, 1-(4-pyridyl)piperazine (L1) and 4-pyrrolidinopyridine (L2), and different inorganic acids (HCl, HBr, HI, HNO3, HClO4, HIO4, H2SO4 and H3PO4). The formation of four fascinating salts, i.e. (H2L12+)·(H2PO4-)2 (1), (H2L12+)·(ClO4-)2 (2), (HL2+)·(ClO4-) (3) and (HL2+)·(IO4-) (4), indicates that N-heterocyclic L1 and L2 are prone to cocrystallize with tetrahedral oxyanions and anionic topologies play a crucial role in the crystallization process. Structural analyses reveal that various intermolecular ring motifs have been generated by robust hydrogen-bonding interactions in compounds 1-4. In particular, interesting substructures were observed in H2PO4- from salts 1 due to its polytopic potential hydrogen-bonding donor and acceptor oxygen atoms, including ring motifs, 1D ribbons and 2D supramolecular framework. Much to our surprise, crystal 4 proves to be a member of few supramolecular salts crystallizing with IO4- anion according to the Cambridge Structure Database (CSD).
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±3.9 kbp. Partialpolh, lef-8 and lef-9 gene sequences of the isolate showed a close relationship with HycuNPV and SpphNPV. Phylogram and K-2-P distances between similar isolates suggested inclusion of the present SpobNPV isolate to group I NPV. The biological activity of the isolate was tested under laboratory conditions against third instar larvae of S. obliqua and the LC50 was 4.37×10(3)OBs/ml occlusion bodies (OBs) per ml. The median survival time (ST50) was 181 h at a dose of 1×10(6)OBs/ml and 167 h 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
Output-Adaptive Tetrahedral Cut-Cell Validation for Sonic Boom Prediction
NASA Technical Reports Server (NTRS)
Park, Michael A.; Darmofal, David L.
2008-01-01
A cut-cell approach to Computational Fluid Dynamics (CFD) that utilizes the median dual of a tetrahedral background grid is described. The discrete adjoint is also calculated, which permits adaptation based on improving the calculation of a specified output (off-body pressure signature) in supersonic inviscid flow. These predicted signatures are compared to wind tunnel measurements on and off the configuration centerline 10 body lengths below the model to validate the method for sonic boom prediction. Accurate mid-field sonic boom pressure signatures are calculated with the Euler equations without the use of hybrid grid or signature propagation methods. Highly-refined, shock-aligned anisotropic grids were produced by this method from coarse isotropic grids created without prior knowledge of shock locations. A heuristic reconstruction limiter provided stable flow and adjoint solution schemes while producing similar signatures to Barth-Jespersen and Venkatakrishnan limiters. The use of cut-cells with an output-based adaptive scheme completely automated this accurate prediction capability after a triangular mesh is generated for the cut surface. This automation drastically reduces the manual intervention required by existing methods.
Spin and structural features of oxygen dissociation on tetrahedral Ag20 and Ag19Au clusters.
Pichugina, D A; Polynskaya, Y G; Kuz'menko, N E
2016-07-21
The spin-crossing mechanism of oxygen dissociation on Ag20 and monodoped Ag19Au clusters was investigated via spin-polarized scalar-relativistic DFT calculations using the PBE, TPSSh, M06L, mPBE, BLYP, OLYP, and B3LYP functionals. In particular, the singlet and triplet O-O bond rupture pathways at vertex-edge and facet-edge sites on the tetrahedral clusters were studied. The calculations reveal that for the Ag20O2 and Ag19AuO2 complexes, the spin inversion from the triplet to singlet state occurs during the last step, which involves O-O bond rupture through a singlet transition state (TS). When spin crossing during oxygen dissociation on the clusters is considered, the activation energies decrease by 10-29 kJ mol(-1); however, they are still high due to the magic nature of the clusters and high vertical spin excitation energies. For these silver clusters, size effects based on the relationship between the TS structure and oxidation activation energy were predicted. PMID:27327106
Chen, Yuanyuan; Farquhar, Erik R.; Chance, Mark R.; Palczewski, Krzysztof; Kiser, Philip D.
2012-01-01
Aminopeptidases are key enzymes involved in the regulation of signaling peptide activity. Here, we present a detailed biochemical and structural analysis of an evolutionary highly conserved aspartyl aminopeptidase called DNPEP. We show that this peptidase can cleave multiple physiologically relevant substrates, including angiotensins, and thus may play a key role in regulating neuron function. Using a combination of x-ray crystallography, x-ray absorption spectroscopy, and single particle electron microscopy analysis, we provide the first detailed structural analysis of DNPEP. We show that this enzyme possesses a binuclear zinc-active site in which one of the zinc ions is readily exchangeable with other divalent cations such as manganese, which strongly stimulates the enzymatic activity of the protein. The plasticity of this metal-binding site suggests a mechanism for regulation of DNPEP activity. We also demonstrate that DNPEP assembles into a functionally relevant tetrahedral complex that restricts access of peptide substrates to the active site. These structural data allow rationalization of the enzyme's preference for short peptide substrates with N-terminal acidic residues. This study provides a structural basis for understanding the physiology and bioinorganic chemistry of DNPEP and other M18 family aminopeptidases. PMID:22356908
Intense turquoise colors of apatite-type compounds with Mn5+ in tetrahedral coordination
NASA Astrophysics Data System (ADS)
Medina, Elena A.; Li, Jun; Stalick, Judith K.; Subramanian, M. A.
2016-02-01
The solid solutions of chlorapatite compounds Ba5Mn3-xVxO12Cl (x = 0-3.0) and Ba5Mn3-xPxO12Cl (x = 0-3.0) have been synthesized through solid state reactions and Pechini or sol-gel method using citric acid. The colors of the samples change from white (x = 3.0) through turquoise (x = 1.5) to dark green (x = 0) with increasing amount of manganese. Optical measurements reveal that the origin of the color is presumably a combination of d-d transitions of Mn5+ and cation-anion charge transfer from transition metals to oxygens. Near IR reflectance measurements indicate that synthesized compounds are promising materials for "cool pigments" applications. Magnetic measurements verify that manganese has two unpaired electrons and exhibits 5 + oxidation state. The IR spectra change systematically with sample compositions and the fingerprint region (700 cm-1 to 1100 cm-1) indicates characteristic bands belonging to (MnO4)3-, (VO4)3- and (PO4)3- functional groups. Structure refinements using neutron data confirm that Mn5+, V5+ and P5+ cations occupy the tetrahedral sites in the apatite structure.
Surface sites and unrelaxed surface energies of tetrahedral silica polymorphs and silicate
NASA Astrophysics Data System (ADS)
Murashov, Vladimir V.; Demchuk, Eugene
2005-12-01
Surface properties of respirable silica, which represents a major occupational safety concern, were investigated computationally, and a model for quantitative characterization of crystalline silica surface sites was developed. It was found that the surface energy of crystalline solids, such as silica and silicates, can be calculated as a product of the surface site density and site energy. The energies of sites formed by faceting tetrahedral silica polymorphs and aluminosilicate were determined by parametric fitting ab initio surface energies to site densities. Boltzmann's statistics was used to describe the distribution of faces as an exponential function of unrelaxed surface energy in the comminuted crystalline solids. Using these findings, crystallographic face distributions on fractured quartz, coesite, tridymite, and cristobalite were derived and average silanol hydroxyl densities in fractured particulate of these materials were estimated as 0.070, 0.059, 0.058, and 0.055 Å -2, respectively. The proposed method of quantitative characterization of the surface bridges the gap between microscopic simulations and measurable observables, such as cytotoxicity of respirable silica.
Zhang, Lijun; Du, Mao-Hua; Singh, David J
2010-01-01
We report the investigation of Zintl-phase Na(K){sub 8}SnSb{sub 4} and related compounds that contain SnSb{sub 4} tetrahedral anions using first principles electronic structure, Boltzmann transport, and density functional phonon calculations. We find that these compounds are narrow-gap semiconductors and there is a combination of heavy and light bands at valence band edge, which may lead to a combination of high thermopower and reasonable conductivity. High values of the thermopower are found for p-type doping within the Boltzmann transport theory. Furthermore, these materials are expected to have low thermal conductivity due to their structures that consist of a network of weakly coupled SnSb{sub 4} clusters, which leads to low phonon frequencies. In particular, we find low-frequency optical phonons that should effectively scatter the heat-carrying acoustic phonons. These results are discussed in terms of the structure, which consists of anionic clusters. Based on the results, it is suggested that such compounds may represent a useful paradigm for finding new thermoelectric materials.
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
Chen, Yuanyuan; Farquhar, Erik R.; Chance, Mark R.; Palczewski, Krzysztof; Kiser, Philip D.
2012-07-11
Aminopeptidases are key enzymes involved in the regulation of signaling peptide activity. Here, we present a detailed biochemical and structural analysis of an evolutionary highly conserved aspartyl aminopeptidase called DNPEP. We show that this peptidase can cleave multiple physiologically relevant substrates, including angiotensins, and thus may play a key role in regulating neuron function. Using a combination of x-ray crystallography, x-ray absorption spectroscopy, and single particle electron microscopy analysis, we provide the first detailed structural analysis of DNPEP. We show that this enzyme possesses a binuclear zinc-active site in which one of the zinc ions is readily exchangeable with other divalent cations such as manganese, which strongly stimulates the enzymatic activity of the protein. The plasticity of this metal-binding site suggests a mechanism for regulation of DNPEP activity. We also demonstrate that DNPEP assembles into a functionally relevant tetrahedral complex that restricts access of peptide substrates to the active site. These structural data allow rationalization of the enzyme's preference for short peptide substrates with N-terminal acidic residues. This study provides a structural basis for understanding the physiology and bioinorganic chemistry of DNPEP and other M18 family aminopeptidases.
Quadratic Measurement and Conditional State Preparation in an Optomechanical System
NASA Astrophysics Data System (ADS)
Brawley, George; Vanner, Michael; Bowen, Warwick; Schmid, Silvan; Boisen, Anja
2014-03-01
An important requirement in the study of quantum systems is the ability to measure non-linear observables at the level of quantum fluctuations. Such measurements enable the conditional preparation of highly non-classical states. Nonlinear measurement, although achieved in a variety of quantum systems including microwave cavity modes and optical fields, remains an outstanding problem in both electromechanical and optomechanical systems. To the best of our knowledge, previous experimental efforts to achieve nonlinear measurement of mechanical motion have not yielded strong coupling, nor the observation of quadratic mechanical motion. Here using a new technique reliant on the intrinsic nonlinearity of the optomechanical interaction, we experimentally observe for the first time a position squared (x2) measurement of the room-temperature Brownian motion of a nanomechanical oscillator. We utilize this measurement to conditionally prepare non-Gaussian bimodal states, which are the high temperature classical analogue of quantum macroscopic superposition states, or cat states. In the future with the aid of cryogenics and state-of-the-art optical cavities, our approach will provide a viable method of generating quantum superposition states of mechanical oscillators. This research was funded by the ARC Center of Excellence for Engineered Quantum Systems.
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.
2015-12-07
We report that 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 Pr_{2}Ir_{2}O_{7}, 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. Lastly, our discovery implies that Pr_{2}Ir_{2}O_{7} 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.
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
Hydroxyl functionalized thermosensitive microgels with quadratic crosslinking density distribution.
Elmas, Begum; Tuncel, Murvet; Senel, Serap; Patir, S; Tuncel, Ali
2007-09-01
N-isopropylacrylamide (NIPA) based uniform thermosensitive microgels were synthesized by dispersion polymerization by using relatively hydrophilic crosslinking agents with hydroxyl functionality. Glycerol dimethacrylate (GDMA), pentaerythritol triacrylate (PETA) and pentaerythritol propoxylate triacrylate (PEPTA) were used as crosslinking agents with different hydrophilicities. A protocol was first proposed to determine the crosslinking density distribution in the thermosensitive microgel particles by confocal laser scanning microscopy (CLSM). The microgels were fluorescently labeled by using hydroxyl group of the crosslinking agent. The CLSM observations performed with the microgels synthesized by three different crosslinking agents showed that the crosslinking density exhibited a quadratic decrease with the increasing radial distance in the spherical microgel particles. This structure led to the formation of more loose gel structure on the particle surface with respect to the center. Then the use of hydrophilic crosslinking agents in the dispersion polymerization of NIPA made possible the synthesis of thermosensitive microgels carrying long, flexible and chemically derivatizable (i.e., hydroxyl functionalized) fringes on the surface by a single-stage dispersion polymerization. The microgels with all crosslinking agents exhibited volume phase transition with the increasing temperature. The microgel obtained by the most hydrophilic crosslinking agent, GDMA exhibited higher hydrodynamic diameters in the fully swollen form at low temperatures than those obtained by PETA and PEPTA. Higher hydrodynamic size decrease from fully swollen form to the fully shrunken form was also observed with the same microgel. PMID:17532327
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, Erdős-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 Erdős-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.
Gap solitons in a nonlinear quadratic negative-index cavity.
Scalora, Michael; de Ceglia, Domenico; D'Aguanno, Giuseppe; Mattiucci, Nadia; Akozbek, Neset; Centini, Marco; Bloemer, Mark J
2007-06-01
We predict the existence of gap solitons in a nonlinear, quadratic Fabry-Pérot negative index cavity. A peculiarity of a single negative index layer is that if magnetic and electric plasma frequencies are different it forms a photonic band structure similar to that of a multilayer stack composed of ordinary, positive index materials. This similarity also results in comparable field localization and enhancement properties that under appropriate conditions may be used to either dynamically shift the band edge, or for efficient energy conversion. We thus report that an intense, fundamental pump pulse is able to shift the band edge of a negative index cavity, and make it possible for a weak second harmonic pulse initially tuned inside the gap to be transmitted, giving rise to a gap soliton. The process is due to cascading, a well-known phenomenon that occurs far from phase matching conditions that limits energy conversion rates, it resembles a nonlinear third-order process, and causes pulse compression due to self-phase modulation. The symmetry of the equations of motion under the action of either an electric or a magnetic nonlinearity suggests that both nonlinear polarization and magnetization, or a combination of both, can lead to solitonlike pulses. More specifically, the antisymmetric localization properties of the electric and magnetic fields cause a nonlinear polarization to generate a dark soliton, while a nonlinear magnetization spawns a bright soliton. PMID:17677375
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(κ)(r)=-κc²r²/2 with κ=9.54×10⁻⁵⁴ cm⁻² induced by cosmic inhomogeneities. When V(κ)(r) is taken in conjunction with both a universal linear potential V(γ₀)(r)=γ₀c²r/2 with γ₀=3.06×10⁻³⁰ 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(κ)(r) being negative, galaxies can only support bound orbits up to distances of order γ₀/κ=100kpc, with global physics imposing a limit on the size of galaxies. PMID:21517292
Quadratic Fermi node in a 3D strongly correlated semimetal
NASA Astrophysics Data System (ADS)
Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.
2015-12-01
Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.
GR angular momentum in the quadratic spinor Lagrangian formulation
NASA Astrophysics Data System (ADS)
Li, Siao-Jing
2016-08-01
We inquire into the question of whether the quadratic spinor Lagrangian (QSL) formulation can describe the angular momentum for a general-relativistic system. The QSL Hamiltonian has previously been shown to be able to yield an energy-momentum quasilocalization which brings a proof of the positive gravitational energy when the spinor satisfies the conformal Witten equation. After inspection, we find that, under the constraint that the spinor on the asymptotic boundary is a constant, the QSL Hamiltonian is successful in giving an angular momentum quasilocalization. We also make certain the spinor in the Hamiltonian plays the role of a gauge field, a warrant of our permission to impose constraints on the spinor. Then, by some adjustment of the QSL Hamiltonian, we gain a covariant center-of-mass moment quasilocalization only under the condition that the displacement on the asymptotic boundary is a Killing boost vector. We expect the spinor expression will bring a proof of some connection between the gravitational energy and angular momentum.
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.; et al
2015-12-07
We report that 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 ismore » predicted, for which we observe some evidence. Lastly, 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.« less
Linear versus quadratic portfolio optimization model with transaction cost
NASA Astrophysics Data System (ADS)
Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah
2014-06-01
Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.
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).
Inverse problem of quadratic time-dependent Hamiltonians
NASA Astrophysics Data System (ADS)
Guo, Guang-Jie; Meng, Yan; Chang, Hong; Duan, Hui-Zeng; Di, Bing
2015-08-01
Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly. Project supported by the National Natural Science Foundation of China (Grant No. 11347171), the Natural Science Foundation of Hebei Province of China (Grant No. A2012108003), and the Key Project of Educational Commission of Hebei Province of China (Grant No. ZD2014052).
Linear quadratic optimal controller for cable-driven parallel robots
NASA Astrophysics Data System (ADS)
Abdolshah, Saeed; Shojaei Barjuei, Erfan
2015-12-01
In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work-space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional- integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.
Junction conditions in quadratic gravity: thin shells and double layers
NASA Astrophysics Data System (ADS)
Reina, Borja; Senovilla, José M. M.; Vera, Raül
2016-05-01
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 consequences of all these results are briefly analyzed.
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
Quadratic isothermal amplification for the detection of microRNA.
Duan, Ruixue; Zuo, Xiaolei; Wang, Shutao; Quan, Xiyun; Chen, Dongliang; Chen, Zhifei; Jiang, Lei; Fan, Chunhai; Xia, Fan
2014-03-01
This protocol describes an isothermal amplification approach for ultrasensitive detection of specific microRNAs (miRNAs). It achieves this level of sensitivity through quadratic amplification of the target oligonucleotide by using a Bst DNA polymerase-induced strand-displacement reaction and a lambda exonuclease-aided recycling reaction. First, the target miRNA binds to a specifically designed molecular beacon, causing it to become a fluorescence emitter. A primer then binds to the activated beacon, and Bst polymerase initiates the synthesis of a double-stranded DNA segment templated on the molecular beacon. This causes the concomitant release of the target miRNA from the beacon--the first round of 'recycling'. Second, the duplex beacon thus produced is a suitable substrate for a nicking enzyme present in solution. After the duplex beacon is nicked, the lambda exonuclease digests the beacon and releases the DNA single strand just synthesized, which is complementary to the molecular beacon, inducing the second round of recycling. The miRNA detection limit of this protocol is 10 fmol at 37 °C and 1 amol at 4 °C. This approach also affords high selectivity when applied to miRNA extracted from MCF-7 and PC3 cell lines and even from breast cancer tissue samples. Upon isolation of miRNA, the detection process can be completed in ∼2 h. PMID:24525753
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.
Application of finite-element method to three-dimensional nuclear reactor analysis
Cheung, K.Y.
1985-01-01
The application of the finite element method to solve a realistic one-or-two energy group, multiregion, three-dimensional static neutron diffusion problem is studied. Linear, quadratic, and cubic serendipity box-shape elements are used. The resulting sets of simultaneous algebraic equations with thousands of unknowns are solved by the conjugate gradient method, without forming the large coefficient matrix explicitly. This avoids the complicated data management schemes to store such a large coefficient matrix. Three finite-element computer programs: FEM-LINEAR, FEM-QUADRATIC and FEM-CUBIC were developed, using the linear, quadratic, and cubic box-shape elements respectively. They are self-contained, using simple nodal labeling schemes, without the need for separate finite element mesh generating routines. The efficiency and accuracy of these computer programs are then compared among themselves, and with other computer codes. The cubic element model is not recommended for practical usage because it gives almost identical results as the quadratic model, but it requires considerably longer computation time. The linear model is less accurate than the quadratic model, but it requires much shorter computation time. For a large 3-D problem, the linear model is to be preferred since it gives acceptable accuracy. The quadratic model may be used if improved accuracy is desired.
Li, Wenzhi; Zhang, Weiqiang; Zhao, Quanyi; Li, Yongmin; Ma, Chunlin; Chen, Liren; Yin, Yuanqi
2004-03-01
The enantioseparation of seven novel chiral transition metal tetrahedral clusters has been achieved for the first time on cellulose derivatized with tris(3,5-dimethylphenylcarbamate) (CDMPC) as chiral stationary phase (CSP) and hexane containing different alcohols as modifiers as mobile phases. The effect of mobile-phase composition on enantioselectivity was studied, and the effect of structural variation of the solutes on their enantioseparation was also investigated. It was found that both the metal in the tetrahedral core and the ligand coordinated to the atom in the tetrahedral core had significant effects on the chromatographic behavior of the analytes. PMID:14735279
Berg, J.W. van der; Maseland, J.E.J.; Oskam, B.
1996-12-31
In this paper an assessment of CFD methods based on the underlying grid type is made. It is safe to say that emerging CFD methods based on hybrid body-fitted grids of tetrahedral and prismatic cells using unstructured data storage schemes have the potential to satisfy the basic requirements of problem-turnaround-time and accuracy for complex geometries. The CFD system described in this paper is based on the hybrid prismatic-tetrahedral grid approach. In an analysis it is shown that the cells in the prismatic layer have to satisfy a central symmetry property in order to obtain a second-order accurate approximation of the viscous terms in the Reynolds-averaged Navier-Stokes equations. Prismatic grid generation is demonstrated for the ONERA M6 wing-alone configuration and the AS28G wing/body configuration.
Chen, Jun; Zhang, Qing; Zheng, Fa-Kun; Liu, Zhi-Fa; Wang, Shuai-Hua; Wu, A-Qing; Guo, Guo-Cong
2015-02-21
Three air-stable tetrahedral manganese(ii) dihalide complexes [MnX2(DPEPO)] (DPEPO = bis[2-(diphenylphosphino)phenyl]ether oxide; X = Cl, Br and I) were prepared. All of the obtained compounds were structurally characterized by single-crystal X-ray diffraction analyses, which reveal that they crystallize in centrosymmetric space groups and feature an isolated mononuclear structure with Mn(2+) in a tetrahedral environment. Interestingly, these complexes show excellent photoluminescent performance in neat solid form, with the highest total quantum yield (Φtotal) of up to 70% recorded for the dibromide complex. Intense green flashes of light could be observed by the naked eye when rubbing the manganese(ii) complexes. PMID:25597698
NASA Astrophysics Data System (ADS)
Rasulov, R. Ya.; Rasulov, V. R.; Eshboltaev, I.
2016-07-01
The ballistic contribution to the current of linear photovoltaic effect under two-photon absorption of light is calculated and theoretically analyzed for the semiconductors of a tetrahedral symmetry with a complex band structure consisting of two closely spaced subbands. The transitions between the branches of one band in cases of the simultaneous absorption of two photons and successive absorption of two single photons are taken into account.
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.
Gong K.; Vukmirovic M.B.; Ma C.; Zhu Y.; Adzic R.R.
2011-11-01
We synthesized the Pt monolayer shell-Pd tetrahedral core electrocatalysts that are notable for their high activity and stable performance. A small number of low-coordination sites and defects, and high content of the (1 1 1)-oriented facets on Pd tetrahedron makes them a suitable support for a Pt monolayer to obtain an active O{sub 2} reduction reaction (ORR) electrocatalyst. The surfactants, used to control size and shape of Pd tetrahedral nanoparticles, are difficult to remove and cause adverse effects on the ORR. We describe a simple and noninvasive method to synthesize high-purity tetrahedral Pd nanocrystals (TH Pd) by combining a hydrothermal route and CO adsorption-induced removal of surfactants. Poly(vinylpyrrolidone) (PVP), used as a protecting and reducing agent in hydrothermal reactions, is strongly bonded to the surface of the resulting nanocrystals. We demonstrate that PVP was displaced efficiently by adsorbed CO. A clean surface was achieved upon CO stripping at a high potential (1.0 V vs RHE). It played a decisive role in improving the activity of the Pt monolayer/TH Pd electrocatalyst for the ORR. Furthermore, the results demonstrate a versatile method for removal of surfactants from various nanoparticles that severely limited their applications.
New type of Weyl semimetal with quadratic double Weyl fermions.
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M Zahid
2016-02-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914
Moments for general quadratic densities in n dimensions
Furman, Miguel A.
2002-03-20
We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.
New type of Weyl semimetal with quadratic double Weyl fermions
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid
2016-01-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin–orbit coupling and that, after the inclusion of spin–orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914
Gravity waves from non-minimal quadratic inflation
Pallis, Constantinos; Shafi, Qaisar
2015-03-12
We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio r≃(2−4)⋅10{sup −3}, and an inflaton mass close to 3⋅10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kähler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s}≃0.963 and r≃0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kähler potential, and the prefactor encountered in it. Increasing slightly the latter above (−3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5−9)⋅10{sup 13} GeV.
Post-Newtonian, quasicircular binary inspirals in quadratic modified gravity
NASA Astrophysics Data System (ADS)
Yagi, Kent; Stein, Leo C.; Yunes, Nicolás; Tanaka, Takahiro
2012-03-01
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 with standard kinetic energy. This class of theories includes Einstein-Dilaton-Gauss-Bonnet and Chern-Simons modified gravity as special cases. We analytically derive and solve the coupled field equations in the post-Newtonian approximation, assuming a comparable-mass, spinning black hole binary source in a quasicircular, weak-field/slow-motion orbit. We find that a naive subtraction of divergent piece associated with the point-particle approximation is ill-suited to represent compact objects in these theories. Instead, we model them by appropriate effective sources built so that known strong-field solutions are reproduced in the far-field limit. In doing so, we prove that black holes in Einstein-Dilaton-Gauss-Bonnet and Chern-Simons theory can have hair, while neutron stars have no scalar monopole charge, in diametrical opposition to results in scalar-tensor theories. We then employ techniques similar to the direct integration of the relaxed Einstein equations to obtain analytic expressions for the scalar field, metric perturbation, and the associated gravitational wave luminosity measured at infinity. We find that scalar field emission mainly dominates the energy flux budget, sourcing electric-type (even-parity) dipole scalar radiation and magnetic-type (odd-parity) quadrupole scalar radiation, correcting the General Relativistic prediction at relative -1PN and 2PN orders. Such modifications lead to corrections in the emitted gravitational waves that can be mapped to the parameterized post-Einsteinian framework. Such modifications could be strongly constrained with gravitational wave observations.
Reduced order parameter estimation using quasilinearization and quadratic programming
NASA Astrophysics Data System (ADS)
Siade, Adam J.; Putti, Mario; Yeh, William W.-G.
2012-06-01
The ability of a particular model to accurately predict how a system responds to forcing is predicated on various model parameters that must be appropriately identified. There are many algorithms whose purpose is to solve this inverse problem, which is often computationally intensive. In this study, we propose a new algorithm that significantly reduces the computational burden associated with parameter identification. The algorithm is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters. The resulting inverse problem therefore becomes a linear regression or quadratic programming problem (QP) for minimizing the sum of squared residuals; the solution becomes an update on the parameter set. This process of linearization and regression is repeated until convergence takes place. This algorithm has not received much attention, as the QPs can become quite large, often infeasible for real-world systems. To alleviate this drawback, proper orthogonal decomposition is applied to reduce the size of the linearized model, thereby reducing the computational burden of solving each QP. In fact, this study shows that the snapshots need only be calculated once at the very beginning of the algorithm, after which no further calculations of the reduced-model subspace are required. The proposed algorithm therefore only requires one linearized full-model run per parameter at the first iteration followed by a series of reduced-order QPs. The method is applied to a groundwater model with about 30,000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated.
Strong anisotropy in nearly ideal tetrahedral superconducting FeS single crystals
NASA Astrophysics Data System (ADS)
Borg, Christopher K. H.; Zhou, Xiuquan; Eckberg, Christopher; Campbell, Daniel J.; Saha, Shanta R.; Paglione, Johnpierre; Rodriguez, Efrain E.
2016-03-01
We report the preparation of single crystals of tetragonal iron sulfide (FeS) which exhibits a nearly ideal tetrahedral geometry with S-Fe-S bond angles of 110.2(2)° and 108.1(2)°. Grown via hydrothermal de-intercalation of K xFe 2 -yS 2 crystals under basic and reducing conditions, the silver, platelike crystals of FeS remain stable up to 200 °C under air and 250°C under inert conditions, even though the mineral "mackinawite" (FeS) is known to be metastable. FeS single crystals exhibit a superconducting state below Tc=4 K as determined by electrical resistivity, magnetic susceptibility, and heat capacity measurements, confirming the presence of a bulk superconducting state. Normal state measurements yield an electronic specific heat of 5 mJ/mol K2, and paramagnetic, metallic behavior with a low residual resistivity of 250 μ Ω cm . Magnetoresistance measurements performed as a function of magnetic field angle tilted toward both transverse and longitudinal orientations with respect to the applied current reveal remarkable two-dimensional behavior. This is paralleled in the superconducting state, which exhibits the largest known upper critical field Hc 2 anisotropy of all iron-based superconductors, with Hc2 ||a b(0 ) /Hc2 ||c(0 ) =(2.75 T ) /(0.275 T ) =10 . Comparisons to theoretical models for two-dimensional and anisotropic three-dimensional superconductors, however, suggest that FeS is the latter case with a large effective mass anisotropy. We place FeS in context to other closely related iron-based superconductors and discuss the role of structural parameters such as anion height on superconductivity.
Fonseca, Gabriel Paiva; Landry, Guillaume; White, Shane; D'Amours, Michel; Yoriyaz, Hélio; Beaulieu, Luc; Reniers, Brigitte; Verhaegen, Frank
2014-10-01
Accounting for brachytherapy applicator attenuation is part of the recommendations from the recent report of AAPM Task Group 186. To do so, model based dose calculation algorithms require accurate modelling of the applicator geometry. This can be non-trivial in the case of irregularly shaped applicators such as the Fletcher Williamson gynaecological applicator or balloon applicators with possibly irregular shapes employed in accelerated partial breast irradiation (APBI) performed using electronic brachytherapy sources (EBS). While many of these applicators can be modelled using constructive solid geometry (CSG), the latter may be difficult and time-consuming. Alternatively, these complex geometries can be modelled using tessellated geometries such as tetrahedral meshes (mesh geometries (MG)). Recent versions of Monte Carlo (MC) codes Geant4 and MCNP6 allow for the use of MG. The goal of this work was to model a series of applicators relevant to brachytherapy using MG. Applicators designed for (192)Ir sources and 50 kV EBS were studied; a shielded vaginal applicator, a shielded Fletcher Williamson applicator and an APBI balloon applicator. All applicators were modelled in Geant4 and MCNP6 using MG and CSG for dose calculations. CSG derived dose distributions were considered as reference and used to validate MG models by comparing dose distribution ratios. In general agreement within 1% for the dose calculations was observed for all applicators between MG and CSG and between codes when considering volumes inside the 25% isodose surface. When compared to CSG, MG required longer computation times by a factor of at least 2 for MC simulations using the same code. MCNP6 calculation times were more than ten times shorter than Geant4 in some cases. In conclusion we presented methods allowing for high fidelity modelling with results equivalent to CSG. To the best of our knowledge MG offers the most accurate representation of an irregular APBI balloon applicator. PMID
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.
Skardal, Aleksander; Zhang, Jianxing; Prestwich, Glenn D
2010-08-01
Bioprinting enables deposition of cells and biomaterials into spatial orientations and complexities that mirror physiologically relevant geometries. To facilitate the development of bioartificial vessel-like grafts, two four-armed polyethylene glycol (PEG) derivatives with different PEG chain lengths, TetraPEG8 and TetraPEG13, were synthesized from tetrahedral pentaerythritol derivatives. The TetraPEGs are unique multi-armed PEGs with a compact and symmetrical core. The TetraPEGs were converted to tetra-acrylate derivatives (TetraPAcs) which were used in turn to co-crosslink thiolated hyaluronic acid and gelatin derivatives into extrudable hydrogels for printing tissue constructs. First, the hydrogels produced by TetraPAc crosslinking showed significantly higher shear storage moduli when compared to PEG diacrylate (PEGDA)-crosslinked synthetic extracellular matrices (sECMs) of similar composition. These stiffer hydrogels have rheological properties more suited to bioprinting high-density cell suspensions. Second, TetraPAc-crosslinked sECMs were equivalent or superior to PEGDA-crosslinked gels in supporting cell growth and proliferation. Third, the TetraPac sECMs were employed in a proof-of-concept experiment by encapsulation of NIH 3T3 cells in sausage-like hydrogel macrofilaments. These macrofilaments were then printed into tubular tissue constructs by layer-by-layer deposition using the Fab@Home printing system. LIVE/DEAD viability/cytotoxicity-stained cross-sectional images showed the bioprinted cell structures to be viable in culture for up to 4 weeks with little evidence of cell death. Thus, biofabrication of cell suspensions in TetraPAc sECMs demonstrates the feasibility of building bioartificial blood vessel-like constructs for research and potentially clinical uses. PMID:20546891
Thermal expansion and structural complexity of Ba silicates with tetrahedrally coordinated Si atoms
NASA Astrophysics Data System (ADS)
Gorelova, Liudmila A.; Bubnova, Rimma S.; Krivovichev, Sergey V.; Krzhizhanovskaya, Maria G.; Filatov, Stanislav K.
2016-03-01
Thermal expansion of Ba silicates with tetrahedrally coordinated Si atoms in the temperature range of 25-1100 °C had been studied by high-temperature X-ray powder diffraction. The volume thermal expansion coefficients (TECs) are in the range 41-50×10-6 °C-1 with an average value of <αV > = 45 ×10-6 °C-1. In the structures with chain and layered silicate anions, thermal expansion is anisotropic: the direction of maximal TEC is parallel to the extension of the zweier chains of silicate tetrahedra, which are strained owing to the interactions with Ba2+. The strain is released during thermal expansion due to the increasing effective size of Ba2+ induced by thermal vibrations. Information-theoretic analysis of the structural and topological complexities of Ba silicates indicates that their structural complexity is a function of the topological complexity of their silicate anions. The latter displays a non-linear behaviour with increasing SiO2 content (=the increasing degree of polymerization and increasing dimensionality): it starts from simple topologies, reaches a maximum at topologies of intermediate complexity, and ends up at simple topologies again. The specificity of the interactions of Ba2+ with the silicate anions results in higher complexity of high-temperature α-BaSi2O5 compared to that of low-temperature β-BaSi2O5. This uncommon behaviour may be explained by the vibrational advantages provided by flatter and more complex silicate layers in the α-phase, which overcome negative differences in configurational entropies of the two modifications apparent in the differences of their structural Shannon information.
Simple shearing flow of dry soap foams with TCP structure[Tetrahedrally Close-Packed
REINELT,DOUGLAS A.; KRAYNIK,ANDREW M.
2000-02-16
The microrheology of dry soap foams subjected to large, quasistatic, simple shearing deformations is analyzed. Two different monodisperse foams with tetrahedrally close-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Laves (C15). The elastic-plastic response is evaluated by calculating foam structures that minimize total surface area at each value of strain. The minimal surfaces are computed with the Surface Evolver program developed by Brakke. The foam geometry and macroscopic stress are piecewise continuous functions of strain. The stress scales as T/V{sup 1/3} where T is surface tension and V is cell volume. Each discontinuity corresponds to large changes in foam geometry and topology that restore equilibrium to unstable configurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a small increase in strain changes the energy profile in the neighborhood of a foam structure from a local minimum to a saddle point, which can lead to symmetry-breaking bifurcations. In general, the new foam topology associated with each stable solution branch results from a cascade of local topology changes called T1 transitions. Each T1 cascade produces different cell neighbors, reduces surface energy, and provides an irreversible, film-level mechanism for plastic yield behavior. Stress-strain curves and average stresses are evaluated by examining foam orientations that admit strain-periodic behavior. For some orientations, the deformation cycle includes Kelvin cells instead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and can even cause strain localization.
Simple shearing flow of dry soap foams with tetrahedrally close-packed structure
Reinelt, Douglas A.; Kraynik, Andrew M.
2000-05-01
The microrheology of dry soap foams subjected to quasistatic, simple shearing flow is analyzed. Two different monodisperse foams with tetrahedrally close-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Laves (C15). The elastic-plastic response is evaluated by using the Surface Evolver to calculate foam structures that minimize total surface area at each value of strain. The foam geometry and macroscopic stress are piecewise continuous functions of strain. The stress scales as T/V{sup 1/3}, where T is surface tension and V is cell volume. Each discontinuity corresponds to large changes in foam geometry and topology that restore equilibrium to unstable configurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a small increase in strain changes the energy profile in the neighborhood of a foam structure from a local minimum to a saddle point, which can lead to symmetry-breaking bifurcations. In general, the new structure associated with each stable solution branch results from an avalanche of local topology changes called T1 transitions. Each T1 cascade produces different cell neighbors, reduces surface energy, and provides an irreversible, film-level mechanism for plastic yield behavior. Stress-strain curves and average stresses are evaluated by examining foam orientations that admit strain-periodic behavior. For some orientations, the deformation cycle includes Kelvin cells instead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and can even cause strain localization. (c) 2000 Society of Rheology.
Hosea, N A; Berman, H A; Taylor, P
1995-09-12
We have examined the specificity of planar carboxyl and tetrahedral phosphonyl esters for mouse cholinesterases and have delineated the orientation of these ligands in the enzyme active center. The approach involved altering acyl pocket dimensions by site-specific mutagenesis of two phenylalanines and varying ligand size and enantiomer presentation. Substrate catalysis rates by wild type acetylcholinesterase (AChE) of acetyl-, butyryl-, and benzoylthiocholine diminished with increasing size of the acyl moiety. In contrast, substitution of the acyl pocket phenylalanines giving the mutants F295L and F297I of AChE yielded more efficient catalysis of the larger substrates and a specificity approaching that of butyrylcholinesterase. Extension from planar substrates to enantiomerically pure organophosphonates allowed for an analysis of enantiomeric selectivity. We found that AChE reactions are 200-fold faster with the Sp than the Rp enantiomer of of cycloheptyl methylphosphonyl thiocholine. Upon the acyl pocket size being enlarged, the Rp enantiomer became more reactive while reaction with the Sp enantiomer was slightly reduced. In fact, the F297I mutant displayed inverted stereospecificity. A visual correlation with the kinetic data has been developed by docking the ligands in the active site. Upon placement of the phosphonyl oxygen in the oxyanion hole and the leaving group being directed out of the gorge, the Rp, but not the Sp, enantiomer engendered steric hindrance between the alkoxyl group and the acyl pocket. Replacing F297 with Ile accommodated the bulky alkoxyl group of the Rp isomer in the acyl pocket, allowing similar orientations of the phosphonyl oxygen and the leaving group to the Sp isomer.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:7547883
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.
Tetra-hedral zinc in tetra-kis-(1-methyl-1H-imidazole-κN)zinc bis-(tetra-fluorido-borate).
Reedijk, Jan; van Albada, Gerard A; Limburg, Bart; Mutikainen, Ilpo; Turpeinen, Urho
2012-01-01
In the title compound, [Zn(C(4)H(6)N(2))(4)](BF(4))(2), the Zn(II) ion is in a slightly distorted tetra-hedral coordination geometry, with Zn-N distances in the range 1.980 (2)-1.991 (2) Å. The tetra-hedral angles are in the range 104.93 (9)-118.81 (9)°. PMID:22259384
NASA Technical Reports Server (NTRS)
Johnson, S. E.; Field, E. I.
1973-01-01
Linear, quadratic, and cubic isoparametric hexahedral solid elements have been added to the element library of NASTRAN. These elements are available for static, dynamic, buckling, and heat-transfer analyses. Because the isoparametric element matrices are generated by direct numerical integration over the volume of the element, variations in material properties, temperatures, and stresses within the elements are represented in the computations. In order to compare the accuracy of the new elements, three similar models of a slender cantilever were developed, one for each element. All elements performed well. As expected, however, the linear element model yielded excellent results only when shear behavior predominated. In contrast, the results obtained from the quadratic and cubic element models were excellent in both shear and bending.
Stability of the equilibrium positions of an engine with nonlinear quadratic springs
NASA Astrophysics Data System (ADS)
Stănescu, Nicolae-Doru; Popa, Dinel
2014-06-01
Our paper realizes a study of the equilibrium positions for an engine supported by four identical nonlinear springs of quadratic characteristic. The systems with quadratic characteristic are generally avoided because they lead to mathematical complications. Our goal is to realize such a study for an engine supported on quadratic springs. For the model purposed, we established the equations of motion and we discussed the possibilities for the equilibrium positions. Because of the quadratic characteristic of the springs and of the approximations made for the small rotations, the equations obtained for the equilibrium lead us to a paradox, which consists in the existence of an open neighborhood in which there exists an infinity of positions of indifferent equilibrium, or a curve where the equilibrium positions are situated. Moreover, the study of the stability shows that the stability is assured for the position at which the springs are not compressed. Finally, a numerical example is presented and completely solved.
The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems
Jiang, Yanan; Han, Maoan; Xiao, Dongmei
2014-01-01
We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ3. PMID:24982980
The existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems.
Jiang, Yanan; Han, Maoan; Xiao, Dongmei
2014-01-01
We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3). PMID:24982980
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.
NASA Astrophysics Data System (ADS)
Brugnano, Luigi; Caccia, Gianluca Frasca; Iavernaro, Felice
2016-06-01
The family of EQUIP (Energy and QUadratic Invariants Preserving) methods for Hamiltonian systems is here recasted in the framework of Line Integral Methods, in order to provide a more efficient discrete problem.
Maximization of Sums of Quotients of Quadratic Forms and Some Generalizations.
ERIC Educational Resources Information Center
Kiers, Henk A. L.
1995-01-01
Monotonically convergent algorithms are described for maximizing sums of quotients of quadratic forms. Six (constrained) functions are investigated. The general formulation of the functions and the algorithms allow for application of the algorithms in various situations in multivariate analysis. (SLD)
NASA Astrophysics Data System (ADS)
Pikulev, A. A.
2001-09-01
The propagation of Hermitian beams in a medium with a distributed quadratic inhomogeneity is studied and is shown that any solution can be represented as a function of some particular solution. This is accomplished by establishing a one-to-one correspondence between optical fields in a homogeneous medium and in a medium with an arbitrary quadratic inhomogeneity. The stability of optical resonators is studied and the condition for their stability is found. Several solutions are found using the method developed.
Bianchi type-I cosmological model with quadratic equation of state
NASA Astrophysics Data System (ADS)
Reddy, D. R. K.; Adhav, K. S.; Purandare, M. A.
2015-05-01
Bianchi type-I cosmological model containing perfect fluid with quadratic equation of state has been studied in general theory of relativity. The general solutions of the Einstein's field equations for Bianchi type-I space-time have been obtained under the assumption of quadratic equation of state (EoS) p= αρ 2- ρ, where α is constant and strictly α≠0. The physical and geometrical aspects of the model are discussed.
NASA Astrophysics Data System (ADS)
Aghaei, S.; Chenaghlou, A.
2014-02-01
The Dirac equation with scalar and vector potentials of equal magnitude is considered. For the two-dimensional harmonic oscillator superintegrable potential, the superintegrable potentials of E8 (case (3b)), S4 and S2, the Schrödinger-like equations are studied. The quadratic algebras of these quasi-Hamiltonians are derived. By using the realization of the quadratic algebras in a deformed oscillator algebra, the structure function and the energy eigenvalues are obtained.
Sandia Higher Order Elements (SHOE) v 0.5 alpha
2013-09-24
SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likely exist.
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
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
Rinnert, Emmanuel; Carteret, Cedric; Humbert, Bernard; Fragneto-Cusani, Giovanna; Ramsay, John D F; Delville, Alfred; Robert, Jean-Louis; Bihannic, Isabelle; Pelletier, Manuel; Michot, Laurent J
2005-12-15
The interaction of water with a synthetic saponite clay sample, with a layer charge of 1 per unit cell (0.165 C m(-2)), was investigated by following along water adsorption and desorption in the relative pressure range from 10(-6) to 0.99 (i) the adsorbed amount by gravimetric and near-infrared techniques, (ii) the basal distance and arrangement of water molecules in the interlayer by X-ray and neutron diffraction under controlled water pressure, and (iii) the molecular structure and interaction of adsorbed water molecules by near-infrared (NIR) and Raman spectroscopy under controlled water pressure. The results thus obtained were confronted with Grand Canonical Monte Carlo (GC/MC) simulations. Using such an approach, various well-distinct hydration ranges can be distinguished. In the two first ranges, at low water relative pressure, adsorption occurs on external surfaces only, with no swelling associated. The next range corresponds to the adsorption of water molecules around the interlayer cation without removing it from its position on top of the ditrigonal cavity of the tetrahedral layer and is associated with limited swelling. In the following range, the cation is displaced toward the mid-interlayer region. The interlamellar spacing thus reached, around 12.3 A, corresponds to what is classically referred to as a "one-layer hydrate," whereas no water layer is present in the interlayer region. The next hydration range corresponds to the filling of the interlayer at nearly constant spacing. This leads to the formation of a well-organized network of interlayer water molecules with significant interactions with the clay layer. The structure thus formed leads to a complete extinction of the d001 line in D2O neutron diffraction patterns that are correctly simulated by directly using the molecular configurations derived by GC/MC. The next range (0.50 < P/P0 < 0.80) corresponds to the final swelling of the structure to reach d spacing values of 15.2 A (usually referred
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
On the complexity of some quadratic Euclidean 2-clustering problems
NASA Astrophysics Data System (ADS)
Kel'manov, A. V.; Pyatkin, A. V.
2016-03-01
Some problems of partitioning a finite set of points of Euclidean space into two clusters are considered. In these problems, the following criteria are minimized: (1) the sum over both clusters of the sums of squared pairwise distances between the elements of the cluster and (2) the sum of the (multiplied by the cardinalities of the clusters) sums of squared distances from the elements of the cluster to its geometric center, where the geometric center (or centroid) of a cluster is defined as the mean value of the elements in that cluster. Additionally, another problem close to (2) is considered, where the desired center of one of the clusters is given as input, while the center of the other cluster is unknown (is the variable to be optimized) as in problem (2). Two variants of the problems are analyzed, in which the cardinalities of the clusters are (1) parts of the input or (2) optimization variables. It is proved that all the considered problems are strongly NP-hard and that, in general, there is no fully polynomial-time approximation scheme for them (unless P = NP).
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.
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.
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
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
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.
NASA Astrophysics Data System (ADS)
Kim, Cheolmin; Yoon, Min-Ju; Hong, Seok Hee; Park, Minjoon; Park, Kwangyong; Kim, Soo Young
2016-05-01
Tetrahedral structures comprising Sn-cored materials with five different types of substituents were synthesized. For the substituents, we employed methyl and tert-butyl as aliphatic groups, and naphthyl and phenyl as aromatic groups. The bandgap is in the range of 3.28 - 3.56 eV. The All the compounds with substituents showed bathochromical photoluminescence characteristics and exhibited aggregation-induced emission characteristics. Specifically, the compounds with aromatic substituents prohibited side-chain packing and π-π stacking. The energy levels of the highest occupied and lowest unoccupied molecular orbitals were measured to be 5.5 - 5.75 and 2.0 - 2.37 eV, respectively. The maximum luminance efficiencies and power efficiencies of the Sn-cored compound-based organic light-emitting diodes (OLEDs) were 0.38 - 0.71 cd/A and 0.15 - 0.28 lm/W. Therefore, it is expected that Sn-cored compounds with a tetrahedral structure, especially those containing aromatic substituents, can be used as an active material in blue OLEDs for prohibiting side-chain packing and π-π stacking. [Figure not available: see fulltext.
NASA Astrophysics Data System (ADS)
Ogurtani, Tarik Ö.; Seeger, Alfred K.
1985-06-01
The energy dissipation per cycle due to the harmonic rigid motion of geometric kinks (built-in) in the atmosphere of light interstitials which are hopping between tetrahedral sites is investigated analytically as well as numerically in terms of discrete Fourier k space plus Laplace transformation technique. In the linear response case a discrete Debye-type relaxation spectrum with six distinct branches is found to represent the anelastic behavior of the system uniquely (the nearest neighbor jumps only) and exactly. It is shown by extensive computer modeling experiments that the induced and dislocation embedded kink-enhanced Snoek peak is composed of six subpeaks, one acoustic and five optical in character. The acoustic part and the optical modes, especially the upper band which is composed of optical modes 6 and 5, are strongly and selectively associated with the isotropic (Cottrell Atmosphere) and the pure shear part (Snoek Cloud) of the elastic dipole tensor of the tetrahedral interstitials, respectively. An extremely accurate and concise analytical expression is deduced which shows that the decoupling procedure of Snoek and Cottrell atmospheres is a reliable approximation.
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 Mn₁₋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
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.
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 ∝ φ{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.
Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
Dehaene, Jeroen; Moor, Bart de
2003-10-01
We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n+1)x(2n+1) binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one- and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation, and possibly quantum computing.
Propagator for the time-dependent charged oscillator via linear and quadratic invariants
Abdalla, M. Sebawe Choi, Jeong-Ryeol
2007-12-15
The problem of a charged particle in the presence of a variable magnetic field is considered. Using the linear and the quadratic invariants as a tool, the wave functions in Fock state as well as in coherent state are obtained. The corresponding propagators which propagate the wave functions in the space-time are derived. Using numerical computations we have managed to draw some plots for the real, imaginary, and absolute values of the propagators. This has been used to analyze the properties of the propagators associated with both of the linear and the quadratic invariants. It has been shown that there is no essential difference between the behavior of the absolute value of the propagators in both of the linear and the quadratic invariants.
NASA Astrophysics Data System (ADS)
Yamada, Katsuhiko; Jikuya, Ichiro
2014-09-01
Singularity analysis and the steering logic of pyramid-type single gimbal control moment gyros are studied. First, a new concept of directional passability in a specified direction is introduced to investigate the structure of an elliptic singular surface. The differences between passability and directional passability are discussed in detail and are visualized for 0H, 2H, and 4H singular surfaces. Second, quadratic steering logic (QSL), a new steering logic for passing the singular surface, is investigated. The algorithm is based on the quadratic constrained quadratic optimization problem and is reduced to the Newton method by using Gröbner bases. The proposed steering logic is demonstrated through numerical simulations for both constant torque maneuvering examples and attitude control examples.
Detection of code spread OFDM based on 0-1 integer quadratic programming
NASA Astrophysics Data System (ADS)
Elghariani, Ali; Zoltowski, Michael D.
2012-05-01
In this paper we introduce Integer Quadratic Programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose combined preprocessing steps that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The first step in this combination is to detect as much as possible symbols using procedures presented in [9], which is basically based on the gradient of quadratic function. The second step detects the undetected symbols from the first step using MMSE estimator. The result of the latter step will be used to predict the initial upper bound of the BB algorithm. Simulation results show that the proposed preprocessing combination when applied prior to BB provides optimal performance with a significantly reduced computational complexity.
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.
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
An efficient algorithm for computing the roots of general quadratic, cubic and quartic equations
NASA Astrophysics Data System (ADS)
Mahmood, Munir; Hammad, Sali; Mahmood, Ibtihal
2014-10-01
While the solution to deriving the roots of the general quadratic equation is adequately covered in a typical classroom environment, the same is not true for the general cubic and quartic equations. To the best of our knowledge, we do not see the roots of the general cubic or quartic equation discussed in any typical algebra textbook at the undergraduate level. In this paper, we propose an efficient algorithm in order to calculate the roots of the general quadratic, cubic and quartic equations. Examples are given to demonstrate the usefulness of this proposed algorithm.
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
OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE
Xie, Xianchao; Kou, S. C.; Brown, Lawrence
2015-01-01
This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results. PMID:27041778
Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl
NASA Astrophysics Data System (ADS)
Lee, T.-W.; An, Keju
2016-06-01
We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.
Analytical solution of the Klein Gordon equation for a quadratic exponential-type potential
NASA Astrophysics Data System (ADS)
Ezzatpour, Somayyeh; Akbarieh, Amin Rezaei
2016-07-01
In this research study, analytical solutions of the Klein Gordon equation by considering the potential as a quadratic exponential will be presented. However, the potential is assumed to be within the framework of an approximation for the centrifugal potential in any state. The Nikiforov-Uvarov method is used to calculate the wave function, as well as corresponding exact energy equation, in bound states. We finally concluded that the quadratic exponential-type potential under which the results were deduced, led to outcomes that were comparable to the results obtained from the well-known potentials in some special cases.
Campoamor-Stursberg, R.
2008-05-15
By means of contractions of Lie algebras, we obtain new classes of indecomposable quasiclassical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from noncompact real simple algebras with nonsimple complexification, where we impose that a nondegenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem and obtain sufficient conditions on integrable cocycles of quasiclassical Lie algebras in order to preserve nondegenerate quadratic Casimir operators by the associated linear deformations.
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.
Nonadiabatic Effects in Ultracold Molecules via Anomalous Linear and Quadratic Zeeman Shifts
NASA Astrophysics Data System (ADS)
McGuyer, B. H.; Osborn, C. B.; McDonald, M.; Reinaudi, G.; Skomorowski, W.; Moszynski, R.; Zelevinsky, T.
2013-12-01
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.
A study of radiation propagation in a medium with quadratic inhomogeneity
Pikulev, A A
2001-09-30
The propagation of Hermitian beams in a medium with a distributed quadratic inhomogeneity is studied and is shown that any solution can be represented as a function of some particular solution. This is accomplished by establishing a one-to-one correspondence between optical fields in a homogeneous medium and in a medium with an arbitrary quadratic inhomogeneity. The stability of optical resonators is studied and the condition for their stability is found. Several solutions are found using the method developed. (physical foundations of quantum electronics)
User's guide for SOL/QPSOL: a Fortran package for quadratic programming
Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.
1983-07-01
This report forms the user's guide for Version 3.1 of SOL/QPSOL, a set of Fortran subroutines designed to locate the minimum value of an arbitrary quadratic function subject to linear constraints and simple upper and lower bounds. If the quadratic function is convex, a global minimum is found; otherwise, a local minimum is found. The method used is most efficient when many constraints or bounds are active at the solution. QPSOL treats the Hessian and general constraints as dense matrices, and hence is not intended for large sparse problems. This document replaces the previous user's guide of June 1982.
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
NASA Astrophysics Data System (ADS)
Ganapathy, S.; Kumar, Rajiv; Montouillout, V.; Fernandez, C.; Amoureux, J. P.
2004-05-01
The silicon sites tetrahedrally connected to aluminum in framework positions of a molecular sieve may be identified by a selective reintroduction of the hetero-nuclear 27Al- 29Si dipolar interaction through Rotational Echo Adiabatic Passage DOuble Resonance (REAPDOR) NMR. In this rotor synchronized 29Si MAS experiment, an effective dipolar dephasing of the Si-O-Al, over Si-O-Si, environments is shown to aid in the identification of silicon sites in the immediate vicinity of aluminum. Application of the method in the structurally interesting and novel molecular sieve ETAS-10 provides valuable insights on the details of aluminum substitution in the zeolite lattice and further leads to the first direct NMR estimate of Al-Si distance ( rAl-Si=323±5 pm) in ETAS-10.
NASA Astrophysics Data System (ADS)
Jiang, Long; Ju, Ping; Meng, Xian-Rui; Kuang, Xiao-Jun; Lu, Tong-Bu
2012-09-01
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.
NASA Astrophysics Data System (ADS)
Yokoyama, Toshihiko; Yonamoto, Yoshiki; Ohta, Toshiaki
1996-12-01
We have measured and analyzed the temperature dependence of extended X-ray absorption fine structure (EXAFS) spectra of tetrahedral systems MBr4 ( M=C, Si, Ge). The EXAFS analysis by means of the cumulant expansion technique enables one to obtain information about force constants including the third-order anharmonicity. The second-order cumulants obtained experimentally are in excellent agreement with the values expected by the vibrational data and the third-order cumulants have been determined successfully. For the first nearest neighbor (NN) Br M shells the stretching motions are apparently dominant to describe EXAFS, while for the second NN Br Br shell the bending modes are found to contribute significantly to the cumulants especially for the third-order anharmonicity. The obtained force constants are compared to each other and the origin of observed bending anharmonicity is discussed.
NASA Astrophysics Data System (ADS)
Verma, A. S.
2008-12-01
In this Letter we present the two expressions relating the bond-stretching force constant ( α in N/m) and bond-bending force constant ( β in N/m) for the A IIIB V and A IIB VI semiconductors with the product of ionic charges ( ZZ) and nearest neighbor distance d (Å). Interatomic force constants of these compounds exhibit a linear relationship when plotted on a log-log scale against the nearest neighbor distance d (Å), but fall on different straight lines according to the ionic charge product of the compounds. A fairly good agreement has been found between the observed and calculated values of the α and β for binary tetrahedral semiconductors.
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
Chen, Wang-Shou; Zhu, Jia-Qi; Han, Jie-Cai; Tian, Gui; Tan, Man-Lin
2009-01-01
Nitrogenated tetrahedral amorphous carbon (ta-C : N) films were prepared on the polished C--Si substrates by introducing highly pure nitrogen gas into the cathode region and the depositing chamber synchronously using filtered cathodic vacuum arc (FCVA) technology. The nitrogen content in the films was controlled by changing the flow rate of nitrogen gas. The configuration of ta-C : N films was investigated by means of X-ray photoelectron spectroscopy (XPS) and visible Raman spectroscopy. It was shown that the nitrogen content in the films increased from 0.84 at% to 5.37 at% monotonously when the nitrogen flow rate was varied from 2 seem to 20 sccm. The peak position of C (1s) core level moved towards higher binding energy with the increase in nitrogen content. The shift of C (1s) peak position could be ascribed to the chemical bonding between carbon and nitrogen atoms even though more three-fold coordinated sp2 configuration as in graphite was formed when the films were doped with more nitrogen atoms. Additionally, the half width of C(1s) peak gradually was also broadened with increasing nitrogen content. In order to discover clearly the changing regularities of the microstructure of the films, the XPS C(1s) spectra and Raman spectra were deconvoluted using a Gaussian-Lorentzian mixed lineshape. It was shown that the tetrahedral hybridization component was still dominant even though the ratio of sp2/sp3 obtained from C(1s) spectra rose with the increase in nitrogen content. The Raman measurements demonstrated that the G peak position shifted towards higher frequency from 1,561 to 1,578 cm(-1) and the ratio of ID/IG also rose with the increase in nitrogen content. Both results indicated that the graphitizing tendency could occur with the increase in nitrogen content in the films. PMID:19385255
Lemaire, Arnaud; Wang, Quan-Yi; Wei, Yingxu; Liu, Zhongmin; Su, Bao-Lian
2011-11-15
A simple synthesis pathway has been developed for the design of hierarchically structured spongy or spherical voids assembled meso-macroporous aluminosilicates with high tetrahedral aluminium content on the basis of the aqueous polymerisation of new stabilized alkoxy-bridged single molecular precursors. The intimate mixing of an aluminosilicate ester (sec-BuO)(2)-Al-O-Si(OEt)(3) and a silica co-reactant (tetramethoxysilane, TMOS) with variable ratios and the use of alkaline solutions (pH 13.0 and 13.5) improve significantly the heterocondensation rates between the highly reactive aluminium alkoxide part of the single precursor and added silica co-reactant, leading to aluminosilicate materials with high intra-framework aluminium content and low Si/Al ratios. The spherically-shaped meso-macroporosity was spontaneously generated by the release of high amount of liquid by-products (water/alcohol molecules) produced during the rapid hydrolysis and condensation processes of this double alkoxide and the TMOS co-reactant. It has been observed that both pH value and Al-Si/TMOS molar ratio can strongly affect the macroporous structure formation. Increasing pH value, even slightly from 13 to 13.5, can significantly favour the incorporation of Al atoms in tetrahedral position of the framework. After the total ionic exchange of Na(+) compensating cations, catalytic tests of obtained materials were realised in the esterification reaction of high free fatty acid (FFA) oils, showing their higher catalytic activity compared to commercial Bentonite clay, and their potential applications as catalyst supports in acid catalysed reactions. PMID:21875708
Graphical Description of Johnson-Neyman Outcomes for Linear and Quadratic Regression Surfaces.
ERIC Educational Resources Information Center
Schafer, William D.; Wang, Yuh-Yin
A modification of the usual graphical representation of heterogeneous regressions is described that can aid in interpreting significant regions for linear or quadratic surfaces. The standard Johnson-Neyman graph is a bivariate plot with the criterion variable on the ordinate and the predictor variable on the abscissa. Regression surfaces are drawn…
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.
Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation
NASA Astrophysics Data System (ADS)
Rousseau, Christiane
We give here a planar quadratic differential system depending on two parameters, λ, δ. There is a curve in the λ-δ space corresponding to a homoclinic loop bifurcation (HLB). The bifurcation is degenerate at one point of the curve and we get a narrow tongue in which we have two limit cycles. This is the first example of such a bifurcation in planar quadratic differential systems. We propose also a model for the bifurcation diagram of a system with two limit cycles appearing at a singular point from a degenerate Hopf bifurcation, and dying in a degenerate HLB. This model shows a deep duality between degenerate Hopf bifurcations and degenerate HLBs. We give a bound for the maximal number of cycles that can appear in certain simultaneous Hopf and homoclinic loop bifurcations. We also give an example of quadratic system depending on three parameters which has at one place a degenerate Hopf bifurcation of order 3, and at another place a Hopf bifurcation of order 2 together with a HLB. We characterize the planar quadratic systems which are integrable in the neighbourhood of a homoclinic loop.
ERIC Educational Resources Information Center
Didis, Makbule Gozde; Erbas, Ayhan Kursat
2015-01-01
This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight…
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…
Technology Transfer Automated Retrieval System (TEKTRAN)
Nearly 150 sq. mi. quadrats were established for long-term monitoring of vegetation dynamics on the Jornada Experimental Range in south central New Mexico in the early 1900s. Today, approximately 120 of those sites are revisited on a five year sampling rotation. Although some of the methods for data...
Optical synthetic-aperture radar processor archietecture with quadratic phase-error correction
Dickey, F.M.; Mason, J.J. )
1990-10-15
Uncompensated phase errors limit the image quality of synthetic-aperture radar. We present an acousto-optic synthetic-aperture radar processor architecture capable of measuring the quadratic phase error. This architecture allows for the error signal to be fed back to the processor to generate the corrected image.
Failures and Inabilities of High School Students about Quadratic Equations and Functions
ERIC Educational Resources Information Center
Memnun, Dilek Sezgin; Aydin, Bünyamin; Dinç, Emre; Çoban, Merve; Sevindik, Fatma
2015-01-01
In this research study, it was aimed to examine failures and inabilities of eleventh grade students about quadratic equations and functions. For this purpose, these students were asked ten open-ended questions. The analysis of the answers given by the students to these questions indicated that a significant part of these students had failures and…
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…
Graphical Representation of Complex Solutions of the Quadratic Equation in the "xy" Plane
ERIC Educational Resources Information Center
McDonald, Todd
2006-01-01
This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.
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.
Endicott, Julia S.; Joubert-Doriol, Loïc; Izmaylov, Artur F.
2014-07-21
We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.
Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method
NASA Astrophysics Data System (ADS)
Bizyaev, I. A.; Kozlov, V. V.
2015-12-01
We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.
Granda, L.N.
2011-04-01
We study a scalar field with non-minimal kinetic coupling to itself and to the curvature. The slow rolling conditions allowing an inflationary background have been found. The quadratic and Higgs type potentials have been considered, and the corresponding values for the scalar fields at the end of inflation allows to recover the connection with particle physics.
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…
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…
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…
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.
Building Students' Understanding of Quadratic Equation Concept Using Naïve Geometry
ERIC Educational Resources Information Center
Fachrudin, Achmad Dhany; Putri, Ratu Ilma Indra; Darmawijoyo
2014-01-01
The purpose of this research is to know how Naïve Geometry method can support students' understanding about the concept of solving quadratic equations. In this article we will discuss one activities of the four activities we developed. This activity focused on how students linking the Naïve Geometry method with the solving of the quadratic…
When does brain aging accelerate? Dangers of quadratic fits in cross-sectional studies.
Fjell, Anders M; Walhovd, Kristine B; Westlye, Lars T; Østby, Ylva; Tamnes, Christian K; Jernigan, Terry L; Gamst, Anthony; Dale, Anders M
2010-05-01
Many brain structures show a complex, non-linear pattern of maturation and age-related change. Often, quadratic models (beta(0) + beta(1)age + beta(2)age(2) + epsilon) are used to describe such relationships. Here, we demonstrate that the fitting of quadratic models is substantially affected by seemingly irrelevant factors, such as the age-range sampled. Hippocampal volume was measured in 434 healthy participants between 8 and 85 years of age, and quadratic models were fit to subsets of the sample with different age-ranges. It was found that as the bottom of the age-range increased, the age at which volumes appeared to peak was moved upwards and the estimated decline in the last part of the age-span became larger. Thus, whether children were included or not affected the estimated decline between 60 and 85 years. We conclude that caution should be exerted in inferring age-trajectories from global fit models, e.g. the quadratic model. A nonparametric local smoothing technique (the smoothing spline) was found to be more robust to the effects of different starting ages. The results were replicated in an independent sample of 309 participants. PMID:20109562
ERIC Educational Resources Information Center
Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.
2011-01-01
Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…
Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.
Kiselev, Aleksei P; Plachenov, Alexandr B
2016-04-01
The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given. PMID:27140777
NASA Astrophysics Data System (ADS)
The Periodic Table of the elements will now have to be updated. An international team of researchers has added element 110 to the Earth's armory of elements. Though short-lived—of the order of microseconds, element 110 bottoms out the list as the heaviest known element on the planet. Scientists at the Heavy Ion Research Center in Darmstadt, Germany, made the 110-proton element by colliding a lead isotope with nickel atoms. The element, which is yet to be named, has an atomic mass of 269.
NASA Astrophysics Data System (ADS)
Hansen, Mikkel Bo; Christiansen, Ove; Hättig, Christof
2009-10-01
Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H2O, CH2O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented.
NASA Astrophysics Data System (ADS)
Tanaka, Hajime
2003-11-01
Recently it was suggested that tetrahedral liquids such as water and silicon exhibit a fragile-to-strong transition while approaching the glass-transition temperature (Tg). Such a drastic change in the fragility of liquid as a function of temperature is very rarely observed. Here we propose that, contrary to the popular fragility transition scenario, this phenomenon should be explained in terms of the crossover from a non-glass-forming to a glass-forming branch. For ordinary glass-forming liquids, there is frustration between long-range density ordering (crystallization) and short-range bond ordering (energetic frustration hidden in the interaction potential), which helps vitrification. For water and silicon, such frustration does not exist near the melting point (Tm) at ambient pressure since the symmetry of their crystals is consistent with that of short-range tetrahedral bond ordering. Thus, we call this high-temperature region near Tm a non-glass-forming branch. In the low-temperature region near Tg, which we call a glass-forming branch, on the other hand, a system tends to have long-range density ordering. Its competition with local tetrahedral ordering induces strong frustration effects, which make the liquid strong. Our scenario suggests that the crossover from a non-glass-forming to a glass-forming branch may be generic to tetrahedral liquids whose specific volume increases upon crystallization.
Mehta, Jugal V; Gajera, Sanjay B; Patel, Mohan N
2014-11-01
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. PMID:25467683
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.
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.
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.
NASA Astrophysics Data System (ADS)
Prasad, Saurav; Chakravarty, Charusita
2016-06-01
Experiments and simulations demonstrate some intriguing equivalences in the effect of pressure and electrolytes on the hydrogen-bonded network of water. Here, we examine the extent and nature of equivalence effects between pressure and salt concentration using relationships between structure, entropy, and transport properties based on two key ideas: first, the approximation of the excess entropy of the fluid by the contribution due to the atom-atom pair correlation functions and second, Rosenfeld-type excess entropy scaling relations for transport properties. We perform molecular dynamics simulations of LiCl-H2O and bulk SPC/E water spanning the concentration range 0.025-0.300 molefraction of LiCl at 1 atm and pressure range from 0 to 7 GPa, respectively. The temperature range considered was from 225 to 350 K for both the systems. To establish that the time-temperature-transformation behaviour of electrolyte solutions and water is equivalent, we use the additional observation based on our simulations that the pair entropy behaves as a near-linear function of pressure in bulk water and of composition in LiCl-H2O. This allows for the alignment of pair entropy isotherms and allows for a simple mapping of pressure onto composition. Rosenfeld-scaling implies that pair entropy is semiquantitatively related to the transport properties. At a given temperature, equivalent state points in bulk H2O and LiCl-H2O (at 1 atm) are defined as those for which the pair entropy, diffusivity, and viscosity are nearly identical. The microscopic basis for this equivalence lies in the ability of both pressure and ions to convert the liquid phase into a pair-dominated fluid, as demonstrated by the O-O-O angular distribution within the first coordination shell of a water molecule. There are, however, sharp differences in local order and mechanisms for the breakdown of tetrahedral order by pressure and electrolytes. Increasing pressure increases orientational disorder within the first
Prasad, Saurav; Chakravarty, Charusita
2016-06-21
Experiments and simulations demonstrate some intriguing equivalences in the effect of pressure and electrolytes on the hydrogen-bonded network of water. Here, we examine the extent and nature of equivalence effects between pressure and salt concentration using relationships between structure, entropy, and transport properties based on two key ideas: first, the approximation of the excess entropy of the fluid by the contribution due to the atom-atom pair correlation functions and second, Rosenfeld-type excess entropy scaling relations for transport properties. We perform molecular dynamics simulations of LiCl-H2O and bulk SPC/E water spanning the concentration range 0.025-0.300 molefraction of LiCl at 1 atm and pressure range from 0 to 7 GPa, respectively. The temperature range considered was from 225 to 350 K for both the systems. To establish that the time-temperature-transformation behaviour of electrolyte solutions and water is equivalent, we use the additional observation based on our simulations that the pair entropy behaves as a near-linear function of pressure in bulk water and of composition in LiCl-H2O. This allows for the alignment of pair entropy isotherms and allows for a simple mapping of pressure onto composition. Rosenfeld-scaling implies that pair entropy is semiquantitatively related to the transport properties. At a given temperature, equivalent state points in bulk H2O and LiCl-H2O (at 1 atm) are defined as those for which the pair entropy, diffusivity, and viscosity are nearly identical. The microscopic basis for this equivalence lies in the ability of both pressure and ions to convert the liquid phase into a pair-dominated fluid, as demonstrated by the O-O-O angular distribution within the first coordination shell of a water molecule. There are, however, sharp differences in local order and mechanisms for the breakdown of tetrahedral order by pressure and electrolytes. Increasing pressure increases orientational disorder within the first
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
Ku, C H; Tsai, W H
1999-01-01
A vision-based approach to obstacle avoidance for autonomous land vehicle (ALV) navigation in indoor environments is proposed. The approach is based on the use of a pattern recognition scheme, the quadratic classifier, to find collision-free paths in unknown indoor corridor environments. Obstacles treated in this study include the walls of the corridor and the objects that appear in the way of ALV navigation in the corridor. Detected obstacles as well as the two sides of the ALV body are considered as patterns. A systematic method for separating these patterns into two classes is proposed. The two pattern classes are used as the input data to design a quadratic classifier. Finally, the two-dimensional decision boundary of the classifier, which goes through the middle point between the two front vehicle wheels, is taken as a local collision-free path. This approach is implemented on a real ALV and successful navigations confirm the feasibility of the approach. PMID:18252315
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.
Error analysis of the quadratic nodal expansion method in slab geometry
Penland, R.C.; Turinsky, P.J.; Azmy, Y.Y.
1994-10-01
As part of an effort to develop an adaptive mesh refinement strategy for use in state-of-the-art nodal diffusion codes, the authors derive error bounds on the solution variables of the quadratic Nodal Expansion Method (NEM) in slab geometry. Closure of the system is obtained through flux discontinuity relationships and boundary conditions. In order to verify the analysis presented, the authors compare the quadratic NEM to the analytic solution of a test problem. The test problem for this investigation is a one-dimensional slab [0,20cm] with L{sup 2} = 6.495cm{sup 2} and D = 0.1429cm. The slab has a unit neutron source distributed uniformly throughout and zero flux boundary conditions. The analytic solution to this problem is used to compute the node-average fluxes over a variety of meshes, and these are used to compute the NEM maximum error on each mesh.
NASA Astrophysics Data System (ADS)
Rañada, Manuel F.
2015-04-01
The superintegrability of four Hamiltonians H r ˜ = λ H r , r = a, b, c, d, where Hr are known Hamiltonians and λ is a certain function defined on the configuration space and depended on a parameter κ, is studied. The new Hamiltonians, and the associated constants of motion Jri, i = 1, 2, 3, are continous functions of the parameter κ. The first part is concerned with separability and quadratic superintegrability (the integrals of motion are quadratic in the momenta) and the second part is devoted to the existence of higher-order superintegrability. The results obtained in the second part are related with the Tremblay-Turbiner-Winternitz and the Post-Winternitz systems.
NASA Astrophysics Data System (ADS)
Li, Run-Bing; Zhou, Lin; Wang, Jin; Zhan, Ming-Sheng
2009-04-01
We demonstrate a technique for directly measuring the quadratic Zeeman shift using stimulated Raman transitions. The quadratic Zeeman shift has been measured yielding Δν=1296.8±3.3 Hz/G 2 for magnetically insensitive sublevels ( 5S,F=2,mF=0→5S,F=3,mF=0) of 85Rb by compensating the magnetic field and cancelling the ac Stark shift. We also measured the cancellation ratio of the differential ac Stark shift due to the imbalanced Raman beams by using two pairs of Raman beams ( σ+, σ+) and it is 1:3.67 when the one-photon detuning is 1.5 GHz in the experiment.
Photonic EPR State from Quadratic Waveguide Array with Alternating Positive and Negative Couplings
NASA Astrophysics Data System (ADS)
Ying, Yang; Ping, Xu; Liang-Liang, Lu; Shi-Ning, Zhu
2016-02-01
We propose the generation of photonic EPR state from quadratic waveguide array. Both the propagation constant and the nonlinearity in the array are designed to possess a periodical modulation along the propagation direction. This ensures that the photon pairs can be generated efficiently through the quasi-phase-matching spontaneous parametric down conversion by holding the spatial EPR entanglement in the fashion of correlated position and anticorrelated momentum. The Schmidt number which denotes the degree of EPR entanglement is calculated and it can approach a high value when the number of illuminated waveguide channels and the length of the waveguide array are properly chosen. These results suggest the quadratic waveguide array as a compact platform for engineering photonic quantum states in a high-dimensional Hilbert space. Supported by the State Key Program for Basic Research in China under Grant No. 2012CB921802, the National Natural Science Foundations of China under Grant Nos. 91321312, 11321063 and 11422438
Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state
NASA Astrophysics Data System (ADS)
Sharov, G. S.
2016-06-01
Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H(z) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale rs(zd). Among the considered models the best value of χ2 is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.
Magneto-optical conductivity of Weyl semimetals with quadratic term in momentum
NASA Astrophysics Data System (ADS)
Shao, J. M.; Yang, G. W.
2016-02-01
Weyl semimetal is a three-dimensional Dirac material whose low energy dispersion is linear in momentum. Adding a quadratic (Schrödinger) term to the Weyl node breaks the original particle-hole symmetry and also breaks the mirror symmetry between the positive and negative Landau levels in present of magnetic field. This asymmetry splits the absorption line of the longitudinal magneto-optical conductivity into a two peaks structure. It also results in an oscillation pattern in the absorption part of the Hall conductivity. The two split peaks in Reσxx (or the positive and negative oscillation in Imσxy) just correspond to the absorptions of left-handed (σ-) and right-handed (σ+) polarization light, respectively. The split in Reσxx and the displacement between the absorption of σ+ and σ- are decided by the magnitude of the quadratic term and the magnetic field.
A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models
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 moderated structural equation method, (d) a fully Bayesian approach, and (e) marginal maximum likelihood estimation. Of the 5 estimation methods, it was found that overall the methods based on maximum likelihood estimation and the Bayesian approach performed best in terms of bias, root-mean-square error, standard error ratios, power, and Type I error control, although key differences were observed. Similarities as well as disparities among methods are highlight and general recommendations articulated. As a point of comparison, all 5 approaches were fit to a reparameterized version of the latent quadratic model to educational reading data. PMID:22429193
Anisotropic models with two fluids in linear and quadratic forms of f( T) gravitational theories
NASA Astrophysics Data System (ADS)
Nashed, Gamal G. L.
2015-06-01
Recent astronomical observations show that the universe may be anisotropic on large scales. The Union2 SnIa data hint that the universe has a preferred direction. If such a cosmological privileged axis indeed exists, one has to consider an anisotropic expanding universe, instead of the isotropic cosmological model. In this study, we apply the field equations of quadratic form of the modified teleparallel gravitational theories, f( T)= T+ ɛT 2, to anisotropic model. We assume two fluid components, the matter components have two equation of states (EoS). We study different equation of states for the linear case and show that there is no recombination era between the two fluids. For the quadratic one, we assume two equations of state corresponding to dark matter. In this model we obtain an inflation model and show that the values of the parameter, in the early universe, ɛ are depend on the sign of the cosmological constant.
Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory
NASA Technical Reports Server (NTRS)
Koppang, Paul; Leland, Robert
1996-01-01
Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.
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.
Model Reduction by Balanced Truncation of Linear Systems with a Quadratic Output
NASA Astrophysics Data System (ADS)
Van Beeumen, Roel; Meerbergen, Karl
2010-09-01
Balanced truncation is a widely used and appreciated projection-based model reduction technique for linear systems. This technique has the following two important properties: approximations by balanced truncation preserve the stability and the H∞-norm (the maximum of the frequency response) of the error system is bounded above by twice the sum of the neglected singular values. This paper tries to extend the framework of linear balanced truncation to systems with a quadratic output. For such systems, the controllability Gramian remains the same. The observability Gramian is computed from a linear system with multiple outputs that is derived from the quadratic output of the original system. We give a numerical example for a large-scale system arising from structural analysis.
Feng, Yong-E
2016-06-01
Malaria parasite secretes various proteins in infected red blood cell for its growth and survival. Thus identification of these secretory proteins is important for developing vaccine or drug against malaria. In this study, the modified method of quadratic discriminant analysis is presented for predicting the secretory proteins. Firstly, 20 amino acids are divided into five types according to the physical and chemical characteristics of amino acids. Then, we used five types of amino acids compositions as inputs of the modified quadratic discriminant algorithm. Finally, the best prediction performance is obtained by using 20 amino acid compositions, the sensitivity of 96 %, the specificity of 92 % with 0.88 of Mathew's correlation coefficient in fivefold cross-validation test. The results are also compared with those of existing prediction methods. The compared results shown our method are prominent in the prediction of secretory proteins. PMID:26286010
Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching
NASA Astrophysics Data System (ADS)
Janssen, Lukas; Herbut, Igor F.
2015-07-01
We construct and discuss the field theory for tensorial nematic order parameter coupled to gapless four-component fermions at the quadratic band touching point in three (spatial) dimensions. Within a properly formulated epsilon-expansion this theory is found to have a quantum critical point, which describes the (presumably continuous) transition from the semimetal into a (nematic) Mott insulator. The latter phase breaks the rotational, but not the time-reversal, symmetry and may be relevant to materials such as gray tin or mercury telluride at low temperatures. The critical point represents a simple quantum analog of the familiar classical isotropic-to-nematic transition in liquid crystals. The properties and the consequences of this quantum critical point are discussed. Its existence supports the scenario of the "fixed-point collision," according to which three-dimensional Fermi systems with quadratic band touching and long-range Coulomb interactions are unstable towards the gapped nematic ground state at low temperatures.
The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter
NASA Technical Reports Server (NTRS)
Townsend, Barbara K.
1987-01-01
A control-system design method, quadratic optimal cooperative control synthesis (CCS), is applied to the design of a stability and control augmentation system (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design method, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and linear quadratic regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.
Remark on the subtractive renormalization of the quadratically divergent scalar mass
Fujikawa, Kazuo
2011-05-15
The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We reexamine some technical aspects of the subtractive renormalization, in particular, the mass-independent renormalization of massive {lambda}{phi}{sup 4} theory with higher derivative regularization. We then discuss an unconventional scheme to introduce the notion of renormalization point {mu} to the subtractive renormalization in a theory defined by a large fixed cutoff M. The resulting renormalization group equation generally becomes inhomogeneous, but it is transformed to be homogeneous. The renormalized scalar mass consists of two components in this scheme, one with the ordinary anomalous dimension and the other which is proportional to the renormalization scale {mu}. This scheme interpolates between the theory defined by dimensional regularization and the theory with unsubtracted quadratic divergences.
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 = δ 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.