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.
Tadepalli, Srinivas C; Erdemir, Ahmet; Cavanagh, Peter R
2011-08-11
Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.
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.
NASA Technical Reports Server (NTRS)
Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.
1992-01-01
A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.
Quadratic finite elements and incompressible viscous flows.
Dohrmann, Clark R.; Gartling, David K.
2005-01-01
Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.
Using quadratic simplicial elements for hierarchical approximation and visualization
NASA Astrophysics Data System (ADS)
Wiley, David F.; Childs, Henry R.; Hamann, Bernd; Joy, Kenneth I.; Max, Nelson
2002-03-01
Best quadratic simplicial spline approximations can be computed, using quadratic Bernstein-Bezier basis functions, by identifying and bisecting simplicial elements with largest errors. Our method begins with an initial triangulation of the domain; a best quadratic spline approximation is computed; errors are computed for all simplices; and simplices of maximal error are subdivided. This process is repeated until a user-specified global error tolerance is met. The initial approximations for the unit square and cube are given by two quadratic triangles and five quadratic tetrahedra, respectively. Our more complex triangulation and approximation method that respects field discontinuities and geometrical features allows us to better approximate data. Data is visualized by using the hierarchy of increasingly better quadratic approximations generated by this process. Many visualization problems arise for quadratic elements. First tessellating quadratic elements with smaller linear ones and then rendering the smaller linear elements is one way to visualize quadratic elements. Our results show a significant reduction in the number of simplices required to approximate data sets when using quadratic elements as compared to using linear elements.
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.
Hollaus, K; Weiss, B; Magele, Ch; Hutten, H
2004-02-01
The acceleration of the solution of the quasi-static electric field problem considering anisotropic complex conductivity simulated by tetrahedral finite elements of first order is investigated by geometric multigrid.
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.
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.
Quadratic solid-shell elements for nonlinear structural analysis and sheet metal forming simulation
NASA Astrophysics Data System (ADS)
Wang, Peng; Chalal, Hocine; Abed-Meraim, Farid
2017-01-01
In this paper, two quadratic solid-shell (SHB) elements are proposed for the three-dimensional modeling of thin structures. These consist of a 20-node hexahedral solid-shell element, denoted SHB20, and its 15-node prismatic counterpart, denoted SHB15. The formulation of these elements is extended in this work to include geometric and material nonlinearities, for application to problems involving large displacements and rotations as well as plasticity. For this purpose, the SHB elements are coupled with large-strain anisotropic elasto-plastic constitutive equations for metallic materials. Although based on a purely three-dimensional approach, several modifications are introduced in the formulation of these elements to provide them with interesting shell features. In particular, a special direction is chosen to represent the thickness, along which a user-defined number of integration points are located. Furthermore, for efficiency requirements and for alleviating locking phenomena, an in-plane reduced-integration scheme is adopted. The resulting formulations are implemented into the finite element software ABAQUS/Standard and, to assess their performance, a variety of nonlinear benchmark problems are investigated. Attention is then focused on the simulation of various complex sheet metal forming processes, involving large strain, anisotropic plasticity, and double-sided contact. From all simulation results, it appears that the SHB elements represent an interesting alternative to traditional shell and solid elements, due to their versatility and capability of accurately modeling selective nonlinear benchmark problems as well as complex sheet metal forming processes.
NASA Astrophysics Data System (ADS)
Artés, Joan C.; Oliveira, Regilene D. S.; Rezende, Alex C.
The study of planar quadratic differential systems is very important not only because they appear in many areas of applied mathematics but due to their richness in structure, stability and questions concerning limit cycles, for example. Even though many papers have been written on this class of 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. In this article, we make a global study of the family QTS¯ of all real quadratic polynomial differential systems which have a finite semi-elemental triple saddle (triple saddle with exactly one zero eigenvalue). This family modulo the action of the affine group and time homotheties is three-dimensional and we give its bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of this normal form. This bifurcation diagram yields 27 phase portraits for systems in QTS¯ counting phase portraits with and without limit cycles. Algebraic invariants are used to construct the bifurcation set and we present the phase portraits on the Poincaré disk. The bifurcation set is not just algebraic due to the presence of a surface found numerically, whose points correspond to connections of separatrices.
NASA Astrophysics Data System (ADS)
Stühler, Sven; Fleissner, Florian; Eberhard, Peter
2016-11-01
We present an extended particle model for the discrete element method that on the one hand is tetrahedral in shape and on the other hand is capable to describe deformations. The deformations of the tetrahedral particles require a framework to interrelate the particle strains and resulting stresses. Hence, adaptations from the finite element method were used. This allows to link the two methods and to adequately describe material and simulation parameters separately in each scope. Due to the complexity arising of the non-spherical tetrahedral geometry, all possible contact combinations of vertices, edges, and surfaces must be considered by the used contact detection algorithm. The deformations of the particles make the contact evaluation even more challenging. Therefore, a robust contact detection algorithm based on an optimization approach that exploits temporal coherence is presented. This algorithm is suitable for general {R}^{{n}} simplices. An evaluation of the robustness of this algorithm is performed using a numerical example. In order to create complex geometries, bonds between these deformable particles are introduced. This coupling via the tetrahedra faces allows the simulation bonding of deformable bodies composed of several particles. Numerical examples are presented and validated with results that are obtained by the same simulation setup modeled with the finite element method. The intention of using these bonds is to be able to model fracture and material failure. Therefore, the bonds between the particles are not lasting and feature a release mechanism based on a predefined criterion.
NASA Astrophysics Data System (ADS)
Ptaszny, Jacek
2015-09-01
In this work, a fast multipole boundary element method for 3D elasticity problem was developed by the application of the fast multipole algorithm and isoparametric 8-node boundary elements with quadratic shape functions. The problem is described by the boundary integral equation involving the Kelvin solutions. In order to keep the numerical integration error on appropriate level, an adaptive method with subdivision of boundary elements into subelements, described in the literature, was applied. An extension of the neighbour list of boundary element clusters, corresponding to near-field computations, was proposed in order to reduce the truncation error of expansions in problems with high stress concentration. Efficiency of the method is illustrated by numerical examples including a solid with single spherical cavity, solids with two interacting spherical cavities, and numerical homogenization of solids with cubic arrangement of spherical cavities. All results agree with analytical models available in the literature. The examples show that the method can be applied to the analysis of porous structures.
Analysis of periodic 3D viscous flows using a quadratic discrete Galerkin boundary element method
NASA Astrophysics Data System (ADS)
Chan, Chiu Y.; Beris, Antony N.; Advani, Suresh G.
1994-05-01
A discrete Galerkin boundary element technique with a quadratic approximation of the variables was developed to simulate the three-dimensional (3D) viscous flow established in periodic assemblages of particles in suspensions and within a periodic porous medium. The Batchelor's unit-cell approach is used. The Galerkin formulation effectively handles the discontinuity in the traction arising in flow boundaries with edges or corners, such as the unit cell in this case. For an ellipsoidal dilute suspension over the range of aspect ratio studied (1 to 54), the numerical solutions of the rotational velocity of the particles and the viscosity correction were found to agree with the analytic values within 0.2% and 2% respectively, even with coarse meshes. In a suspension of cylindrical particles the calculated period of rotation agreed with the experimental data. However, Burgers' predictions for the correction to the suspension viscosity were found to be 30% too low and therefore the concept of the equivalent ellipsoidal ratio is judged to be inadequate. For pressure-driven flow through a fixed bed of fibers, the prediction on the permeability was shown to deviate by as much as 10% from the value calculated based on approximate permeability additivity rules using the corresponding values for planar flow past a periodic array of parallel cylinders. These applications show the versatility of the technique for studying viscous flows in complicated 3D geometries.
NASA Astrophysics Data System (ADS)
Usui, Yoshiya; Ogawa, Yasuo; Aizawa, Koki; Kanda, Wataru; Hashimoto, Takeshi; Koyama, Takao; Yamaya, Yusuke; Kagiyama, Tsuneomi
2017-03-01
Asama Volcano is an andesitic composite volcano and one of the most active volcanoes in Japan. In order to reveal electrical resistivity structure beneath the volcano accurately, we performed a 3-D inversion of dense magnetotelluric survey data. In order to prevent misinterpretation of the subsurface resistivity due to the steep topography around Asama Volcano, we used an unstructured tetrahedral mesh to represent the topography. Furthermore, we reduced the calculation time by transforming the inverse problem from the model space into the data space. Comparison of the new data-space method to the original model-space method showed that the calculation time required to update the model parameters was reduced as a result of the transformation, whereas the resistivity structure obtained remained unchanged. In the subsurface resistivity structure around Asama Volcano that was estimated from the inversion, resistive bodies were discovered to be located under the old eruption centres. In particular, under the 24 ka collapse caldera to the west of the presently active crater, a spherical resistive body was found to exist in isolation. In addition, there was a widespread conductive layer below the resistive surface layer. By comparison with previous hydrological and geochemical studies, the conductive layer was interpreted as being a high-water-content layer and an overlying layer rich in altered clay minerals. Because the western part of the volcanic conduit was considered to be the resistive area, which is inferred to consist of unfractured rocks with lower permeability than their surroundings, it would appear that the area obstructs the westward flow of the hydrothermal fluid beneath the summit, thereby contributing to higher concentrations of SO42- and Cl- in the spring water at the northern and eastern feet as well as the uneven location of a diffuse CO2 anomaly.
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.
2016-10-01
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.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; Rossi, Simone
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less
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…
Uniformity in Tetrahedral Hohlraums
NASA Astrophysics Data System (ADS)
Craxton, R. S.; Schnittman, J. D.; Pollaine, S. M.
1996-11-01
Tetrahedral hohlraums, i.e., spherical hohlraums with four laser entrance holes (LEH's), offer an alternative means of obtaining good time-independent capsule irradiation uniformity. Since the laser spots are spread fairly uniformly over the hohlraum wall, time-dependent uniformity swings are minimized. Using the 3-D view-factor code BUTTERCUP we have found, for both OMEGA and the NIF, that the uniformity is typically ~2% rms at all times, mainly in the Y_32 mode, but can be reduced to ~1% by independently varying the power in each beam. We have investigated the sensitivity of tetrahedral hohlraums to errors in beam-energy balance and pointing, and we have examined how large the LEH's must be to allow the beams to go through without refraction or absorption. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC03-92SF19460. *Also Lawrence Livermore National Laboratory.
Tetrahedral and Hexahedral Mesh Adaptation for CFD Problems
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger C.; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically without mesh quality problems. Furthermore, hexahedral meshes yield more accurate solutions than their tetrahedral counterparts for the same number of edges. Both the tetrahedral and hexahedral mesh adaptation procedures use edge-based data structures that facilitate efficient subdivision by allowing individual edges to be marked for refinement or coarsening. However, for hexahedral adaptation, pyramids, prisms, and tetrahedra are used as buffer elements between refined and unrefined regions to eliminate hanging vertices. Computational results indicate that the hexahedral adaptation procedure is a viable alternative to adaptive tetrahedral schemes.
Acoustic Detection and Tracking of a Class I UAS with a Small Tetrahedral Microphone Array
2014-09-01
Acoustic Detection and Tracking of a Class I UAS with a Small Tetrahedral Microphone Array by Minas Benyamin and Geoffrey H Goldman ARL...20783-1138 ARL-TR-7086 September 2014 Acoustic Detection and Tracking of a Class I UAS with a Small Tetrahedral Microphone Array Minas...with a Small Tetrahedral Microphone Array 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Minas Benyamin and
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…
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…
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.
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.
Interactive isosurface ray tracing of time-varying tetrahedral volumes.
Wald, Ingo; Friedrich, Heiko; Knoll, Aaron; Hansen, Charles D
2007-01-01
We describe a system for interactively rendering isosurfaces of tetrahedral finite-element scalar fields using coherent ray tracing techniques on the CPU. By employing state-of-the art methods in polygonal ray tracing, namely aggressive packet/frustum traversal of a bounding volume hierarchy, we can accomodate large and time-varying unstructured data. In conjunction with this efficiency structure, we introduce a novel technique for intersecting ray packets with tetrahedral primitives. Ray tracing is flexible, allowing for dynamic changes in isovalue and time step, visualization of multiple isosurfaces, shadows, and depth-peeling transparency effects. The resulting system offers the intuitive simplicity of isosurfacing, guaranteed-correct visual results, and ultimately a scalable, dynamic and consistently interactive solution for visualizing unstructured volumes.
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...
Octahedrality versus tetrahedrality in stoichiometric ceria nanoparticles.
Migani, Annapaola; Neyman, Konstantin M; Bromley, Stefan T
2012-05-04
We predict that tetrahedral Ce(n)O(2n) nanoparticles <2 nm in size become more stable than those experimentally observed at larger sizes with truncated octahedral morphologies, based on global optimisation and density functional calculations.
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.
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.
List-mode image reconstruction for positron emission tomography using tetrahedral voxels
NASA Astrophysics Data System (ADS)
Gillam, John E.; Angelis, Georgios I.; Meikle, Steven R.
2016-09-01
Image space decomposition based on tetrahedral voxels are interesting candidates for use in emission tomography. Tetrahedral voxels provide many of the advantages of point clouds with irregular spacing, such as being intrinsically multi-resolution, yet they also serve as a volumetric partition of the image space and so are comparable to more standard cubic voxels. Additionally, non-rigid displacement fields can be applied to the tetrahedral mesh in a straight-forward manner. So far studies incorporating tetrahedral decomposition of the image space have concentrated on pre-calculated, node-based, system matrix elements which reduces the flexibility of the tetrahedral approach and the capacity to accurately define regions of interest. Here, a list-mode on-the-fly calculation of the system matrix elements is described using a tetrahedral decomposition of the image space and volumetric elements—voxels. The algorithm is demonstrated in the context of awake animal PET which may require both rigid and non-rigid motion compensation, as well as quantification within small regions of the brain. This approach allows accurate, event based, motion compensation including non-rigid deformations.
Quadratic spline subroutine package
Rasmussen, Lowell A.
1982-01-01
A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)
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]…
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.
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…
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
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
Methods for prismatic/tetrahedral grid generation and adaptation
NASA Technical Reports Server (NTRS)
Kallinderis, Y.
1995-01-01
The present work involves generation of hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is a method for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A High Speed Civil Transport (HSCT) type of aircraft geometry is considered. The generated hybrid grid required only 170 K tetrahedra instead of an estimated two million had a tetrahedral mesh been used in the prisms region as well. A solution adaptive scheme for viscous computations on hybrid grids is also presented. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples 3-D, isotropic division of tetrahedra and 2-D, directional division of prisms.
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.
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.
Measure of disorder in tetrahedrally bonded semiconductors
Sundari, S. Tripura; Raghavan, G.
2005-06-13
A measure of crystalline order in tetrahedrally bonded semiconductors is proposed based on optical response. This measure is obtained from the <111> critical point structure in the dielectric spectra. This descriptor is sensitive to the nature and extent of disorder in specimens and distinguishes differences in medium and short-order present in amorphous materials. Application to Ar{sup +}-irradiated Si specimens yields the threshold amorphization dose and this technique is sensitive to structural changes which occur as a function of irradiation fluence both above and beyond the amorphization threshhold. Systematic variations are also obtained in hydrogenated amorphous-Si. The general validity of the method is indicated.
A tetrahedral mesh generation approach for 3D marine controlled-source electromagnetic modeling
NASA Astrophysics Data System (ADS)
Um, Evan Schankee; Kim, Seung-Sep; Fu, Haohuan
2017-03-01
3D finite-element (FE) mesh generation is a major hurdle for marine controlled-source electromagnetic (CSEM) modeling. In this paper, we present a FE discretization operator (FEDO) that automatically converts a 3D finite-difference (FD) model into reliable and efficient tetrahedral FE meshes for CSEM modeling. FEDO sets up wireframes of a background seabed model that precisely honors the seafloor topography. The wireframes are then partitioned into multiple regions. Outer regions of the wireframes are discretized with coarse tetrahedral elements whose maximum size is as large as a skin depth of the regions. We demonstrate that such coarse meshes can produce accurate FE solutions because numerical dispersion errors of tetrahedral meshes do not accumulate but oscillates. In contrast, central regions of the wireframes are discretized with fine tetrahedral elements to describe complex geology in detail. The conductivity distribution is mapped from FD to FE meshes in a volume-averaged sense. To avoid excessive mesh refinement around receivers, we introduce an effective receiver size. Major advantages of FEDO are summarized as follow. First, FEDO automatically generates reliable and economic tetrahedral FE meshes without adaptive meshing or interactive CAD workflows. Second, FEDO produces FE meshes that precisely honor the boundaries of the seafloor topography. Third, FEDO derives multiple sets of FE meshes from a given FD model. Each FE mesh is optimized for a different set of sources and receivers and is fed to a subgroup of processors on a parallel computer. This divide and conquer approach improves the parallel scalability of the FE solution. Both accuracy and effectiveness of FEDO are demonstrated with various CSEM examples.
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…
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.
Use of quadratic components for buckling calculations
Dohrmann, C.R.; Segalman, D.J.
1996-12-31
A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.
A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions
Jian Jinbao Hu Qingjie; Tang Chunming; Zheng Haiyan
2007-12-15
In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported.
Quadratic Generalized Scale Invariance
NASA Astrophysics Data System (ADS)
Lovejoy, S.; Schertzer, D.; Addor, J. B.
Nearly twenty years ago, two of us argued that in order to account for the scaling strat- ification of the atmosphere, that an anisotropic "unified scaling model" of the atmo- sphere was required with elliptical dimension 23/9=2.555... "in between" the standard 3-D (small scale) and 2-D large scale model. This model was based on the formal- ism of generalized scale invariance (GSI). Physically, GSI is justified by arguing that various conserved fluxes (energy, buoyancy force variance etc.) should define the ap- propriate notion of scale. In a recent large scale satellite cloud image analysis, we directly confirmed this model by studying the isotropic (angle averaged) horizontal cloud statistics. Mathematically, GSI is based on a a group of scale changing opera- tors and their generators but to date, both analyses (primarily of cloud images) and nu- merical (multifractal) simulations, have been limited to the special case of linear GSI. This has shown that cloud texture can plausibly be associated with local linearizations. However realistic morphologies involve spatially avarying textures; the full non linear GSI is clearly necessary. In this talk, we first show that the observed angle averaged (multi)scaling statistics only give a realtively weak constraint on the nonlinear gner- ator: that the latter can be expressed by self-similar (isotropic) part, and a deviatoric part described (in two dimensions) by an arbitrary scalar potential which contains all the information about the cloud morphology. We then show (using a theorem due to Poincaré) how to reduce nonlinear GSI to linear GSI plus a nonlinear coordinate trans- formation numerically, using this to take multifractal GSI modelling to the next level of approximation: quadratic GSI. We show many examples of the coresponding simu- lations which include transitions from various morphologies (including cyclones) and we discuss the results in relation to satellite cloud images.
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
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.
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.
Computer model of tetrahedral amorphous diamond
NASA Astrophysics Data System (ADS)
Djordjević, B. R.; Thorpe, M. F.; Wooten, F.
1995-08-01
We computer generate a model of amorphous diamond using the Wooten-Weaire method, with fourfold coordination everywhere. We investigate two models: one where four-membered rings are allowed and the other where the four-membered rings are forbidden; each model consisting of 4096 atoms. Starting from the perfect diamond crystalline structure, we first randomize the structure by introducing disorder through random bond switches at a sufficiently high temperature. Subsequently, the temperature is reduced in stages, and the topological and geometrical relaxation of the structure takes place using the Keating potential. After a long annealing process, a random network of comparatively low energy is obtained. We calculate the pair distribution function, mean bond angle, rms angular deviation, rms bond length, rms bond-length deviation, and ring statistics for the final relaxed structures. We minimize the total strain energy by adjusting the density of the sample. We compare our results with similar computer-generated models for amorphous silicon, and with experimental measurement of the structure factor for (predominantly tetrahedral) amorphous carbon.
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.
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.
Hoop/column and tetrahedral truss electromagnetic tests
NASA Technical Reports Server (NTRS)
Bailey, M. C.
1987-01-01
The distortion of antennas was measured with a metric camera system at discrete target locations on the surface. Given are surface distortion for hoop column reflector antennas, for tetrahedral truss reflector antennas, and distortion contours for the tetrahedral truss reflector. Radiation patterns at 2.27-GHz, 4.26-GHz, 7.73-GHz and 11.6-GHz are given for the hoop column antenna. Also given are radiation patterns at 4.26-GHz and 7.73-GHz for the tetrahedral truss antenna.
Transport of phase space densities through tetrahedral meshes using discrete flow mapping
NASA Astrophysics Data System (ADS)
Bajars, Janis; Chappell, David J.; Søndergaard, Niels; Tanner, Gregor
2017-01-01
Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximation of a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space.
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.
Interactive point-based rendering of higher-order tetrahedral data.
Zhou, Yuan; Garland, Michael
2006-01-01
Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, such solutions may often be expressed using non-linear basis functions. Certain solution techniques, such as discontinuous Galerkin methods, may even produce non-conforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to non-conforming meshes. We introduce a point-based visualization system for interactive rendering of large, potentially non-conforming, tetrahedral meshes. We propose methods for adaptively sampling points from non-linear solution data and for decimating points at run time to fit GPU memory limits. Because these are streaming processes, memory consumption is independent of the input size. We also present an order-independent point rendering method that can efficiently render volumes on the order of 20 million tetrahedra at interactive rates.
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.
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.
Analytical and Photogrammetric Characterization of a Planar Tetrahedral Truss
NASA Technical Reports Server (NTRS)
Wu, K. Chauncey; Adams, Richard R.; Rhodes, Marvin D.
1990-01-01
Future space science missions are likely to require near-optical quality reflectors which are supported by a stiff truss structure. This support truss should conform closely with its intended shape to minimize its contribution to the overall surface error of the reflector. The current investigation was conducted to evaluate the planar surface accuracy of a regular tetrahedral truss structure by comparing the results of predicted and measured node locations. The truss is a 2-ring hexagonal structure composed of 102 equal-length truss members. Each truss member is nominally 2 meters in length between node centers and is comprised of a graphite/epoxy tube with aluminum nodes and joints. The axial stiffness and the length variation of the truss components were determined experimentally and incorporated into a static finite element analysis of the truss. From this analysis, the root mean square (RMS) surface error of the truss was predicted to be 0.11 mm (0004 in). Photogrammetry tests were performed on the assembled truss to measure the normal displacements of the upper surface nodes and to determine if the truss would maintain its intended shape when subjected to repeated assembly. Considering the variation in the truss component lengths, the measures rms error of 0.14 mm (0.006 in) in the assembled truss is relatively small. The test results also indicate that a repeatable truss surface is achievable. Several potential sources of error were identified and discussed.
Capozziello, Salvatore; Lattanzi, Alessandra
2006-08-01
On the basis of empirical Fischer projections, we develop an algebraic approach to the central molecular chirality of tetrahedral molecules. The elements of such an algebra are obtained from the 24 projections which a single chiral tetrahedron can generate in S and R absolute configurations. They constitute a matrix representation of the O4 orthogonal group. According to this representation, given a molecule with n chiral centres, it is possible to define an "index of chirality chi identical with {n, p}", where n is the number of stereogenic centres of the molecule and p the number of permutations observed under rotations and superimpositions of the tetrahedral molecule to its mirror image. The chirality index not only assigns the global chirality of a given tetrahedral chain, but indicates also a way to predict the same property for new compounds, which can be built up consistently.
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.
Low-energy tetrahedral polymorphs of carbon, silicon, and germanium
NASA Astrophysics Data System (ADS)
Mujica, Andrés; Pickard, Chris J.; Needs, Richard J.
2015-06-01
Searches for low-energy tetrahedral polymorphs of carbon and silicon have been performed using density functional theory computations and the ab initio random structure searching approach. Several of the hypothetical phases obtained in our searches have enthalpies that are lower or comparable to those of other polymorphs of group 14 elements that have either been experimentally synthesized or recently proposed as the structure of unknown phases obtained in experiments, and should thus be considered as particularly interesting candidates. A structure of P b a m symmetry with 24 atoms in the unit cell was found to be a low-energy, low-density metastable polymorph in carbon, silicon, and germanium. In silicon, P b a m is found to have a direct band gap at the zone center with an estimated value of 1.4 eV, which suggests applications as a photovoltaic material. We have also found a low-energy chiral framework structure of P 41212 symmetry with 20 atoms per cell containing fivefold spirals of atoms, whose projected topology is that of the so-called Cairo-type two-dimensional pentagonal tiling. We suggest that P 41212 is a likely candidate for the structure of the unknown phase XIII of silicon. We discuss P b a m and P 41212 in detail, contrasting their energetics and structures with those of other group 14 elements, particularly the recently proposed P 42/n c m structure, for which we also provide a detailed interpretation as a network of tilted diamondlike tetrahedra.
Concretising Factorisation of Quadratic Expressions
ERIC Educational Resources Information Center
Hoong, Leong Yew; Fwe, Yap Sook; Yvonne, Teo Mei Lin; Subramaniam, Thilagam d/o; Zaini, Irni Karen Bte Mohd; Chiew, Quek Eng; Karen, Tan Kang Ling
2010-01-01
The way quadratic factorisation was usually taught to students in Bukit View Secondary was through the familiar "cross-method." However, some teachers felt that a significant number of students could not use the method effectively even after careful demonstration through repeated examples. In addition, many secondary mathematics teachers…
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.
Stabilized Finite Elements in FUN3D
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Newman, James C.; Karman, Steve L.
2017-01-01
A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.
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.
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.
Properties of surjective real quadratic maps
NASA Astrophysics Data System (ADS)
Arutyunov, A. V.; Zhukovskiy, S. E.
2016-09-01
The properties of surjective real quadratic maps are investigated. Sufficient conditions for the property of surjectivity to be stable under various perturbations are obtained. Examples of surjective quadratic maps whose surjectivity breaks down after an arbitrarily small perturbation are constructed. Sufficient conditions for quadratic maps to have nontrivial zeros are obtained. For a smooth even map in a neighbourhood of the origin an inverse function theorem in terms of the degree of the corresponding quadratic map is obtained. A canonical form of surjective quadratic maps from {R}^3 to {R}^3 is constructed. Bibliography: 27 titles.
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.
Optimization with quadratic support functions in nonconvex smooth optimization
NASA Astrophysics Data System (ADS)
Khamisov, O. V.
2016-10-01
Problem of global minimization of twice continuously differentiable function with Lipschitz second derivatives over a polytope is considered. We suggest a branch and bound method with polytopes as partition elements. Due to the Lipschitz property of the objective function we can construct a quadratic support minorant at each point of the feasible set. Global minimum of of this minorant provides a lower bound of the objective over given partition subset. The main advantage of the suggested method consists in the following. First quadratic minorants usually are nonconvex and we have to solve auxiliary global optimization problem. This problem is reduced to a mixed 0-1 linear programming problem and can be solved by an advanced 0-1 solver. Then we show that the quadratic minorants are getting convex as soon as partition elements are getting smaller in diameter. Hence, at the final steps of the branch and bound method we solve convex auxiliary quadratic problems. Therefore, the method accelerates when we are close to the global minimum of the initial problem.
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
Indirect-drive radiation uniformity in tetrahedral hohlraums
Schnittman, J.D.; Craxton, R.S.
1996-10-01
Tetrahedral hohlraums, by which are understood spherical hohlraums with four laser entrance holes (LEH{close_quote}s) placed at or near the vertices of a tetrahedron, are proposed for the National Ignition Facility (NIF) [J. Lindl, Phys. Plasmas {bold 2}, 3933 (1995)] and the upgraded OMEGA laser [T. R. Boehly {ital et} {ital al}., Rev. Sci. Instrum. {bold 66}, 508 (1995)]. All but four of the 48 NIF beams can irradiate a tetrahedral hohlraum, assuming that 72 beam ports are provided to accommodate direct drive. On OMEGA, the target chamber provides an exact tetrahedral symmetry, permitting the irradiation of tetrahedral hohlraums with all 60 beams. Hohlraum designs are optimized using a new three-dimensional view-factor program called Buttercup, which traces all beam paths through the hohlraum and calculates the radiation flux on the capsule for different values of the albedo. Good irradiation uniformity ({approximately}2{percent} rms) can be obtained on the capsule at all times during the implosion, even with identical beam temporal histories, in contrast to the case of cylindrical hohlraums where {open_quote}{open_quote}beam phasing{close_quote}{close_quote} is needed. {copyright} {ital 1996 American Institute of Physics.}
Indirect-drive radiation uniformity in tetrahedral hohlraums
NASA Astrophysics Data System (ADS)
Schnittman, J. D.; Craxton, R. S.
1996-10-01
Tetrahedral hohlraums, by which are understood spherical hohlraums with four laser entrance holes (LEH's) placed at or near the vertices of a tetrahedron, are proposed for the National Ignition Facility (NIF) [J. Lindl, Phys. Plasmas 2, 3933 (1995)] and the upgraded OMEGA laser [T. R. Boehly et al., Rev. Sci. Instrum. 66, 508 (1995)]. All but four of the 48 NIF beams can irradiate a tetrahedral hohlraum, assuming that 72 beam ports are provided to accommodate direct drive. On OMEGA, the target chamber provides an exact tetrahedral symmetry, permitting the irradiation of tetrahedral hohlraums with all 60 beams. Hohlraum designs are optimized using a new three-dimensional view-factor program called Buttercup, which traces all beam paths through the hohlraum and calculates the radiation flux on the capsule for different values of the albedo. Good irradiation uniformity (˜2% rms) can be obtained on the capsule at all times during the implosion, even with identical beam temporal histories, in contrast to the case of cylindrical hohlraums where ``beam phasing'' is needed.
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…
Pegg, Elise C; Gill, Harinderjit S
2016-09-06
A new software tool to assign the material properties of bone to an ABAQUS finite element mesh was created and compared with Bonemat, a similar tool originally designed to work with Ansys finite element models. Our software tool (py_bonemat_abaqus) was written in Python, which is the chosen scripting language for ABAQUS. The purpose of this study was to compare the software packages in terms of the material assignment calculation and processing speed. Three element types were compared (linear hexahedral (C3D8), linear tetrahedral (C3D4) and quadratic tetrahedral elements (C3D10)), both individually and as part of a mesh. Comparisons were made using a CT scan of a hemi-pelvis as a test case. A small difference, of -0.05kPa on average, was found between Bonemat version 3.1 (the current version) and our Python package. Errors were found in the previous release of Bonemat (version 3.0 downloaded from www.biomedtown.org) during calculation of the quadratic tetrahedron Jacobian, and conversion of the apparent density to modulus when integrating over the Young׳s modulus field. These issues caused up to 2GPa error in the modulus assignment. For these reasons, we recommend users upgrade to the most recent release of Bonemat. Processing speeds were assessed for the three different element types. Our Python package took significantly longer (110s on average) to perform the calculations compared with the Bonemat software (10s). Nevertheless, the workflow advantages of the package and added functionality makes 'py_bonemat_abaqus' a useful tool for ABAQUS users.
Is there tetrahedral Fe/sup 3 +/ in biotite
Dyar, M.D.; Burns, R.G.; Rossman, G.R.
1985-01-01
Tetrahedral Fe/sup 3 +/ has been observed in Moessbauer and optical studies of Al-deficient micas, including synthetic ferri-annites, annites from banded iron formations and phlogopites from deep-seated rocks. In such samples Si + Al < 4 (per 11 0), and 0.10-0.67 formula units of Fe/sup 3 +/ fill the tetrahedral sites in the structure. The authors also discovered several Al-rich biotites which contain small amounts of Fe/sub tet//sup 3 +/ based on their spectroscopic data. Fe/sup 3 +/ appears to be displacing some of the Al/sup 3 +/ into the octahedral site. Examination of the literature shows nine other cases of Fe/sub tet//sup 3 +/ in trioctahedral 1M micas where Si + Al > 4. Traditionally, the effects of cation substitutions on the physical properties have been considered to be dependent on the size difference between the octahedral and tetrahedral layers of the structure. Much attention has focused on the substitution of the larger Fe/sup 2 +/ for Mg/sup 2 +/ and other cations in the octahedra of relatively simple synthetic compositions. However, in the natural micas studied here high fO/sub 2/ and high proportions of Al/sup 3 +/, Fe/sup 3 +/, and Ti/sup 4 +/ in the compositions raise the issue of structural readjustments based on substitution of small cations into the structure. In our samples, the average octahedral cation size is 0.67 A. If many small octahedral cations are incorporated into the structure during biotite formation, considerable octahedral flattening and (in response) tetrahedral rotation must occur to stabilize the mica. Perhaps the high degree of tetrahedral rotation allows accommodation of the larger Fe/sub tet//sup 3 +/ instead of Al/sub tet//sup 3 +/.
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
The Random Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Paul, Gerald; Shao, Jia; Stanley, H. Eugene
2011-11-01
The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.
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
NASA Technical Reports Server (NTRS)
Mikulas, M. M., Jr.; Bush, H. G.; Card, M. F.
1977-01-01
Physical characteristics of large skeletal frameworks for space applications are investigated by analyzing one concept: the tetrahedral truss, which is idealized as a sandwich plate with isotropic faces. Appropriate analytical relations are presented in terms of the truss column element properties which for calculations were taken as slender graphite/epoxy tubes. Column loads, resulting from gravity gradient control and orbital transfer, are found to be small for the class structure investigated. Fundamental frequencies of large truss structures are shown to be an order of magnitude lower than large earth based structures. Permissible loads are shown to result in small lateral deflections of the truss due to low-strain at Euler buckling of the slender graphite/epoxy truss column elements. Lateral thermal deflections are found to be a fraction of the truss depth using graphite/epoxy columns.
Coarse-grained theory of a realistic tetrahedral liquid model
NASA Astrophysics Data System (ADS)
Procaccia, I.; Regev, I.
2012-02-01
Tetrahedral liquids such as water and silica-melt show unusual thermodynamic behavior such as a density maximum and an increase in specific heat when cooled to low temperatures. Previous work had shown that Monte Carlo and mean-field solutions of a lattice model can exhibit these anomalous properties with or without a phase transition, depending on the values of the different terms in the Hamiltonian. Here we use a somewhat different approach, where we start from a very popular empirical model of tetrahedral liquids —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.
NASA Astrophysics Data System (ADS)
Venkatachari, Balaji Shankar; Chang, Chau-Lyan
2016-11-01
The focus of this study is scale-resolving simulations of the canonical normal shock- isotropic turbulence interaction using unstructured tetrahedral meshes and the space-time conservation element solution element (CESE) method. Despite decades of development in unstructured mesh methods and its potential benefits of ease of mesh generation around complex geometries and mesh adaptation, direct numerical or large-eddy simulations of turbulent flows are predominantly carried out using structured hexahedral meshes. This is due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for unstructured meshes that can resolve multiple physical scales and flow discontinuities simultaneously. The 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 accurately simulate turbulent flows using tetrahedral meshes. As part of the study, various regimes of the shock-turbulence interaction (wrinkled and broken shock regimes) will be investigated along with a study on how adaptive refinement of tetrahedral meshes benefits this problem. The research funding for this paper has been provided by Revolutionary Computational Aerosciences (RCA) subproject under the NASA Transformative Aeronautics Concepts Program (TACP).
A Trivariate Clough-Tocher Scheme for Tetrahedral Data.
1984-06-01
data, for arbitrary m and in arbitrarily many variables. However, all of the existing tetrahedral schemes yield rational interpolants . One would like...from the cardinal properties of barycentric coordinates that =bk 6 5 _ bki (2.3) where 6 is the Kronecker delta. The piecewise cubic interpolant (on a...1984 Abstract -An interpolation scheme is described for values of position, gradient and Hessian at scattered points in three variables. The domain is
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.
Detection and accumulation of tetrahedral intermediates in elastase catalysis.
Fink, A L; Meehan, P
1979-01-01
Tetrahedral intermediates in the reaction of elastase with specific di- and tripeptide p-nitroanilide substrates have been detected, accumulated, and stabilized at high pH by using subzero temperatures and fluid aqueous/organic cryosolvents. The tetrahedral adducts are characterized by spectra with lambda max of 359 +/- 2 nm, compared with thata of 380 nm for p-nitroaniline and 315-320 nm for the substrates. The maximal concentration of intermediate that could be accumulated varied with the different substrates from 40 to 100% of the active enzyme present. The pH dependence of the reactions indicated that formation of the tetrahedral intermediates was rate-limiting at low pH (pK* = 7.0 at -39 degrees C) and that collapse to the acylenzymes was rate-determining at high pH. When corrected for the effect of temperature and cosolvent, the rate of intermediate formation was in good agreement with that measured at 25 degrees C in aqueous solution by stopped-flow techniques. PMID:36609
On Quantization of Quadratic Poisson Structures
NASA Astrophysics Data System (ADS)
Manchon, D.; Masmoudi, M.; Roux, A.
Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.
Shan, Xiao; Connor, J N L
2012-11-26
A previous paper by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392) reported the surprising result that four simple parametrized S matrices can reproduce the forward-angle glory scattering of the H + D(2)(v(i)=0,j(i)=0) → HD(v(f)=3,j(f)=0) + D reaction, whose differential cross section (DCS) had been computed in a state-of-the-art scattering calculation for a state-of-the-art potential energy surface. Here, v and j are vibrational and rotational quantum numbers, respectively, and the translational energy is 1.81 eV. This paper asks the question: Can we replace the analytic functions (of class C(ω)) used by Shan-Connor with simpler mathematical functions and still reproduce the forward-angle glory scattering? We first construct S matrix elements (of class C(0)) using a quadratic phase and a piecewise-continuous pre-exponential factor consisting of three pieces. Two of the pieces are constants, with one taking the value N (a real normalization constant) at small values of the total angular momentum number, J; the other piece has the value 0 at large J. These two pieces are joined at intermediate values of J by either a straight line, giving rise to the linear parametrization (denoted param L), or a quadratic curve, which defines the quadratic parametrization (param Q). We find that both param L and param Q can reproduce the glory scattering for center-of-mass reactive scattering angles, θ(R) ≲ 30°. Second, we use a piecewise-discontinuous pre-exponential factor and a quadratic phase, giving rise to a step-function parametrization (param SF) and a top-hat parametrization (param TH). We find that both param SF and param TH can reproduce the forward-angle scattering, even though these class C(-1) parametrizations are usually considered too simplistic to be useful for calculations of DCSs. We find that an ultrasimplistic param THz, which is param TH with a phase of zero, can also reproduce the glory scattering at forward angles. The S matrix elements for
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)
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.
Self-assembly of a tetrahedral 58-nuclear barium vanadium oxide cluster.
Kastner, Katharina; Puscher, Bianka; Streb, Carsten
2013-01-07
We report the synthesis and characterization of a molecular barium vanadium oxide cluster featuring high nuclearity and high symmetry. The tetrameric, 2.3 nm cluster H(5)[Ba(10)(NMP)(14)(H(2)O)(8)[V(12)O(33)](4)Br] is based on a bromide-centred, octahedral barium scaffold which is capped by four previously unknown [V(12)O(33)](6-) clusters in a tetrahedral fashion. The compound represents the largest polyoxovanadate-based heterometallic cluster known to date. The cluster is formed in organic solution and it is suggested that the bulky N-methyl-2-pyrrolidone (NMP) solvent ligands allow the isolation of this giant molecule and prevent further condensation to a solid-state metal oxide. The cluster is fully characterized using single-crystal XRD, elemental analysis, ESI mass spectrometry and other spectroscopic techniques.
Practical implementation of tetrahedral mesh reconstruction in emission tomography
NASA Astrophysics Data System (ADS)
Boutchko, R.; Sitek, A.; Gullberg, G. T.
2013-05-01
This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio
Practical implementation of tetrahedral mesh reconstruction in emission tomography.
Boutchko, R; Sitek, A; Gullberg, G T
2013-05-07
This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio
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.
Platelet adhesion on phosphorus-incorporated tetrahedral amorphous carbon films
NASA Astrophysics Data System (ADS)
Liu, Aiping; Zhu, Jiaqi; Liu, Meng; Dai, Zhifei; Han, Xiao; Han, Jiecai
2008-11-01
The haemocompatibility of phosphorus-incorporated tetrahedral amorphous carbon (ta-C:P) films, synthesized by filtered cathodic vacuum arc technique with PH 3 as the dopant source, was assessed by in vitro platelet adhesion tests. Results based on scanning electron microscopy and contact angle measurements reveal that phosphorus incorporation improves the wettability and blood compatibility of ta-C film. Our studies may provide a novel approach for the design and synthesis of doped ta-C films to repel platelet adhesion and reduce thrombosis risk.
Search for Fingerprints of Tetrahedral Symmetry in ^{156}Gd
Doan, Q. T.; Curien, D.; Stezowski, O.; Dudek, J.; Mazurek, K.; Gozdz, A.; Piot, J.; Duchene, G.; Gall, B.; Molique, H.; Richet, M.; Guinet, D.; Redon, N.; Schmitt, Ch.; Jones, P.; Peura, P.; Ketelhut, S.; Nyman, M.; Jakobsson, U.; Greenlees, P. T.; Julin, R.; Juutinen, S.; Rahkila, P.; Maj, A.; Zuber, K.; Bednarczyk, P.; Schunck, N.; Dobaczewski, J.; Astier, A.; Deloncle, I.; Verney, D.; Gerl, J.
2009-01-01
Theoretical predictions suggest the presence of tetrahedral symmetry as an explanation for the vanishing intra-band E2 transitions at the bottom of the odd-spin negative-parity band in ^{156}Gd. The present study reports on experiment performed to address this phenomenon. It allowed to remove certain ambiguities related to the intra-band E2 transitions in the negative-parity bands to determine the new inter-band transitions and reduced probability ratios B(E2)/B(E1) and, for the first time, to determine the experimental uncertainties related to the latter observable.
WHAT IS A SATISFACTORY QUADRATIC EQUATION SOLVER?
The report discusses precise requirements for a satisfactory computer program to solve a quadratic equation with floating - point coefficients. The principal practical problem is coping with overflow and underflow.
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.)
Linear quadratic optimal control for symmetric systems
NASA Technical Reports Server (NTRS)
Lewis, J. H.; Martin, C. F.
1983-01-01
Special symmetries are present in many control problems. This paper addresses the problem of determining linear-quadratic optimal control problems whose solutions preserve the symmetry of the initial linear control system.
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.
Test spaces and characterizations of quadratic spaces
NASA Astrophysics Data System (ADS)
Dvurečenskij, Anatolij
1996-10-01
We show that a test space consisting of nonzero vectors of a quadratic space E and of the set all maximal orthogonal systems in E is algebraic iff E is Dacey or, equivalently, iff E is orthomodular. In addition, we present another orthomodularity criteria of quadratic spaces, and using the result of Solèr, we show that they can imply that E is a real, complex, or quaternionic Hilbert space.
Numerical Simulation of the Radiation Symmetry in Tetrahedral Hohlraums.
NASA Astrophysics Data System (ADS)
Macfarlane, J. J.; Magelssen, G.; Delamater, N.; Wallace, J.; Murphy, T.; Klare, K.
1997-11-01
The successful implosion of a capsule in indirect-drive ICF experiments requires the ability to diagnose and control the radiation symmetry at its surface. Recently, there has been increased interest in studying whether ``tetrahedral'' hohlraums can produce a radiation field on the capsule which is more symmetric than cylindrical hohlraums. Asymmetries in the 3-D radiation field are influenced by: the size and shape of the hohlraum, the wall albedo, the capsule radius, the LEH and diagnostic holes, and the laser beam pointing and power/energy imbalances. Time-dependent asymmetries are caused by the laser pulse history, changing wall albedos, and wall motion. We have recently developed a 3-D view factor code to investigate the time-dependent radiation asymmetry in indirect-drive ICF experiments. This code includes algorithms for the accurate solution of configuration factors, as well as laser ray-trace algorithms for modeling OMEGA, NOVA, and NIF laser/target chamber geometries. Time-dependent albedos are based on 1-D radiation-hydrodynamics simulations using UTA opacities for the high-Z wall. We will present results from simulations of OMEGA tetrahedral hohlraum experiments, as well as simulations showing how asymmetries scale with capsule/hohlraum configuration.
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.
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.
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,…
NASA Astrophysics Data System (ADS)
Chang, Chau-Lyan; Venkatachari, Balaji
2016-11-01
Flow physics near the viscous wall is intrinsically anisotropic in nature, namely, the gradient along the wall normal direction is much larger than that along the other two orthogonal directions parallel to the surface. Accordingly, high aspect ratio meshes are employed near the viscous wall to capture the physics and maintain low grid count. While such arrangement works fine for structured-grid based methods with dimensional splitting that handles derivatives in each direction separately, similar treatments often lead to numerical instability for unstructured-mesh based methods when triangular or tetrahedral meshes are used. The non-splitting treatment of near-wall gradients for high-aspect ratio triangular or tetrahedral elements results in an ill-conditioned linear system of equations that is closely related to the numerical instability. Altering the side lengths of the near wall tetrahedrons in the gradient calculations would make the system less unstable but more dissipative. This research presents recent progress in applying numerical dissipation control in the space-time conservation element solution element (CESE) method to reduce or alleviate the above-mentioned instability while maintaining reasonable solution accuracy.
Spiegel, Martin; Redel, Thomas; Zhang, Y Jonathan; Struffert, Tobias; Hornegger, Joachim; Grossman, Robert G; Doerfler, Arnd; Karmonik, Christof
2011-01-01
Haemodynamic factors, in particular wall shear stresses (WSSs) may have significant impact on growth and rupture of cerebral aneurysms. Without a means to measure WSS reliably in vivo, computational fluid dynamic (CFD) simulations are frequently employed to visualise and quantify blood flow from patient-specific computational models. With increasing interest in integrating these CFD simulations into pretreatment planning, a better understanding of the validity of the calculations in respect to computation parameters such as volume element type, mesh size and mesh composition is needed. In this study, CFD results for the two most common aneurysm types (saccular and terminal) are compared for polyhedral- vs. tetrahedral-based meshes and discussed regarding future clinical applications. For this purpose, a set of models were constructed for each aneurysm with spatially varying surface and volume mesh configurations (mesh size range: 5119-258, 481 volume elements). WSS distribution on the model wall and point-based velocity measurements were compared for each configuration model. Our results indicate a benefit of polyhedral meshes in respect to convergence speed and more homogeneous WSS patterns. Computational variations of WSS values and blood velocities are between 0.84 and 6.3% from the most simple mesh (tetrahedral elements only) and the most advanced mesh design investigated (polyhedral mesh with boundary layer).
Nuclear tetrahedral symmetry: possibly present throughout the periodic table.
Dudek, J; Goźdź, A; Schunck, N; Miśkiewicz, M
2002-06-24
More than half a century after the fundamental, spherical shell structure in nuclei had been established, theoretical predictions indicated that the shell gaps comparable or even stronger than those at spherical shapes may exist. Group-theoretical analysis supported by realistic mean-field calculations indicate that the corresponding nuclei are characterized by the TD(d) ("double-tetrahedral") symmetry group. Strong shell-gap structure is enhanced by the existence of the four-dimensional irreducible representations of TD(d); it can be seen as a geometrical effect that does not depend on a particular realization of the mean field. Possibilities of discovering the TD(d) symmetry in experiment are discussed.
Structural and electronic properties of a tetrahedral amorphous carbon surface
NASA Astrophysics Data System (ADS)
Dong, Jianjun; Drabold, D. A.
1997-03-01
We present ab initio studies of a model of tetrahedral amorphous carbon (ta-C) surface. Our methodology is LDA (with Harris functional and local basis) molecular dynamics simulations. The surface is modeled by a 216 atom slab supercell. Several candidate slabs are constructed by starting with the DTW model (B.R. Djordjevic, M.F. Thorpe and F. Wooten, Phys. Rev. B 52) 5685 (1995) and applying various simulated heating/quenching cycles. We analyze the structural and electronic properties of the surface , with special attention forcused on the electronic signatures of surface structural defects. Preliminary results indicate that the surface layer significantly graphitizes, and many surface gap states are present in the electronic density of states.
Photonuclear sum rules and the tetrahedral configuration of He4
NASA Astrophysics Data System (ADS)
Gazit, Doron; Barnea, Nir; Bacca, Sonia; Leidemann, Winfried; Orlandini, Giuseppina
2006-12-01
Three well-known photonuclear sum rules (SR), i.e., the Thomas-Reiche-Kuhn, the bremsstrahlungs and the polarizability SR are calculated for He4 with the realistic nucleon-nucleon potential Argonne V18 and the three-nucleon force Urbana IX. The relation between these sum rules and the corresponding energy weighted integrals of the cross section is discussed. Two additional equivalences for the bremsstrahlungs SR are given, which connect it to the proton-neutron and neutron-neutron distances. Using them, together with our result for the bremsstrahlungs SR, we find a deviation from the tetrahedral symmetry of the spatial configuration of He4. The possibility to access this deviation experimentally is discussed.
A radiative model of quark masses with binary tetrahedral symmetry
NASA Astrophysics Data System (ADS)
Natale, Alexander
2017-01-01
A radiative model of quark and lepton masses utilizing the binary tetrahedral (T‧) flavor symmetry, or horizontal symmetry, is proposed which produces the first two generation of quark masses through their interactions with vector-like quarks that carry charges under an additional U (1). By softly-breaking the T‧ to a residual Z4 through the vector-like quark masses, a CKM mixing angle close to the Cabibbo angle is produced. In order to generate the cobimaximal neutrino oscillation pattern (θ13 ≠ 0 ,θ23 = π / 4 ,δCP = ± π / 2) and protect the horizontal symmetry from arbitrary corrections in the lepton sector, there are automatically two stabilizing symmetries in the dark sector. Several benchmark cases where the correct relic density is achieved in a multi-component DM scenario, as well as the potential collider signatures of the vector-like quarks are discussed.
Photoconductive detection of tetrahedrally coordinated hydrogen in ZnO.
Koch, S G; Lavrov, E V; Weber, J
2012-04-20
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. 6, 44 (2007)]. The two LVMs of the hydrogen substituting oxygen in ZnO are identified at 742 and 792 cm(-1). The modes belong to a nondegenerated A(1) and a twofold degenerated E representations of the C(3v) point group. The tetrahedral coordination of the hydrogen atom is the result of a newly detected multicenter bond for defects in solids.
Slave fermion formalism for the tetrahedral spin chain
NASA Astrophysics Data System (ADS)
Mohan, Priyanka; Rao, Sumathi
2016-09-01
We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2 chain, which is a one-dimensional generalization of the two dimensional Kitaev honeycomb model. Using the mean field theory, coupled with a gauge fixing procedure to implement the single occupancy constraint, we obtain the phase diagram of the model. We then show that it matches the exact results obtained earlier using the Majorana fermion representation. We also compute the spin-spin correlation in the gapless phase and show that it is a spin liquid. Finally, we map the one-dimensional model in terms of the slave fermions to the model of 1D p-wave superconducting model with complex parameters and show that the parameters of our model fall in the topological trivial regime and hence does not have edge Majorana modes.
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.
How does tetrahedral structure grow in liquid silicon upon supercooling?
Morishita, Tetsuya
2006-10-20
We present an extensive set of isothermal-isobaric first-principles molecular-dynamics simulations of liquid silicon over a temperature range of 950-1700 K. We find that the tetrahedral order gradually grows upon cooling to approximately 1200 K, but that the growth accelerates significantly below approximately 1200 K. This growth process gives rise to anomalous changes in density and liquid structure upon supercooling. In particular, we find that the atomic coordination number remains constant to approximately 1200 K and then begins to decrease below approximately 1200 K, which resolves the existing controversy regarding liquid structure in the supercooled regime [T. H. Kim, Phys. Rev. Lett. 95, 085501 (2005)10.1103/PhysRevLett.95.085501].
Self-assembly of tetrahedral plasmonic nanoclusters for optical metafluids
NASA Astrophysics Data System (ADS)
Schade, Nicholas; Manoharan, Vinothan
2015-03-01
We direct the assembly of clusters of gold nanospheres that behave as nanoscale electromagnetic resonators. We use spherical gold nanoparticles that are exceptionally smooth, monocrystalline, and monodisperse. These particles exhibit highly reproducible scattering spectra compared with gold colloids that are available commercially. We mix these positively charged particles with negatively charged dielectric particles. The gold particles stick to the dielectric particles permanently and randomly in a process that can be modeled mathematically as ``random parking,'' a type of non-equilibrium self-assembly. By controlling the particles' sizes, stoichiometry, and interactions, we maximize the yield of tetrahedral clusters, the ideal structures for isotropic metamaterials. We measure the optical properties of these structures with dark-field spectroscopy to characterize their suitability as building blocks for a bulk, isotropic, optical metafluid.
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.
PSQP -- Puzzle Solving by Quadratic Programming.
Andalo, Fernanda; Taubin, Gabriel; Goldenstein, Siome
2016-03-25
In this article we present the first effective global method for the reconstruction of image puzzles comprising rectangle pieces - Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
PSQP: Puzzle Solving by Quadratic Programming.
Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome
2017-02-01
In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
Quintessence with quadratic coupling to dark matter
Boehmer, Christian G.; Chan, Nyein; Caldera-Cabral, Gabriela; Lazkoz, Ruth; Maartens, Roy
2010-04-15
We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.
Guises and disguises of quadratic divergences
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.
Guises and disguises of quadratic divergences
NASA Astrophysics Data System (ADS)
Cherchiglia, A. L.; Vieira, A. R.; Hiller, Brigitte; Baêta Scarpelli, A. P.; Sampaio, Marcos
2014-12-01
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale 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.
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…
Collision-broadened linewidths of tetrahedral molecules. III - Dispersion and induction interactions
NASA Technical Reports Server (NTRS)
Varanasi, P.
1975-01-01
Expressions for the interruption functions S2(b) have been derived for the dispersion interaction between a tetrahedral molecule and a linear molecule, and for the interaction between the octopole moment of a tetrahedral molecule and the octopole-induced dipole moment in a perturbing molecule.
Investigating Students' Mathematical Difficulties with Quadratic Equations
ERIC Educational Resources Information Center
O'Connor, Bronwyn Reid; Norton, Stephen
2016-01-01
This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…
Target manifold formation using a quadratic SDF
NASA Astrophysics Data System (ADS)
Hester, Charles F.; Risko, Kelly K. D.
2013-05-01
Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.
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.
A note on the fundamental unit in some types of the real quadratic number fields
NASA Astrophysics Data System (ADS)
Özer, Ö.
2016-10-01
Let k =Q (√{d }) be a real quadratic numbefield where d > 0 is a positive square-free integer. The map d →Q (√{d }) is a bijection from the set off all square-free integers d ≠ 0, 1 to the set of all quadratic fields Q (√{d })={ x +y √{d }|x ,y ∈Q } . Furthermore, integral basis element of algebraic integer's ring in real quadratic fields is determined by either wd=√{d }=[ a0;a1,a2,⋯,aℓ (d)-1,2 a0 ¯ ] in the case of d ≡ 2,3(mod 4) or wd=1/+√{d } 2 =[ a0;a1,a2,⋯,aℓ (d)-1,2 a0-1 ¯ ] in the case of d ≡ 1(mod 4) where ℓ (d ) is the period length of continued fraction expansion. The purpose of this paper is to obtain classification of some types of real quadratic fields Q (√{d }) , which include the specific form of continued fraction expansion of integral basis element wd, for which has all partial quotient elements are equal to each other and written as ξs (except the last digit of the period) for ξ positive even integer where period length is ℓ =ℓ (d ) and d ≡ 2,3(mod 4) is a square free positive integer. Moreover, the present paper deals with determining new certain parametric formula of fundamental unit ɛd=t/d+ud√{d } 2 >1 with norm N (ɛd)=(-1) ℓ (d ) for such types of real quadratic fields. Besides, Yokoi's d-invariants nd and md in the relation to continued fraction expansion of wd are calculated by using coefficients of fundamental unit. All supported results are given in numerical tables. These new results and tables are not known in the literature of real quadratic fields.
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.
Connectivity, dynamics, and structure in a tetrahedral network liquid.
Roldán-Vargas, Sándalo; Rovigatti, Lorenzo; Sciortino, Francesco
2017-01-04
We report a detailed computational study by Brownian dynamics simulations of the structure and dynamics of a liquid of patchy particles which forms an amorphous tetrahedral network upon decreasing the temperature. The highly directional particle interactions allow us to investigate the system connectivity by discriminating the total set of particles into different populations according to a penta-modal distribution of bonds per particle. With this methodology we show how the particle bonding process is not randomly independent but it manifests clear bond correlations at low temperatures. We further explore the dynamics of the system in real space and establish a clear relation between particle mobility and particle connectivity. In particular, we provide evidence of anomalous diffusion at low temperatures and reveal how the dynamics is affected by the short-time hopping motion of the weakly bounded particles. Finally we widely investigate the dynamics and structure of the system in Fourier space and identify two quantitatively similar length scales, one dynamic and the other static, which increase upon cooling the system and reach distances of the order of few particle diameters. We summarize our findings in a qualitative picture where the low temperature regime of the viscoelastic liquid is understood in terms of an evolving network of long time metastable cooperative domains of particles.
TET peptidases: A family of tetrahedral complexes conserved in prokaryotes.
Appolaire, Alexandre; Colombo, Matteo; Basbous, Hind; Gabel, Frank; Girard, E; Franzetti, Bruno
2016-03-01
The TET peptidases are large polypeptide destruction machines present among prokaryotes. They form 12-subunits hollow tetrahedral particles, and belong to the family of M42 metallo-peptidases. Structural characterization of various archaeal and bacterial complexes has revealed a unique mechanism of internal compartmentalization and peptide trafficking that distinguishes them from the other oligomeric peptidases. Different versions of the TET complex often co-exist in the cytosol of microorganisms. In depth enzymatic studies have revealed that they are non-processive cobalt-activated aminopeptidases and display contrasting substrate specificities based on the properties of the catalytic chambers. Recent studies have shed light on the assembly mechanism of homo and hetero-dodecameric TET complexes and shown that the activity of TET aminopeptidase towards polypeptides is coupled with its assembly process. These findings suggested a functional regulation based on oligomerization control in vivo. This review describes a current knowledge on M42 TET peptidases biochemistry and discuss their possible physiological roles. This article is a part of the Special Issue entitled: «A potpourri of proteases and inhibitors: from molecular toolboxes to signalling scissors».
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.
Tetrahedral Arrangements of Perylene Bisimide Columns via Supramolecular Orientational Memory.
Sahoo, Dipankar; Peterca, Mihai; Aqad, Emad; Partridge, Benjamin E; Heiney, Paul A; Graf, Robert; Spiess, Hans W; Zeng, Xiangbing; Percec, Virgil
2017-01-24
Chiral, shape, and liquid crystalline memory effects are well-known to produce commercial macroscopic materials with important applications as springs, sensors, displays, and memory devices. A supramolecular orientational memory effect that provides complex nanoscale arrangements was only recently reported. This supramolecular orientational memory was demonstrated to preserve the molecular orientation and packing within supramolecular units of a self-assembling cyclotriveratrylene crown at the nanoscale upon transition between its columnar hexagonal and Pm3̅n cubic periodic arrays. Here we report the discovery of supramolecular orientational memory in a dendronized perylene bisimide (G2-PBI) that self-assembles into tetrameric crowns and subsequently self-organizes into supramolecular columns and spheres. This supramolecular orientation memory upon transition between columnar hexagonal and body-centered cubic (BCC) mesophases preserves the 3-fold cubic [111] orientations rather than the 4-fold [100] axes, generating an unusual tetrahedral arrangement of supramolecular columns. These results indicate that the supramolecular orientational memory concept may be general for periodic arrays of self-assembling dendrons and dendrimers as well as for other periodic and quasiperiodic nanoscale organizations comprising supramolecular spheres, generated from other organized complex soft matter including block copolymers and surfactants.
Superlattice Quantum Dots of Self-assembled Tetrahedral Nanocrystals
NASA Astrophysics Data System (ADS)
Wang, Z. L.; Yin, J. S.
1998-03-01
Size and shape selected CoO nanocrystals dominated by tetrahedral shape have been synthesized and assembled to form superlattices with long-range translation order and short-range orientation order [1]. The crystallography of self-assembled nanocrystal superlattices (NCSs) is determined not only by the size of the nanocrystals and the length of the passivation thiolates, but by the shape of the nanocrystals. The structure of the nanocrystals are determined by high-resolution transmission electron microscopy (TEM). A model is suggested to explain the observed orientation order and the result supports that the thiolates molecules distributed on the nanocrystal surfaces form bundles, and the nanocrystals are assembled in such a way that the bundles tend to fill the entire space. The stability of the NCSs has been examined in-situ using TEM. The result suggests the strong effect of the substrate on NCSs. [1] J.S. Yin and Z.L. Wang, Phys. Rev. Lett., 79 (No. 13) (1997) 2570-2573. [2] J.S. Yin and Z.L. Wang, J. Phys. Chem., 101 (1997) 8979-8983.
Geometric Approaches to Quadratic Equations from Other Times and Places.
ERIC Educational Resources Information Center
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Bifurcations in biparametric quadratic potentials. II.
Lanchares, V.; Elipe, A.
1995-09-01
Quadratic Hamiltonians with the phase space on the S (2) sphere represent numerous dynamical systems. There are only two classes of quadratic Hamiltonians depending on two parameters. We analyze the occurrence of bifurcations and we obtain the bifurcation lines in the parameter plane for one of these classes, thus complementing the work done in a previous paper where the other class was analyzed. As the parameters evolve, the appearance-disappearance of homoclinic orbits in the phase portrait is governed by four types of bifurcations: namely the pitchfork, the butterfly, the oyster and the pentadent bifurcations. We find also values where the system is degenerate, that is, there are nonisolated equilibria. (c) 1995 American Institute of Physics.
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...
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.
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.
Monotone and convex quadratic spline interpolation
NASA Technical Reports Server (NTRS)
Lam, Maria H.
1990-01-01
A method for producing interpolants that preserve the monotonicity and convexity of discrete data is described. It utilizes the quadratic spline proposed by Schumaker (1983) which was subsequently characterized by De Vore and Yan (1986). The selection of first order derivatives at the given data points is essential to this spline. An observation made by De Vore and Yan is generalized, and an improved method to select these derivatives is proposed. The resulting spline is completely local, efficient, and simple to implement.
Stochastic Linear Quadratic Optimal Control Problems
Chen, S.; Yong, J.
2001-07-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; Charest, Marc R.; Canfield, Thomas R.; Wohlbier, John G.
2015-02-24
We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.
A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...
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
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.
Quadratic optimization in ill-posed problems
NASA Astrophysics Data System (ADS)
Ben Belgacem, F.; Kaber, S.-M.
2008-10-01
Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.
Optical and magnetic properties of transition-metal ions in tetrahedral and octahedral compounds
NASA Astrophysics Data System (ADS)
Li, Huifang; Wang, Huaiqian; Kuang, Xiaoyu
2011-10-01
This paper presents the complete energy matrix of the 3d2 system containing the electron-electron interaction, the ligand-field interaction, the spin-orbit coupling interaction, and the Zeeman interaction, in which the optical spectra and g-factor of V3+and Ti2+ ions in the series of tetrahedral AIIBVI (AII=Zn, Cd, BVI=S, Se, Te) semiconductor materials are determined. In the investigation of the optical and magnetic properties of these transition-metal ions in the tetrahedral coordination complexes, we compared the data obtained from the transition-metal ions in the tetrahedral coordination complexes with those obtained from the corresponding ions in the octahedral ones, and found that the tetrahedral complexes have weaker crystal-field strength, inverse energy level ordering and stronger covalence effect.
Shape effects on the random-packing density of tetrahedral particles.
Zhao, Jian; Li, Shuixiang; Jin, Weiwei; Zhou, Xuan
2012-09-01
Regular tetrahedra have been demonstrated recently giving high packing density in random configurations. However, it is unknown whether the random-packing density of tetrahedral particles with other shapes can reach an even higher value. A numerical investigation on the random packing of regular and irregular tetrahedral particles is carried out. Shape effects of rounded corner, eccentricity, and height on the packing density of tetrahedral particles are studied. Results show that altering the shape of tetrahedral particles by rounding corners and edges, by altering the height of one vertex, or by lateral displacement of one vertex above its opposite face, all individually have the effect of reducing the random-packing density. In general, the random-packing densities of irregular tetrahedral particles are lower than that of regular tetrahedra. The ideal regular tetrahedron should be the shape which has the highest random-packing density in the family of tetrahedra, or even among convex bodies. An empirical formula is proposed to describe the rounded corner effect on the packing density, and well explains the density deviation of tetrahedral particles with different roundness ratios. The particles in the simulations are verified to be randomly packed by studying the pair correlation functions, which are consistent with previous results. The spherotetrahedral particle model with the relaxation algorithm is effectively applied in the simulations.
Constrained neural approaches to quadratic assignment problems.
Ishii, S; Sato, M
1998-08-01
In this paper, we discuss analog neural approaches to the quadratic assignment problem (QAP). These approaches employ a hard constraints scheme to restrict the domain space, and are able to obtain much improved solutions over conventional neural approaches. Since only a few strong heuristics for QAP have been known to date, our approaches are good alternatives, capable of obtaining fairly good solutions in a short period of time. Some of them can also be applied to large-scale problems, say of size N>/=300.
Some Randomized Algorithms for Convex Quadratic Programming
Goldbach, R.
1999-01-15
We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a unified and elegant presentation and analysis. We also show that LP-type problems include minimization of a convex quadratic function subject to convex quadratic constraints as a special case, for which the algorithms can be implemented efficiently, if only linear constraints are present. We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical results. Even though the framework of LP-type problems may appear rather abstract at first, application of the methods considered in this paper to a given problem of that type is easy and efficient. Moreover, our proofs are in fact rather simple, since many technical details of more explicit problem representations are handled in a uniform manner by our approach. In particular, we do not assume boundedness of the feasible set as required in related methods.
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.
Ngo, Phong D; Mansoorabadi, Steven O; Frey, Perry A
2016-08-04
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.
Implementation of tetrahedral-mesh geometry in Monte Carlo radiation transport code PHITS.
Furuta, Takuya; Sato, Tatsuhiko; Han, Min; Yeom, Yeon; Kim, Chan; Brown, Justin; Bolch, Wesley
2017-04-04
A new function to treat tetrahedral-mesh geometry was implemented in the Particle and Heavy Ion Transport code Systems (PHITS). To accelerate the computational speed in the transport process, an original algorithm was introduced to initially prepare decomposition maps for the container box of the tetrahedral-mesh geometry. The computational performance was tested by conducting radiation transport simulations of 100 MeV protons and 1 MeV photons in a water phantom represented by tetrahedral mesh. The simulation was repeated with varying number of meshes and the required computational times were then compared with those of the conventional voxel representation. Our results show that the computational costs for each boundary crossing of the region mesh are essentially equivalent for both representations. This study suggests that the tetrahedral-mesh representation offers not only a flexible description of the transport geometry but also improvement of computational efficiency for the radiation transport. Due to the adaptability of tetrahedrons in both size and shape, dosimetrically equivalent objects can be represented by tetrahedrons with a much fewer number of meshes as compared its voxelized representation. Our study additionally included dosimetric calculations using a computational human phantom. A significant acceleration of the computational speed, about 4 times, was confirmed by the adoption of a tetrahedral mesh over the traditional voxel mesh geometry.
Some Aspects of Quadratic Generalized White Noise Functionals
NASA Astrophysics Data System (ADS)
Si, Si; Hida, Takeyuki
2009-02-01
We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.
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.
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
Implementation of mixed formulation elements in PC/NASTRAN
NASA Technical Reports Server (NTRS)
Schaeffer, Harry G.
1993-01-01
The purpose of this paper is to describe the implementation and use of a consistent family of two and three dimensional elements in NASTRAN. The elements which are based on a mixed formulation include a replacement of the original NASTRAN shear element and the addition of triangular quadrilateral shell elements and tetrahedral, pentahedral and hexahedral solid elements. These elements support all static loads including temperature gradient and pressure load. The mass matrix is also generated to support all dynamic rigid formats.
Security analysis of quadratic phase based cryptography
NASA Astrophysics Data System (ADS)
Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.
2016-09-01
The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.
Digital image restoration using quadratic programming.
Abdelmalek, N N; Kasvand, T
1980-10-01
The problem of digital image restoration is considered by obtaining an approximate solution to the Fredholm integral equation of the first kind in two variables. The system of linear equations resulting from the discretization of the integral equation is converted to a consistent system of linear equations. The problem is then solved as a quadratic programming problem with bounded variables where the unknown solution is minimized in the L(2) norm. In this method minimum computer storage is needed, and the repeated solutions are obtained in an efficient way. Also the rank of the consistent system which gives a best or near best solution is estimated. Computer simulated examples using spatially separable pointspread functions are presented. Comments and conclusion are given.
On Coupled Rate Equations with Quadratic Nonlinearities
Montroll, Elliott W.
1972-01-01
Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013
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.
Forced oscillations in quadratically damped systems
NASA Technical Reports Server (NTRS)
Bayliss, A.
1978-01-01
Bayliss (1975) has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations. In the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear. The properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution. By using the Lipschitz continuity of the mapping and the contracting mapping principle, almost periodic solutions can be found for perturbations of the considered equation. Attention is also given to the Lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory.
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.
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.
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.
Natural off-stoichiometry causes carrier doping in half-Heusler filled tetrahedral structures
NASA Astrophysics Data System (ADS)
Yu, Yonggang G.; Zhang, Xiuwen; Zunger, Alex
2017-02-01
The half-Heusler filled tetrahedral structures (FTSs) are zinc-blende-like compounds, where an additional atom is filling its previously empty interstitial site. The FTSs having 18 valence electrons per formula unit are an emerging family of functional materials, whose intrinsic doping trends underlying a wide range of electronic functionalities are yet to be understood. Interestingly, even pristine compounds without any attempt at impurity/chemical doping exhibit intriguing trends in the free carriers they exhibit. Applying the first principles theory of doping to a few prototype compounds in the AIVBXCIV and AIVBIXCV groups, we describe the key ingredients controlling the materials' propensity for both intrinsic and extrinsic doping: (a) The spontaneous deviations from 1:1:1 stoichiometry reflect predictable thermodynamic stability of specific competing phases. (b) Bulk ABC compounds containing 3 d elements in the B position (ZrNiSn and ZrCoSb) are predicted to be naturally 3 d rich. The B =3 d interstitials are the prevailing shallow donors, whereas the potential acceptors (e.g., Zr vacancy and Sn-on-Zr antisite) are ineffective electron killers, resulting in an overall uncompensated n -type character, even without any chemical doping. In these materials, the band edges are "natural impurity bands" due to non-Daltonian off-stoichiometry, such as B interstitials, not intrinsic bulk controlled states as in a perfect crystal. (c) Bulk ABC compounds containing 5 d elements in the B position (ZrPtSn, ZrIrSb, and TaIrGe) are predicted to be naturally C rich and A poor. This promotes the hole-producing C -on-A antisite defects rather than B -interstitial donors. The resultant p -type character (without chemical doping) therein is "latent" for C =Sn and Sb; however, as the C -on-A hole-producing acceptors are rather deep and p typeness is manifest only at high temperature or via impurity doping. In contrast, in TaIrGe (B =Ir , 5 d ) , the prevailing hole-producing Ge
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.
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.)
Some Paradoxical Results for the Quadratically Weighted Kappa
ERIC Educational Resources Information Center
Warrens, Matthijs J.
2012-01-01
The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories "n" it is shown that if one of the raters uses the same…
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…
Convexity preserving C2 rational quadratic trigonometric spline
NASA Astrophysics Data System (ADS)
Dube, Mridula; Tiwari, Preeti
2012-09-01
A C2 rational quadratic trigonometric spline interpolation has been studied using two kind of rational quadratic trigonometric splines. It is shown that under some natural conditions the solution of the problem exits and is unique. The necessary and sufficient condition that constrain the interpolation curves to be convex in the interpolating interval or subinterval are derived.
Sketching the General Quadratic Equation Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Stols, G. H.
2005-01-01
This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…
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…
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.
DNA tetrahedral scaffolds-based platform for the construction of electrochemiluminescence biosensor.
Feng, Qiu-Mei; Zhou, Zhen; Li, Mei-Xing; Zhao, Wei; Xu, Jing-Juan; Chen, Hong-Yuan
2017-04-15
Proximal metallic nanoparticles (NPs) could quench the electrochemiluminescence (ECL) emission of semiconductor quantum dots (QDs) due to Förster energy transfer (FRET), but at a certain distance, the coupling of light-emission with surface plasmon resonance (SPR) result in enhanced ECL. Thus, the modification strategies and distances control between QDs and metallic NPs are critical for the ECL intensity of QDs. In this strategy, a SPR enhanced ECL sensor based on DNA tetrahedral scaffolds modified platform was reported for the detection of telomerase activity. Due to the rigid three-dimensional structure, DNA tetrahedral scaffolds grafting on the electrode surface could accurately modulate the distance between CdS QDs and luminol labelled gold nanoparticles (L-Au NPs), meanwhile provide an enhanced spatial dimension and accessibility for the assembly of multiple L-Au NPs. The ECL intensities of both CdS QDs (-1.25V vs. SCE) and luminol (+0.33V vs. SCE) gradually increased along with the formation of multiple L-Au NPs at the vertex of DNA tetrahedral scaffolds induced by telomerase, bringing in a dual-potential ECL analysis. The proposed method showed high sensitivity for the identification of telomerase and was successfully applied for the differentiation of cancer cells from normal cells. This work suggests that DNA tetrahedral scaffolds could serve as an excellent choice for the construction of SPR-ECL system.
Automated Tetrahedral Mesh Generation for CFD Analysis of Aircraft in Conceptual Design
NASA Technical Reports Server (NTRS)
Ordaz, Irian; Li, Wu; Campbell, Richard L.
2014-01-01
The paper introduces an automation process of generating a tetrahedral mesh for computational fluid dynamics (CFD) analysis of aircraft configurations in early conceptual design. The method was developed for CFD-based sonic boom analysis of supersonic configurations, but can be applied to aerodynamic analysis of aircraft configurations in any flight regime.
Fostering Teacher Development to a Tetrahedral Orientation in the Teaching of Chemistry
ERIC Educational Resources Information Center
Lewthwaite, Brian; Wiebe, Rick
2011-01-01
This paper reports on the initial outcomes from the end of the fourth year of a 5 year research and professional development project to improve chemistry teaching among three cohorts of chemistry teachers in Manitoba, Canada. The project responds to a new curriculum introduction advocating a tetrahedral orientation (Mahaffy, "Journal of…
Mixed-metal chalcogenide tetrahedral clusters with an exo-polyhedral metal fragment.
Yuvaraj, K; Roy, Dipak Kumar; Anju, V P; Mondal, Bijnaneswar; Varghese, Babu; Ghosh, Sundargopal
2014-12-07
The reaction of metal carbonyl compounds with group 6 and 8 metallaboranes led us to report the synthesis and structural characterization of several novel mixed-metal chalcogenide tetrahedral clusters. Thermolysis of arachno-[(Cp*RuCO)2B2H6], 1, and [Os3(CO)12] in the presence of 2-methylthiophene yielded [Cp*Ru(CO)2(μ-H){Os3(CO)9}S], 3, and [Cp*Ru(μ-H){Os3(CO)11}], 4. In a similar fashion, the reaction of [(Cp*Mo)2B5H9], 2, with [Ru3(CO)12] and 2-methylthiophene yielded [Cp*Ru(CO)2(μ-H){Ru3(CO)9}S], 5, and conjuncto-[(Cp*Mo)2B5H8(μ-H){Ru3(CO)9}S], 6. Both compounds 3 and 5 can be described as 50-cve (cluster valence electron) mixed-metal chalcogenide clusters, in which a sulfur atom replaces one of the vertices of the tetrahedral core. Compounds 3 and 5 possess a [M3S] tetrahedral core, in which the sulfur is attached to an exo-metal fragment, unique in the [M3S] metal chalcogenide tetrahedral arrangements. All the compounds have been characterized by mass spectrometry, IR, and (1)H, (11)B and (13)C NMR spectroscopy in solution, and the solid state structures were unequivocally established by crystallographic analysis of compounds 3, 5 and 6.
A Review of Defects and Disorder in Multinary Tetrahedrally Bonded Semiconductors
Baranowski, Lauryn L.; Zawadzki, Pawel; Lany, Stephan; Toberer, Eric S.; Zakutayev, Andriy
2016-12-01
Defects are critical to understanding the electronic properties of semiconducting compounds, for applications such as light-emitting diodes, transistors, photovoltaics, and thermoelectrics. In this review, we describe our work investigating defects in tetrahedrally bonded, multinary semiconductors, and discuss the place of our research within the context of publications by other groups. We applied experimental and theory techniques to understand point defects, structural disorder, and extended antisite defects in one semiconductor of interest for photovoltaic applications, Cu2SnS3. We contrast our findings on Cu2SnS3 with other chemically related Cu-Sn-S compounds, as well as structurally related compounds such as Cu2ZnSnS4 and Cu(In,Ga)Se2. We find that evaluation of point defects alone is not sufficient to understand defect behavior in multinary tetrahedrally bonded semiconductors. In the case of Cu2SnS3 and Cu2ZnSnS4, structural disorder and entropy-driven cation clustering can result in nanoscale compositional inhomogeneities which detrimentally impact the electronic transport. Therefore, it is not sufficient to assess only the point defect behavior of new multinary tetrahedrally bonded compounds; effects such as structural disorder and extended antisite defects must also be considered. Overall, this review provides a framework for evaluating tetrahedrally bonded semiconducting compounds with respect to their defect behavior for photovoltaic and other applications, and suggests new materials that may not be as prone to such imperfections.
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.
A review of defects and disorder in multinary tetrahedrally bonded semiconductors
NASA Astrophysics Data System (ADS)
Baranowski, Lauryn L.; Zawadzki, Pawel; Lany, Stephan; Toberer, Eric S.; Zakutayev, Andriy
2016-12-01
Defects are critical to understanding the electronic properties of semiconducting compounds, for applications such as light-emitting diodes, transistors, photovoltaics, and thermoelectrics. In this review, we describe our work investigating defects in tetrahedrally bonded, multinary semiconductors, and discuss the place of our research within the context of publications by other groups. We applied experimental and theory techniques to understand point defects, structural disorder, and extended antisite defects in one semiconductor of interest for photovoltaic applications, Cu2SnS3. We contrast our findings on Cu2SnS3 with other chemically related Cu-Sn-S compounds, as well as structurally related compounds such as Cu2ZnSnS4 and Cu(In,Ga)Se2. We find that evaluation of point defects alone is not sufficient to understand defect behavior in multinary tetrahedrally bonded semiconductors. In the case of Cu2SnS3 and Cu2ZnSnS4, structural disorder and entropy-driven cation clustering can result in nanoscale compositional inhomogeneities which detrimentally impact the electronic transport. Therefore, it is not sufficient to assess only the point defect behavior of new multinary tetrahedrally bonded compounds; effects such as structural disorder and extended antisite defects must also be considered. Overall, this review provides a framework for evaluating tetrahedrally bonded semiconducting compounds with respect to their defect behavior for photovoltaic and other applications, and suggests new materials that may not be as prone to such imperfections.
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
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
Extremal Optimization for Quadratic Unconstrained Binary Problems
NASA Astrophysics Data System (ADS)
Boettcher, S.
We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.
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 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.
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.
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
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.
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.
Chaos synchronization based on quadratic optimum regulation and control
NASA Astrophysics Data System (ADS)
Gong, Lihua
2005-03-01
Based on the method of the quadratic optimum control, a quadratic optimal regulator used for synchronizing chaotic systems is constructed to realize chaos synchronization. The synchronization method can maintain the least error with less control energy, and then realize the optimization on both sides of energy and error synthetically. In addition, the control cost can also be reduced by using this method intermittently. The simulation results of the chaotic Chua's circuit and the Rossler chaos system prove that the method is effective.
Quadratic bulk viscosity and the topology of space time.
NASA Astrophysics Data System (ADS)
Wolf, C.
1997-12-01
By considering a homogeneous isotropic universe admitting quadratic bulk viscosity the author shows that if the bulk viscosity coefficient is large the effective topology of space time attains an antiintuitive interpretation in the sense that a positive curvature space time is ever-expanding. This is true for all cosmologies studied except in the case of small quadratic bulk viscosity (3γ+1-kβ ≥ 0, 3γ+1 > 0).
Miao, Peng; Wang, Bidou; Chen, Xifeng; Li, Xiaoxi; Tang, Yuguo
2015-03-25
MicroRNAs are not only important regulators of a wide range of cellular processes but are also identified as promising disease biomarkers. Due to the low contents in serum, microRNAs are always difficult to detect accurately . In this study, an electrochemical biosensor for ultrasensitive detection of microRNA based on tetrahedral DNA nanostructure is developed. Four DNA single strands are engineered to form a tetrahedral nanostructure with a pendant stem-loop and modified on a gold electrode surface, which largely enhances the molecular recognition efficiency. Moreover, taking advantage of strand displacement polymerization, catalytic recycling of microRNA, and silver nanoparticle-based solid-state Ag/AgCl reaction, the proposed biosensor exhibits high sensitivity with the limit of detection down to 0.4 fM. This biosensor shows great clinical value and may have practical utility in early diagnosis and prognosis of certain diseases.
Investigation of negative-parity states in Dy156: Search for evidence of tetrahedral symmetry
Hartley, D. J.; Riedinger, L. L.; Janssens, R. V. F.; ...
2017-01-20
In this paper, an experiment populating low/medium-spin states in 156Dy was performed to investigate the possibility of tetrahedral symmetry in this nucleus. In particular, focus was placed on the low-spin, negative-parity states since recent theoretical studies suggest that these may be good candidates for this high-rank symmetry. The states were produced in the 148Nd(12C,4n) reaction and the Gammasphere array was utilized to detect the emitted γ rays. B(E2)/B(E1) ratios of transition probabilities from the low-spin, negative-parity bands were determined and used to interpret whether these structures are best associated with tetrahedral symmetry or, as previously assigned, to octupole vibrations. Finally,more » in addition, several other negative-parity structures were observed to higher spin and two new sequences were established.« less
Investigation of negative-parity states in Dy156 : Search for evidence of tetrahedral symmetry
Hartley, D. J.; Riedinger, L. L.; Janssens, R. V. F.; ...
2017-01-01
An experiment populating low/medium-spin states in 156Dy was performed to investigate the possibility of tetrahedral symmetry in this nucleus. In particular, focus was placed on the low-spin, negative-parity states since recent theoretical studies suggest that these may be good candidates for this high-rank symmetry. The states were produced in the 148Nd(12C,4 n) reaction and the Gammasphere array was utilized to detect the emitted rays. B(E 2) /B(E1) ratios of transition probabilities from the low-spin, negative-parity bands were determined and used to interpret whether these structures are best associated with tetrahedral symmetry or, as previously assigned, to octupole vibrations. Additionally, severalmore » other negative-parity structures were observed to higher spin and two new sequences were established« less
Fostering Teacher Development to a Tetrahedral Orientation in the Teaching of Chemistry
NASA Astrophysics Data System (ADS)
Lewthwaite, Brian; Wiebe, Rick
2011-11-01
This paper reports on the initial outcomes from the end of the fourth year of a 5 year research and professional development project to improve chemistry teaching among three cohorts of chemistry teachers in Manitoba, Canada. The project responds to a new curriculum introduction advocating a tetrahedral orientation (Mahaffy, Journal of Chemical Education 83(1), 49-55, 2006) to the teaching of chemistry. The project in its entirety is based upon several theoretical models in fostering chemistry teacher development (in particular Bronfenbrenner's bio-ecological model). These models are described, as is the progress made by teachers based upon the use of a Chemistry Teacher Inventory and associated teacher responses. Overall, statistical analysis of perceptions of their own teaching and comments made by teachers suggests they are showing limited development towards a tetrahedral orientation, albeit in a manner consistent with the curriculum. Ongoing research-based activities in this project are also described.
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme
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
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.
Near-field testing of the 5-meter model of the tetrahedral truss antenna
NASA Astrophysics Data System (ADS)
Kefauver, Neill; Cencich, Tom; Osborn, Jim; Osmanski, J. T.
1986-08-01
This report documents the technical results from near-field testing of the General Dynamics 5-meter model of the tetrahedral truss antenna at the Martin Marietta Denver Aerospace facility. A 5-meter square side of the tetrahedral served as the perimeter of the antenna, and a mesh surface and extensive surface contouring cord network was used to create a parabolic aperture shape to within an rms accuracy of 30 mils or better. Pattern measurements were made with offset feed systems radiating at frequencies of 7.73, 11.60, 2.27, and 4.26 (all in GHz). This report discusses the method of collecting the data, system measurement accuracy, the test data compiled, and diagostics and isolation of causes of pattern results. The technique of using near-field phase for measuring surface mechanical tolerances is included. Detailed far field antenna patterns and their implications are provided for all tests conducted.
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme
Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; Nguyen, Manh Cuong; Wang, Cai -Zhuang; Lin, Zijing; Zhu, Zi -Zhong; Ho, Kai -Ming
2015-10-26
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A_{2}MSiO_{4} with A = Li or Na and M = Mn, Fe or Co. In addition to finding all previously reported structures, we discovered many other different tetrahedral-network-based crystal structures which are highly degenerate in energy. In addition, these structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs.
A 3D finite-volume scheme for the Euler equations on adaptive tetrahedral grids
Vijayan, P.; Kallinderis, Y. )
1994-08-01
The paper describes the development and application of a new Euler solver for adaptive tetrahedral grids. Spatial discretization uses a finite-volume, node-based scheme that is of central-differencing type. A second-order Taylor series expansion is employed to march the solution in time according to the Lax-Wendroff approach. Special upwind-like smoothing operators for unstructured grids are developed for shock-capturing, as well as for suppression of solution oscillations. The scheme is formulated so that all operations are edge-based, which reduces the computational effort significantly. An adaptive grid algorithm is employed in order to resolve local flow features. This is achieved by dividing the tetrahedral cells locally, guided by a flow feature detection algorithm. Application cases include transonic flow around the ONERA M6 wing and transonic flow past a transport aircraft configuration. Comparisons with experimental data evaluate accuracy of the developed adaptive solver. 31 refs., 33 figs.
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. These structures can be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear trend of the structural preference in different systems was revealed and possible indicators that affect the structure stabilities were introduced. For the case of Na systems which have been much less investigated in the literature relative to the Li systems, we predicted their ground state structures and found evidence for the existence of new structural motifs.
Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme
Zhao, Xin; Wu, Shunqing; Lv, Xiaobao; ...
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
Investigation of negative-parity states in 156Dy: Search for evidence of tetrahedral symmetry
NASA Astrophysics Data System (ADS)
Hartley, D. J.; Riedinger, L. L.; Janssens, R. V. F.; Majola, S. N. T.; Riley, M. A.; Allmond, J. M.; Beausang, C. W.; Carpenter, M. P.; Chiara, C. J.; Cooper, N.; Curien, D.; Gall, B. J. P.; Garrett, P. E.; Kondev, F. G.; Kulp, W. D.; Lauritsen, T.; McCutchan, E. A.; Miller, D.; Miller, S.; Piot, J.; Redon, N.; Sharpey-Schafer, J. F.; Simpson, J.; Stefanescu, I.; Wang, X.; Werner, V.; Wood, J. L.; Yu, C.-H.; Zhu, S.; Dudek, J.
2017-01-01
An experiment populating low/medium-spin states in 156Dy was performed to investigate the possibility of tetrahedral symmetry in this nucleus. In particular, focus was placed on the low-spin, negative-parity states since recent theoretical studies suggest that these may be good candidates for this high-rank symmetry. The states were produced in the 148Nd(12C,4 n ) reaction and the Gammasphere array was utilized to detect the emitted γ rays. B (E 2 )/B (E 1 ) ratios of transition probabilities from the low-spin, negative-parity bands were determined and used to interpret whether these structures are best associated with tetrahedral symmetry or, as previously assigned, to octupole vibrations. In addition, several other negative-parity structures were observed to higher spin and two new sequences were established.
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.
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.
Hua, T D; Lamaty, F; Souriau, C; Rolland-Fulcrand, V; Lazaro, R; Viallefont, P; Lefranc, M P; Weill, M
1996-06-01
In order to obtain antibodies able to catalyse a peptide synthesis, a naive combinatorial library of human Fab antibody fragments was screened with the phosphonamidate transition state analogue of the reaction. Several Fab fragments were able to bind the analogue. Competitive binding studies performed with molecules containing representative parts of the hapten showed that two Fabs were able to recognize specifically the tetrahedral phosphorus present in the hapten.
A study of pH-dependence of shrink and stretch of tetrahedral DNA nanostructures.
Wang, Ping; Xia, Zhiwei; Yan, Juan; Liu, Xunwei; Yao, Guangbao; Pei, Hao; Zuo, Xiaolei; Sun, Gang; He, Dannong
2015-04-21
We monitored the shrink and stretch of the tetrahedral DNA nanostructure (TDN) and the i-motif connected TDN structure at pH 8.5 and pH 4.5, and we found that not only the i-motif can change its structure when the pH changes, but also the TDN and the DNA double helix change their structures when the pH changes.
Anomalous properties of liquids for a family of models with short range tetrahedral interactions
NASA Astrophysics Data System (ADS)
Buldyrev, Sergey; Franzese, Giancarlo
2012-02-01
Liquids with tetrahedral symmetry of the first coordination shell often display anomalous thermodynamic and dynamic behavior. The main reason for these anomalies is that pressurizing such liquids leads to the disordering of this local symmetry by the particles migrating from the second to the first coordination shell. This in some case may lead to the increase of entropy upon pressurizing and consequently to the volume increase upon cooling. Molecular simulations of various models with tetrahedral symmetry are able to reproduce this anomalous behavior. We study a family of simple models in which we can gradually change the degree of tetrahedrality and investigate the associated changes of the phase diagram by discrete molecular dynamics. A molecule in these models consist of a hard sphere and four point particles attached to the center of the hard sphere by directional bonds arranged in tetrahedral geometry. Each of these four particles has a narrow attractive square well so that the particles belonging to different molecules can attract to each other. We also impose a condition which does not allow a point particle in one molecule to include in its attractive well more than one point particle belonging to different molecules. We investigate how the phase diagram of the system depends on the parameters of the models. None of these models has a liquid -liquid phase transition in the accessible region of the phase. However, adding weak attractive square well to the hard sphere, or wider weak attractive square wells to the point particles can create a liquid-liquid critical point. A comparison with other simple models of the anomalous liquids is made.
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.
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.
A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TETRAHEDRAL DOMAINS
Fu, Zhisong; Kirby, Robert M.; Whitaker, Ross T.
2014-01-01
Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper presents a parallel algorithm for solving the eikonal equation on fully unstructured tetrahedral meshes. The method is appropriate for the type of fine-grained parallelism found on modern massively-SIMD architectures such as graphics processors and takes into account the particular constraints and capabilities of these computing platforms. This work builds on previous work for solving these equations on triangle meshes; in this paper we adapt and extend previous two-dimensional strategies to accommodate three-dimensional, unstructured, tetrahedralized domains. These new developments include a local update strategy with data compaction for tetrahedral meshes that provides solutions on both serial and parallel architectures, with a generalization to inhomogeneous, anisotropic speed functions. We also propose two new update schemes, specialized to mitigate the natural data increase observed when moving to three dimensions, and the data structures necessary for efficiently mapping data to parallel SIMD processors in a way that maintains computational density. Finally, we present descriptions of the implementations for a single CPU, as well as multicore CPUs with shared memory and SIMD architectures, with comparative results against state-of-the-art eikonal solvers. PMID:25221418
A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TETRAHEDRAL DOMAINS.
Fu, Zhisong; Kirby, Robert M; Whitaker, Ross T
2013-01-01
Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper presents a parallel algorithm for solving the eikonal equation on fully unstructured tetrahedral meshes. The method is appropriate for the type of fine-grained parallelism found on modern massively-SIMD architectures such as graphics processors and takes into account the particular constraints and capabilities of these computing platforms. This work builds on previous work for solving these equations on triangle meshes; in this paper we adapt and extend previous two-dimensional strategies to accommodate three-dimensional, unstructured, tetrahedralized domains. These new developments include a local update strategy with data compaction for tetrahedral meshes that provides solutions on both serial and parallel architectures, with a generalization to inhomogeneous, anisotropic speed functions. We also propose two new update schemes, specialized to mitigate the natural data increase observed when moving to three dimensions, and the data structures necessary for efficiently mapping data to parallel SIMD processors in a way that maintains computational density. Finally, we present descriptions of the implementations for a single CPU, as well as multicore CPUs with shared memory and SIMD architectures, with comparative results against state-of-the-art eikonal solvers.
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.
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.
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.
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.
New approach based on tetrahedral-mesh geometry for accurate 4D Monte Carlo patient-dose calculation
NASA Astrophysics Data System (ADS)
Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Kim, Seonghoon; Sohn, Jason W.
2015-02-01
In the present study, to achieve accurate 4D Monte Carlo dose calculation in radiation therapy, we devised a new approach that combines (1) modeling of the patient body using tetrahedral-mesh geometry based on the patient’s 4D CT data, (2) continuous movement/deformation of the tetrahedral patient model by interpolation of deformation vector fields acquired through deformable image registration, and (3) direct transportation of radiation particles during the movement and deformation of the tetrahedral patient model. The results of our feasibility study show that it is certainly possible to construct 4D patient models (= phantoms) with sufficient accuracy using the tetrahedral-mesh geometry and to directly transport radiation particles during continuous movement and deformation of the tetrahedral patient model. This new approach not only produces more accurate dose distribution in the patient but also replaces the current practice of using multiple 3D voxel phantoms and combining multiple dose distributions after Monte Carlo simulations. For routine clinical application of our new approach, the use of fast automatic segmentation algorithms is a must. In order to achieve, simultaneously, both dose accuracy and computation speed, the number of tetrahedrons for the lungs should be optimized. Although the current computation speed of our new 4D Monte Carlo simulation approach is slow (i.e. ~40 times slower than that of the conventional dose accumulation approach), this problem is resolvable by developing, in Geant4, a dedicated navigation class optimized for particle transportation in tetrahedral-mesh geometry.
Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Kim, Seonghoon; Sohn, Jason W
2015-02-21
In the present study, to achieve accurate 4D Monte Carlo dose calculation in radiation therapy, we devised a new approach that combines (1) modeling of the patient body using tetrahedral-mesh geometry based on the patient's 4D CT data, (2) continuous movement/deformation of the tetrahedral patient model by interpolation of deformation vector fields acquired through deformable image registration, and (3) direct transportation of radiation particles during the movement and deformation of the tetrahedral patient model. The results of our feasibility study show that it is certainly possible to construct 4D patient models (= phantoms) with sufficient accuracy using the tetrahedral-mesh geometry and to directly transport radiation particles during continuous movement and deformation of the tetrahedral patient model. This new approach not only produces more accurate dose distribution in the patient but also replaces the current practice of using multiple 3D voxel phantoms and combining multiple dose distributions after Monte Carlo simulations. For routine clinical application of our new approach, the use of fast automatic segmentation algorithms is a must. In order to achieve, simultaneously, both dose accuracy and computation speed, the number of tetrahedrons for the lungs should be optimized. Although the current computation speed of our new 4D Monte Carlo simulation approach is slow (i.e. ~40 times slower than that of the conventional dose accumulation approach), this problem is resolvable by developing, in Geant4, a dedicated navigation class optimized for particle transportation in tetrahedral-mesh geometry.
Effects of classroom instruction on students' understanding of quadratic equations
NASA Astrophysics Data System (ADS)
Vaiyavutjamai, Pongchawee; Clements, M. A. (Ken)
2006-05-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of transcripts of 36 interviews with 18 interviewees (a high performer, a medium performer, and a low performer from each of the six classes), were analysed. Using a rubric for assessing students' understanding, the analysis revealed that at the post-teaching stage students improved their performance on quadratic equations and had a better understanding of associated concepts than they had at the pre-teaching stage. However, many were still confused about the concepts of a variable and of a "solution" to a quadratic equation. After the lessons, most students had acquired neither an instrumental nor a relational understanding of the mathematics associated with solving elementary quadratic equations.
A Projection Neural Network for Constrained Quadratic Minimax Optimization.
Liu, Qingshan; Wang, Jun
2015-11-01
This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.
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.
The generalized quadratic knapsack problem. A neuronal network approach.
Talaván, Pedro M; Yáñez, Javier
2006-05-01
The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Fernández, Francisco M.
2016-06-15
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. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.
Convergence properties of the softassign quadratic assignment algorithm.
Rangarajan, A; Vuille, A; Mjolsness, E
1999-08-15
The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.
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.
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.
Orsi, R. J.; Mahony, R. E.; Moore, J. B.
1999-09-15
This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.
A Model for Quadratic Outliers in Linear Regression.
ERIC Educational Resources Information Center
Elashoff, Janet Dixon; Elashoff, Robert M.
This paper introduces a model for describing outliers (observations which are extreme in some sense or violate the apparent pattern of other observations) in linear regression which can be viewed as a mixture of a quadratic and a linear regression. The maximum likelihood estimators of the parameters in the model are derived and their asymptotic…
Solving quadratic programming problems by delayed projection neural network.
Yang, Yongqing; Cao, Jinde
2006-11-01
In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.
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…
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…
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.
Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.
Wang, Di; Kleinberg, Robert D
2009-11-28
Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.
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.
Entanglement entropy of fermionic quadratic band touching model
NASA Astrophysics Data System (ADS)
Chen, Xiao; Cho, Gil Young; Fradkin, Eduardo
2014-03-01
The entanglement entropy has been proven to be a useful tool to diagnose and characterize strongly correlated systems such as topologically ordered phases and some critical points. Motivated by the successes, we study the entanglement entropy (EE) of a fermionic quadratic band touching model in (2 + 1) dimension. This is a fermionic ``spinor'' model with a finite DOS at k=0 and infinitesimal instabilities. The calculation on two-point correlation functions shows that a Dirac fermion model and the quadratic band touching model both have the asymptotically identical behavior in the long distance limit. This implies that EE for the quadratic band touching model also has an area law as the Dirac fermion. This is in contradiction with the expectation that dense fermi systems with a finite DOS should exhibit LlogL violations to the area law of entanglement entropy (L is the length of the boundary of the sub-region) by analogy with the Fermi surface. We performed numerical calculations of entanglement entropies on a torus of the lattice models for the quadratic band touching point and the Dirac fermion to confirm this. The numerical calculation shows that EE for both cases satisfy the area law. We further verify this result by the analytic calculation on the torus geometry. This work was supported in part by the NSF grant DMR-1064319.
Clustered Self Organising Migrating Algorithm for the Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Davendra, Donald; Zelinka, Ivan; Senkerik, Roman
2009-08-01
An approach of population dynamics and clustering for permutative problems is presented in this paper. Diversity indicators are created from solution ordering and its mapping is shown as an advantage for population control in metaheuristics. Self Organising Migrating Algorithm (SOMA) is modified using this approach and vetted with the Quadratic Assignment Problem (QAP). Extensive experimentation is conducted on benchmark problems in this area.
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…
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.
Evaluating the Contributions of Individual Variables to a Quadratic Form.
Garthwaite, Paul H; Koch, Inge
2016-03-01
Quadratic forms capture multivariate information in a single number, making them useful, for example, in hypothesis testing. When a quadratic form is large and hence interesting, it might be informative to partition the quadratic form into contributions of individual variables. In this paper it is argued that meaningful partitions can be formed, though the precise partition that is determined will depend on the criterion used to select it. An intuitively reasonable criterion is proposed and the partition to which it leads is determined. The partition is based on a transformation that maximises the sum of the correlations between individual variables and the variables to which they transform under a constraint. Properties of the partition, including optimality properties, are examined. The contributions of individual variables to a quadratic form are less clear-cut when variables are collinear, and forming new variables through rotation can lead to greater transparency. The transformation is adapted so that it has an invariance property under such rotation, whereby the assessed contributions are unchanged for variables that the rotation does not affect directly. Application of the partition to Hotelling's one- and two-sample test statistics, Mahalanobis distance and discriminant analysis is described and illustrated through examples. It is shown that bootstrap confidence intervals for the contributions of individual variables to a partition are readily obtained.
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.
Beam steering and routing in quadratic nonlinear media
Aceves, A.B.; Santos, M.C.; Torner, L.
1997-04-01
We show how the spatial phase modulation of weak second-harmonic signals controls the overall direction of propagation of spatial solitons in quadratic nonlinear media. We investigate numerically such a process and discuss its applications to all-optical beam routing. 5 refs., 3 figs.
Finding the Best Quadratic Approximation of a Function
ERIC Educational Resources Information Center
Yang, Yajun; Gordon, Sheldon P.
2011-01-01
This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…
NASA Astrophysics Data System (ADS)
Bonelli, M.; Ferrari, A. C.; Fioravanti, A.; Li Bassi, A.; Miotello, A.; Ossi, P. M.
2002-02-01
Tetrahedral amorphous carbon films have been produced by pulsed laser deposition, at a wavelength of 248 nm, ablating highly oriented pyrolytic graphite at room temperature, in a 10-2 Pa vacuum, at fluences ranging between 0.5 and 35 Jcm-2. Both (100) Si wafers and wafers covered with a SiC polycrystalline interlayer were used as substrates. Film structure was investigated by Raman spectroscopy at different excitation wavelength from 633 nm to 229 nm and by transmission Electron Energy Loss Spectroscopy. The films, which are hydrogen-free, as shown by Fourier Transform Infrared Spectroscopy, undergo a transition from mainly disordered graphitic to up to 80% tetrahedral amorphous carbon (ta-C) above a threshold laser fluence of 5 J cm-2. By X-ray reflectivity roughness, density and cross-sectional layering of selected samples were studied. Film hardness as high as 70 GPa was obtained by nanoindentation on films deposited with the SiC interlayer. By scratch test film adhesion and friction coefficients between 0.06 and 0.11 were measured. By profilometry we obtained residual stress values not higher than 2 GPa in as-deposited 80% sp3 ta-C films.
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.
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.
Octahedral versus tetrahedral coordination of Al in synthetic micas determined by XANES
Mottana, A.; Ventura, G.D.; Robert, J.L.
1997-05-01
We used the JUMBO monochromator at SSRL to measure the Al K-edge X-ray absorption spectra of synthetic micas having variable Al content and occupancy, from 0 to 2/3 in the octahedral M positions, and 0 to 2/3 in the tetrahedral T positions. The measured Al K edges differ markedly, but the differences may have a common explanation: (1) Micas containing 1/3 Al in M or {1/4} Al in T have K edges that differ in the energy and intensity of the first two features, which are related to interaction of Al with its first-shell nearest neighbors (O and OH or F). They are nearly identical to the K edges of reference minerals such as albite (tetrahedral Al only) or grossular (octahedral Al only). (2) Micas containing Al in both M and T have K edges that can be interpreted as a weighed combination of the simple edges. 39 refs., 4 figs., 1 tab.
NASA Astrophysics Data System (ADS)
Durben, Daniel John
The ambient temperature structural and vibrational properties of a series of network forming tetrahedral oxide glasses have been investigated as a function of pressure with Raman spectroscopy. Glass samples were chosen to examine a range of network structures, from the fully polymerized GeO_2, to the partially depolymerized alkali tetrasilicates and disilicates, to the fully depolymerized forsterite. The Raman data suggest that fully polymerized oxide glass structures undergo network cation coordination changes in response to extreme compression through the involvement of bridging oxygens, without requiring bond breaking reactions. Spectral changes observed in partially depolymerized network glass structures are consistent with an increase in Si coordination during compression at the expense of nonbridging oxygens. The pressure range over which the coordination change occurs appears to be controlled by the size and concentration of alkali cations in the structure and depends on a balance between the competing beta-state conversion mechanism at low alkali content and steric considerations at higher alkali content. High pressure structural changes are largely reversible upon decompression, albeit with a large hysteresis. However, the spectra suggest that the breakup of the high coordinated network during the backtransformation to tetrahedral Si coordination occurs without a memory of the original Q -speciation or Si-O ring distribution. Thus, the backtransformation to low coordinated species upon decompression, occurring while the glass is compacted, favors a redistribution of Q-species and ring statistics relative to the original ambient structure.
NASA Astrophysics Data System (ADS)
Pelties, Christian; de la Puente, Josep; Ampuero, Jean-Paul; Brietzke, Gilbert B.; Käser, Martin
2012-02-01
Accurate and efficient numerical methods to simulate dynamic earthquake rupture and wave propagation in complex media and complex fault geometries are needed to address fundamental questions in earthquake dynamics, to integrate seismic and geodetic data into emerging approaches for dynamic source inversion, and to generate realistic physics-based earthquake scenarios for hazard assessment. Modeling of spontaneous earthquake rupture and seismic wave propagation by a high-order discontinuous Galerkin (DG) method combined with an arbitrarily high-order derivatives (ADER) time integration method was introduced in two dimensions by de la Puente et al. (2009). The ADER-DG method enables high accuracy in space and time and discretization by unstructured meshes. Here we extend this method to three-dimensional dynamic rupture problems. The high geometrical flexibility provided by the usage of tetrahedral elements and the lack of spurious mesh reflections in the ADER-DG method allows the refinement of the mesh close to the fault to model the rupture dynamics adequately while concentrating computational resources only where needed. Moreover, ADER-DG does not generate spurious high-frequency perturbations on the fault and hence does not require artificial Kelvin-Voigt damping. We verify our three-dimensional implementation by comparing results of the SCEC TPV3 test problem with two well-established numerical methods, finite differences, and spectral boundary integral. Furthermore, a convergence study is presented to demonstrate the systematic consistency of the method. To illustrate the capabilities of the high-order accurate ADER-DG scheme on unstructured meshes, we simulate an earthquake scenario, inspired by the 1992 Landers earthquake, that includes curved faults, fault branches, and surface topography.
A unified multigrid solver for the Navier-Stokes equations on mixed element meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.
NASA Astrophysics Data System (ADS)
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.
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.
Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Adamian, A.
1988-01-01
An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.
NASA Astrophysics Data System (ADS)
Brahma, Sanjoy; Datta, Biswa
2009-07-01
The partial quadratic eigenvalue assignment problem (PQEVAP) concerns the reassignment of a small number of undesirable eigenvalues of a quadratic matrix pencil, while leaving the remaining large number of eigenvalues and the corresponding eigenvectors unchanged. The problem arises in controlling undesirable resonance in vibrating structures and in stabilizing control systems. The solution of this problem requires computations of a pair of feedback matrices. For practical effectiveness, these feedback matrices must be computed in such a way that their norms and the condition number of the closed-loop eigenvector matrix are as small as possible. These considerations give rise to the minimum norm partial quadratic eigenvalue assignment problem (MNPQEVAP) and the robust partial quadratic eigenvalue assignment problem (RPQEVAP), respectively. In this paper we propose new optimization based algorithms for solving these problems. The problems are solved directly in a second-order setting without resorting to a standard first-order formulation so as to avoid the inversion of a possibly ill-conditioned matrix and the loss of exploitable structures of the original model. The algorithms require the knowledge of only the open-loop eigenvalues to be replaced and their corresponding eigenvectors. The remaining open-loop eigenvalues and their corresponding eigenvectors are kept unchanged. The invariance of the large number of eigenvalues and eigenvectors under feedback is guaranteed by a proven mathematical result. Furthermore, the gradient formulas needed to solve the problems by using the quasi-Newton optimization technique employed are computed in terms of the known quantities only. Above all, the proposed methods do not require the reduction of the model order or the order of the controller, even when the underlying finite element model has a very large degree of freedom. These attractive features, coupled with minimal computational requirements, such as solutions of small
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.
Le Pape, Pierre; Blanchard, Marc; Brest, Jessica; Boulliard, Jean-Claude; Ikogou, Maya; Stetten, Lucie; Wang, Shuaitao; Landrot, Gautier; Morin, Guillaume
2017-01-03
Pyrite is a ubiquitous mineral in reducing environments and is well-known to incorporate trace elements such as Co, Ni, Se, Au, and commonly As. Indeed, As-bearing pyrite is observed in a wide variety of sedimentary environments, making it a major sink for this toxic metalloid. Based on the observation of natural hydrothermal pyrites, As(-I) is usually assigned to the occupation of tetrahedral S(-I) sites, with the same oxidation state as in arsenopyrite (FeAsS), although rare occurrences of As(III) and As(II) have been reported. However, the modes of As incorporation into pyrite during its crystallization under low-temperature diagenetic conditions have not yet been elucidated because arsenic acts as an inhibitor for pyrite nucleation at ambient temperature. Here, we provide evidence from X-ray absorption spectroscopy for As(II,III) incorporation into pyrite at octahedral Fe(II) sites and for As(-I) at tetrahedral S(-I) sites during crystallization at ambient temperature. Extended X-ray absorption fine structure (EXAFS) spectra of these As-bearing pyrites are explained by local structure models obtained using density functional theory (DFT), assuming incorporation of As at the Fe and S sites, as well as local clustering of arsenic. Such observations of As(-I) incorporation at ambient temperature can aid in the understanding of the early formation of authigenic arsenian pyrite in subsurface sediments. Moreover, evidence for substitution of As(II,III) for Fe in our synthetic samples raises questions about both the possible occurrence and the geochemical reactivity of such As-bearing pyrites in low-temperature subsurface environments.
NASA Astrophysics Data System (ADS)
Tang Kai, A.; Annersten, H.; Ericsson, T.
1980-04-01
The MSXα method has been used to calculate the s-electron densities at the nucleus for tetrahedrally coordinated ferric iron, (FeO4)5-, comparing the observed increase in isomer shift values with increasing Fe-O separation. The results give an isomer shift calibration constant of -0.3 (a.u. mm×s-1) assuming a constant ratio for the iron and oxygen sphere radii for the different polyhedra sizes. It is suggested that increasing bonding distances in tetrahedral coordination polyhedra are the dominant factors determining the value of the isomer shifts in Fe-Mg-silicates.
Gravitomagnetic effects in quadratic gravity with a scalar field
NASA Astrophysics Data System (ADS)
Finch, Andrew; Said, Jackson Levi
2016-10-01
The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.
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)].
Three-dimensional modeling of capsule implosions in OMEGA tetrahedral hohlraums
Schnittman, J. D.; Craxton, R. S.
2000-07-01
Tetrahedral hohlraums have been proposed as a means for achieving the highly uniform implosions needed for ignition with inertial confinement fusion (ICF) [J. D. Schnittman and R. S. Craxton, Phys. Plasmas 3, 3786 (1996)]. Recent experiments on the OMEGA laser system have achieved good drive uniformity consistent with theoretical predictions [J. M. Wallace et al., Phys. Rev. Lett. 82, 3807 (1999)]. To better understand these experiments and future investigations of high-convergence ICF implosions, the three-dimensional (3-D) view-factor code BUTTERCUP has been expanded to model the time-dependent radiation transport in the hohlraum and the hydrodynamic implosion of the capsule. Additionally, a 3-D postprocessor has been written to simulate x-ray images of the imploded core. Despite BUTTERCUP's relative simplicity, its predictions for radiation drive temperatures, fusion yields, and core deformation show close agreement with experiment. (c) 2000 American Institute of Physics.
Three-dimensional modeling of capsule implosions in OMEGA tetrahedral hohlraums
NASA Astrophysics Data System (ADS)
Schnittman, J. D.; Craxton, R. S.
2000-07-01
Tetrahedral hohlraums have been proposed as a means for achieving the highly uniform implosions needed for ignition with inertial confinement fusion (ICF) [J. D. Schnittman and R. S. Craxton, Phys. Plasmas 3, 3786 (1996)]. Recent experiments on the OMEGA laser system have achieved good drive uniformity consistent with theoretical predictions [J. M. Wallace et al., Phys. Rev. Lett. 82, 3807 (1999)]. To better understand these experiments and future investigations of high-convergence ICF implosions, the three-dimensional (3-D) view-factor code BUTTERCUP has been expanded to model the time-dependent radiation transport in the hohlraum and the hydrodynamic implosion of the capsule. Additionally, a 3-D postprocessor has been written to simulate x-ray images of the imploded core. Despite BUTTERCUP's relative simplicity, its predictions for radiation drive temperatures, fusion yields, and core deformation show close agreement with experiment.
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.
Supported Tetrahedral Oxo-Sn Catalyst: Single Site, Two Modes of Catalysis
Beletskiy, Evgeny V.; Hou, Xianliang; Shen, Zhongliang; Gallagher, James R.; Miller, Jeffrey T.; Wu, Yuyang; Li, Tiehu; Kung, Mayfair C.; Kung, Harold H.
2016-03-17
Mild calcination in ozone of a (POSS)-Sn- (POSS) complex grafted on silica generated a heterogenized catalyst that mostly retained the tetrahedral coordination of its homogeneous precursor, as evidenced by spectroscopic characterizations using EXAFS, NMR, UV-vis, and DRIFT. The Sn centers are accessible and uniform and can be quantified by stoichiometric pyridine poisoning. This Sn-catalyst is active in hydride transfer reactions as a typical solid Lewis acid. However, the Sn centers can also create Brønsted acidity with alcohol by binding the alcohol strongly as alkoxide and transferring the hydroxyl H to the neighboring Sn-O-Si bond. The resulting acidic silanol is active in epoxide ring opening and acetalization reactions.
NASA Technical Reports Server (NTRS)
Lalvani, Haresh; Collins, Timothy J.
1991-01-01
Morphology (the study of structure and form) of the octahedral-tetrahedral (octet) truss is described. Both the geometry and symmetry of the octet truss are considered. Morphological techniques based on symmetry operations are presented which enable the derivation of reduced-part-count truss configurations from the octet truss by removing struts and nodes. These techniques are unique because their Morphological origination and they allow for the systematic generation and analysis of a large variety of structures. Methods for easily determining the part count and redundancy of infinite truss configurations are presented. Nine examples of truss configurations obtained by applying the derivation techniques are considered. These configurations are structurally stable while at the same time exhibiting significant reductions in part count. Some practical and analytical considerations, such as structural performance, regarding the example reduced-part-count truss geometries are briefly discussed.
NASA Astrophysics Data System (ADS)
Dabiri, Zohreh; Kazempour, Ali; Sadeghzadeh, Mohammad Ali
2016-11-01
The strength of phonon anharmonicity is investigated in the framework of the Density Functional Perturbation Theory via an applied constant electric field. In contrast to routine approaches, we have employed the electric field as an effective probe to quest after the quasi-harmonic and anharmonic effects. Two typical tetrahedral semiconductors (diamond and silicon) have been selected to test the efficiency of this approach. In this scheme the applied field is responsible for establishing the perturbation and also inducing the anharmonicity in systems. The induced polarization is a result of changing the electronic density while ions are located at their ground state coordinates or at a specified strain. Employing this method, physical quantities of the semiconductors are calculated in presence of the electron-phonon interaction directly and, phonon-phonon interaction, indirectly. The present approach, which is in good agreement with previous theoretical and experimental studies, can be introduced as a benchmark to simply investigate the anharmonicity and pertinent consequences in materials.
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.
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.
A generalized quadratic flow law for sheet metals
NASA Astrophysics Data System (ADS)
Jones, S. E.; Gillis, P. P.
1984-01-01
A planar quadratic flow law is proposed for anisotropic sheet materials. This law is similar to the anisotropic strength criterion of Tsai and Wu. It has six experimentally determinable coefficients as compared to four in Hill’s flow law and, thus, allows more experimental information to be accommodated. However, the resulting strain increment vector, while unique, is not necessarily normal to the flow surface.
Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications
NASA Astrophysics Data System (ADS)
Li, Jibin; Feng, Zhaosheng
We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.
Quantum integrals of motion for variable quadratic Hamiltonians
Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.
2010-09-15
We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Design of Linear Quadratic Regulators and Kalman Filters
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L.
1986-01-01
AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.
Quadratic performance index generation for optimal regular design.
NASA Technical Reports Server (NTRS)
Bullock, T. E.; Elder, J. M.
1971-01-01
Application of optimal control theory to practical problems has been limited by the difficulty of prescribing a performance index which accurately reflects design requirements. The task of deriving equivalent performance indices is considered in the present paper for a plant that is a completely controllable, scalar linear system with state feedback. A quadratic index is developed which leads to an optimal design performance satisfying some of the classical performance criteria.
Quantifying tetrahedral adduct formation and stabilization in the cysteine and the serine proteases.
Cleary, Jennifer A; Doherty, William; Evans, Paul; Malthouse, J Paul G
2015-10-01
Two new papain inhibitors have been synthesized where the terminal α-carboxyl groups of Z-Phe-Ala-COOH and Ac-Phe-Gly-COOH have been replaced by a proton to give Z-Phe-Ala-H and Ac-Phe-Gly-H. We show that for papain, replacing the terminal carboxylate group of a peptide inhibitor with a hydrogen atom decreases binding 3-4 fold while replacing an aldehyde or glyoxal group with a hydrogen atom decreases binding by 300,000-1,000,000 fold. Thiohemiacetal formation by papain with aldehyde or glyoxal inhibitors is shown to be ~10,000 times more effective than hemiacetal or hemiketal formation with chymotrypsin. It is shown using effective molarities, that for papain, thiohemiacetal stabilization is more effective with aldehyde inhibitors than with glyoxal inhibitors. The effective molarity obtained when papain is inhibited by an aldehyde inhibitor is similar to the effective molarity obtained when chymotrypsin is inhibited by glyoxal inhibitors showing that both enzymes can stabilize tetrahedral adducts by similar amounts. Therefore the greater potency of aldehyde and glyoxal inhibitors with papain is not due to greater thiohemiacetal stabilization by papain compared to the hemiketal and hemiacetal stabilization by chymotrypsin, instead it reflects the greater intrinsic reactivity of the catalytic thiol group of papain compared to the catalytic hydroxyl group of chymotrypsin. It is argued that while the hemiacetals and thiohemiacetals formed with the serine and cysteine proteases respectively can mimic the catalytic tetrahedral intermediate they are also analogues of the productive and non-productive acyl intermediates that can be formed with the cysteine and serine proteases.
Evaluation of a 3D point cloud tetrahedral tomographic reconstruction method
Pereira, N F; Sitek, A
2011-01-01
Tomographic reconstruction on an irregular grid may be superior to reconstruction on a regular grid. This is achieved through an appropriate choice of the image space model, the selection of an optimal set of points and the use of any available prior information during the reconstruction process. Accordingly, a number of reconstruction-related parameters must be optimized for best performance. In this work, a 3D point cloud tetrahedral mesh reconstruction method is evaluated for quantitative tasks. A linear image model is employed to obtain the reconstruction system matrix and five point generation strategies are studied. The evaluation is performed using the recovery coefficient, as well as voxel- and template-based estimates of bias and variance measures, computed over specific regions in the reconstructed image. A similar analysis is performed for regular grid reconstructions that use voxel basis functions. The maximum likelihood expectation maximization reconstruction algorithm is used. For the tetrahedral reconstructions, of the five point generation methods that are evaluated, three use image priors. For evaluation purposes, an object consisting of overlapping spheres with varying activity is simulated. The exact parallel projection data of this object are obtained analytically using a parallel projector, and multiple Poisson noise realizations of these exact data are generated and reconstructed using the different point generation strategies. The unconstrained nature of point placement in some of the irregular mesh-based reconstruction strategies has superior activity recovery for small, low-contrast image regions. The results show that, with an appropriately generated set of mesh points, the irregular grid reconstruction methods can out-perform reconstructions on a regular grid for mathematical phantoms, in terms of the performance measures evaluated. PMID:20736496
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.
Primal-Dual Interior Methods for Quadratic Programming
NASA Astrophysics Data System (ADS)
Shustrova, Anna
Interior methods are a class of computational methods for solving a con- strained optimization problem. Interior methods follow a continuous path to the solution that passes through the interior of the feasible region (i.e., the set of points that satisfy the constraints). Interior-point methods may also be viewed as methods that replace the constrained problem by a sequence of unconstrained problems in which the objective function is augmented by a weighted "barrier" term that is infinite at the boundary of the feasible region. Convergence to a solution of the constrained problem is achieved by solving a sequence of unconstrained problems in which the weight on the barrier term is steadily reduced to zero. This thesis concerns the formulation and analysis of interior methods for the solution of a quadratic programming (QP) problem, which is an optimization problem with a quadratic objective function and linear constraints. The linear constraints may include an arbitrary mixture of equality and inequality constraints, where the inequality constraints may be subject to lower and/or upper bounds. QP problems arise in a wide variety of applications. An important application is in sequential quadratic programming methods for nonlinear optimization, which involve minimizing a sequence of QP subproblems based on a quadratic approximation of the nonlinear objective function and a set of linearized nonlinear constraints. Two new interior methods for QP are proposed. Each is based on the properties of a barrier function defined in terms of both the primal and dual variables. The first method is suitable for a QP with all inequality constraints. At each iteration, the Newton equations for minimizing a quadratic model of the primal-dual barrier function are reformulated in terms of a symmetric indefinite system of equations that is solved using an inertia controlling factorization. This factorization provides an effective method for the detection and convexification of
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)
The role of fcc tetrahedral subunits in the phase behavior of medium sized Lennard-Jones clusters.
Saika-Voivod, Ivan; Poon, Louis; Bowles, Richard K
2010-08-21
The free energy of a 600-atom Lennard-Jones cluster is calculated as a function of surface and bulk crystallinity in order to study the structural transformations that occur in the core of medium sized clusters. Within the order parameter range studied, we find the existence of two free energy minima at temperatures near freezing. One minimum, at low values of both bulk and surface order, belongs to the liquid phase. The second minimum exhibits a highly ordered core with a disordered surface and is related to structures containing a single fcc-tetrahedral subunit, with an edge length of seven atoms (l=7), located in the particle core. At lower temperatures, a third minimum appears at intermediate values of the bulk order parameter which is shown to be related to the formation of multiple l=6 tetrahedra in the core of the cluster. We also use molecular dynamics simulations to follow a series of nucleation events and find that the clusters freeze to structures containing l=5, 6, 7, and 8 sized tetrahedra as well as those containing no tetrahedral units. The structural correlations between bulk and surface order with the size of the tetrahedral units in the cluster core are examined. Finally, the relationships between the formation of fcc tetrahedral subunits in the core, the phase behavior of medium sized clusters and the nucleation of noncrystalline global structures such as icosahedra and decahedra are discussed.
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.
Asymmetric Simple Exclusion Process with Open Boundaries and Quadratic Harnesses
NASA Astrophysics Data System (ADS)
Bryc, Włodek; Wesołowski, Jacek
2017-02-01
We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.
Neural network for solving convex quadratic bilevel programming problems.
He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie
2014-03-01
In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.
Solving the quadratic assignment problem with clues from nature.
Nissen, V
1994-01-01
This paper describes a new evolutionary approach to solving quadratic assignment problems. The proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies (ES). These methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems, particularly in continuous optimization. The combinatorial variant of ES presented here performs very well on the given test problems as compared with the standard 2-Opt heuristic and results with simulated annealing and tabu search. Extensions for practical applications in factory layout are described.
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.
Restart-Based Genetic Algorithm for the Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Misevicius, Alfonsas
The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.
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.
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.
On stability of the Kasner solution in quadratic gravity
NASA Astrophysics Data System (ADS)
Toporensky, A.; Müller, D.
2017-01-01
We consider the dynamics of a flat anisotropic Universe filled by a perfect fluid near a cosmological singularity in quadratic gravity. Two possible regimes are described—the Kasner anisotropic solution and an isotropic "vacuum radiation" solution which has three sub cases depending on whether the equation of state parameter w is bigger, smaller or equals to 1 / 3. Initial conditions for numerical integrations have been chosen near a General Relativity anisotropic solution with matter (Jacobs solution). We have found that for such initial conditions there is a range of values of the coupling constants so that the resulting cosmological singularity is isotropic.
Compact stellar models obeying quadratic equation of state
NASA Astrophysics Data System (ADS)
Bhar, Piyali; Singh, Ksh. Newton; Pant, Neeraj
2016-10-01
In present paper we obtain a new model of compact star by considering quadratic equation of state for the matter distribution and assuming a physically reasonable choice for metric coefficient g_{rr}. The solution is singularity free and well behaved inside the stellar interior. Several features are described analytically as well as graphically. From our analysis we have shown that our model is compatible with the observational data of the compact stars. We have discussed a detail analysis of neutron star PSR J1614-2230 via different graphs after determining all the constant parameters from boundary conditions.
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).
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.
Split-Cell, Linear Characteristic Transport Method for Unstructured Tetrahedral Meshes
Mathews, Kirk A.; Miller, Rodney L.; Brennan, Charles R.
2000-10-15
The linear characteristic (LC) method is extended to unstructured meshes of tetrahedral cells in three-dimensional Cartesian coordinates. For each ordinate in a discrete ordinates sweep, each cell is split into subcells along a line parallel to the ordinate. Direct affine transformations among appropriate oblique Cartesian coordinate systems for the faces and interior of each cell and subcell are used to simplify the characteristic transport through each subcell. This approach is straightforward and eliminates computationally expensive trigonometric functions. An efficient and well-conditioned technique for evaluating the required integral moments of exponential functions is presented. Various test problems are used to demonstrate (a) the approach to cubic convergence as the mesh is refined, (b) insensitivity to the details of irregular meshes, and (c) numerical robustness. These tests also show that meshes should represent volumes of regions with curved as well as planar boundaries exactly and that cells should have optical thicknesses throughout the mesh that are more or less equal. A hybrid Monte Carlo/discrete ordinates method, together with MCNP, is used to distinguish between error introduced by the angular and the spatial quadratures. We conclude that the LC method should be a practical and reliable scheme for these meshes, presuming that the cells are not optically too thick.
NASA Technical Reports Server (NTRS)
Birnbaum, G.; Borysow, A.; Buechele, A.
1993-01-01
The far infrared absorption of a CH4-N2 mixture was measured at 297, 195, and 162 K from 30 to 650/cm. The spectral invariants gamma1 and alpha1, proportional, respectively, to the zeroth and first spectral moments, due to bimolecular collisions between CH4 and N2 were obtained from these data and compared with theoretical values. The theory for collision-induced dipoles between a tetrahedral and a diatomic or symmetrical linear molecule includes contributions not previously considered. Whereas the theoretical values of gamma1 are only somewhat greater than experiment at all temperatures, the theoretical values of alpha1 are significantly lower than the experimental values. From the theoretical spectral moments for the various induced dipole components, the parameters of the BC shape were computed, and theoretical spectra were constructed. Good agreement was obtained at the lower frequencies, but with increasing frequencies the theoretical spectra were increasingly less intense than the experimental spectra. Although the accuracy of the theoretical results may suffer from the lack of a reliable potential function, it does not appear that this high frequency discrepancy can be removed by any conceivable modification in the potential.
Non-Axial Octupole Deformations and Tetrahedral Symmetry in Heavy Nuclei
Mazurek, Katarzyna; Dudek, Jerzy
2005-11-21
The total energies of about 120 nuclei in the Thorium region have been calculated within the macroscopic-microscopic method in the 5-dimensional space of deformation parameters {alpha}20, {alpha}22, {alpha}30, {alpha}32 and {alpha}40. The macroscopic energy term contains the nuclear surface-curvature dependence as proposed within the LSD approach. The microscopic energies are calculated with the Woods-Saxon single particle potential employing the universal set of parameters.We study a possible presence of the octupole axial and non-axial degrees of freedom all-over in the ({beta}, {gamma})-plane focussing on the ground-states, secondary minima and in the saddle points. In fact, a competition between axial and tri-axial octupole deformation parameters is obtained at the saddle points and in the secondary minima for many isotones with N > 136. The presence of the tetrahedral symmetry minima is predicted in numerous nuclei in the discussed region, although most of the time at relatively high excitation energies.
Chen, Yuanyuan; Farquhar, Erik R.; Chance, Mark R.; Palczewski, Krzysztof; Kiser, Philip D.
2012-07-11
Aminopeptidases are key enzymes involved in the regulation of signaling peptide activity. Here, we present a detailed biochemical and structural analysis of an evolutionary highly conserved aspartyl aminopeptidase called DNPEP. We show that this peptidase can cleave multiple physiologically relevant substrates, including angiotensins, and thus may play a key role in regulating neuron function. Using a combination of x-ray crystallography, x-ray absorption spectroscopy, and single particle electron microscopy analysis, we provide the first detailed structural analysis of DNPEP. We show that this enzyme possesses a binuclear zinc-active site in which one of the zinc ions is readily exchangeable with other divalent cations such as manganese, which strongly stimulates the enzymatic activity of the protein. The plasticity of this metal-binding site suggests a mechanism for regulation of DNPEP activity. We also demonstrate that DNPEP assembles into a functionally relevant tetrahedral complex that restricts access of peptide substrates to the active site. These structural data allow rationalization of the enzyme's preference for short peptide substrates with N-terminal acidic residues. This study provides a structural basis for understanding the physiology and bioinorganic chemistry of DNPEP and other M18 family aminopeptidases.
Friedmann, T.A.; Siegal, M.P.; Tallant, D.R.; Simpson, R.L.; Dominguez, F.
1994-05-01
We are studying carbon thin films by using a pulsed excimer laser to ablate pyrolytic graphite targets to form highly tetrahedral coordinated amorphous carbon ({alpha}t-C) films. These films have been grown on room temperature p-type Si (100) substrates without the intentional incorporation of hydrogen. In order to understand and optimize the growth of {alpha}t-C films, parametric studies of the growth parameters have been performed. We have also introduced various background gases (H{sub 2}, N{sub 2} and Ar) and varied the background gas pressure during deposition. The residual compressive stress levels in the films have been measured and correlated to changes in the Raman spectra of the {alpha}t-C band near 1565 cm{sup {minus}1}. The residual compressive stress falls with gas pressure, indicating a decreasing atomic sp{sup 3}-bonded carbon fraction. We find that reactive gases such as hydrogen and nitrogen significantly alter the Raman spectra at higher pressures. These effects are due to a combination of chemical incorporation of nitrogen and hydrogen into the film as well as collisional cooling of the ablation plume. In contrast, films grown in non-reactive Ar background gases show much less dramatic changes in the Raman spectra at similar pressures.
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.
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.
Adsorption of carbon oxide on tetrahedral bimetallic gold-copper clusters
NASA Astrophysics Data System (ADS)
Gogol', V. V.; Pichugina, D. A.; Kuz'menko, N. E.
2016-12-01
The interaction between carbon oxide and [Au20-nCun]q clusters ( n = 0, 1, 19, 20 and q = 0, ±1) is studied by means of DFT/PBE in the scalar relativistic approximation. To establish the composition and structure of an adsorption site, isomers of bimetallic Au19Cu and AuCu19 particles with different positions of the heteroatom at an apex, edge, and face of the tetrahedral framework are considered. The optimized structures are used as the basis to determine the electronic properties of clusters (average bond energy per atom, difference of energies between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), ionization potential, electron affinity energy). The calculated parameters shrink as the copper content in clusters grows. Among the uncharged models, the highest CO adsorption energy is typical of Au19Cu, the heteroatom of which lies at a cluster's apex. The CO adsorption energy for cationic and anionic clusters grows in comparison to neutral clusters.
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.
A spherical hohlraum design with tetrahedral 4 laser entrance holes and high radiation performance
NASA Astrophysics Data System (ADS)
Jiang, Shaoen; Jing, Longfei; Huang, Yunbao; Li, Haiyan; Huang, Tianxuan; Ding, Yongkun
2016-12-01
As usual cylindrical hohlraum with double laser ring cones may lead to serious laser-plasma interaction, such as the simulated Raman scatter and cross-beam energy transfer effect, spherical hohlraum with octahedral 6 Laser Entrance Holes (LEHs) and single cone laser beams, was investigated and reported to have a consistent high radiation symmetry during the whole implosion process. However, it has several potential challenges such as the smaller space left for diagnosis and the assembly of centrally located capsule. In this paper, based on the view-factor model, we investigate the radiation symmetry and the drive temperature on the capsule located in the spherical hohlraum with tetrahedral 4 LEHs and single cone laser beams, since there is more available space for laser disposition and diagnosis. Then, such target is optimized on the laser beam pointing direction to achieve a high radiation performance, i.e., the radiation symmetry and drive temperature on the capsule. Finally, an optimal spherical hohlraum with optimal laser beam pointing has been demonstrated and compared with the spherical hohlraum with octahedral 6 LEHs. The resulting radiation symmetry and the drive temperature shows that it has almost a similar radiation symmetry (the radiation asymmetry variation is no more than 0.2%), and higher drive temperature (the temperature has been increased by 1.73%, and an additional 133 kJ energy of 2 MJ energy for fusion can be saved).
NASA Astrophysics Data System (ADS)
Jing, Longfei; Huang, Yunbao; Jiang, Shaoen; Li, Haiyan; Huang, Tianxuan; Ding, Yongkun
2016-10-01
As usual cylindrical hohlraum with double laser ring cones may lead to serious CBET effect, spherical hohlraum with octahedral 6 LEHs and single laser ring cone is presented to achieve higher radiation symmetry during the fusion process. However, it has several potential problems such as the long run distance, smaller space is left for diagnose, and the assembly of centrally located capsule. In this paper, we investigate the radiation performance, i.e., radiation symmetry and drive temperature on the capsule in the spherical hohlraum with tetrahedral 4 LEHs and single laser ring cone, since there is more available space for laser disposition and diagnose. Then, such target is optimized on the laser beam pointing direction and shape sizes to achieve high radiation performance, or the radiation symmetry and drive temperature on the capsule. Finally, a novel spherical hohlraum with optimal laser beam pointing and shape size has been demonstrated to have almost similar radiation symmetry (the radiation asymmetry variation is no more than 0.2%), and higher drive temperature (the temperature has been increased by 1.73%, and additional 133 KJ energy of 2MJ energy for fusion can be utilized).. This work was supportedby NSAF#U1430124, and NSFC#51375185, #51405177, #11475154.
NASA Astrophysics Data System (ADS)
Huang, Yunbao; Jing, Longfei; Jiang, Shaoen
2016-10-01
As usual cylindrical hohlraum with double laser ring cones may lead to serious CBET, and LPI effect, spherical hohlraum with octahedral 6 LEHs and single laser ring cone is investigated and presented to achieve higher radiation symmetry during the fusion process. However, it has several potential problems such as the long run distance and the close distance between the spot and their closet LEH for the laser beams, smaller space is left for diagnose, and the assembly of centrally located capsule. In this paper, based on view-factor transportation model, we investigate the radiation symmetry and the drive temperature on the centrally located capsule in the spherical hohlraum with tetrahedral 4 LEHs and single laser ring cone, since there is more available space for laser disposition and diagnose. Then, such target is optimized on the laser beam pointing direction and shape sizes to achieve high radiation performance, or the radiation symmetry and drive temperature on the capsule. Finally, a novel spherical hohlraum with optimal laser beam pointing and shape size has been demonstrated to have almost similar radiation symmetry (the radiation asymmetry variation is no more than 0.2%), and higher drive temperature (the temperature has been increased by 1.73%, and additional 133 KJ energy of 2MJ energy for fusion can be utilized).
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.
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.
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.
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.
Electric current quadratic in an applied electric field
NASA Astrophysics Data System (ADS)
Deyo, Eric
The theory of the photogalvanic effect in a low frequency electric field is developed. We complete the semiclassical theory of the effect in bulk samples lacking inversion symmetry, taking into account contributions from the asymmetry of scattering, the shift current, and the effect of Berry's phase. We consider the effect in such samples both in the presence and absence of a constant magnetic field. It is found that by experimentally measuring this effect, that Berry's curvature and the average shift of the center of mass of an electron during a scattering event can be extracted. We also investigate the magnetic field dependence of the part of the electrical current which is quadratic in voltage in mesoscopic conductors. We find that the part of the current which is quadratic in bias voltage, and linear in an applied magnetic field can be related to the effective electron-electron interaction strength. We also find that in the case when the magnetic field is oriented parallel to the plane of a two dimensional sample, that the spin-orbit scattering rate can be measured.
NASA Astrophysics Data System (ADS)
Jeschke, Anja; Behrens, Jörn
2015-04-01
In tsunami modeling, two different systems of dispersive long wave equations are common: The nonhydrostatic pressure correction for the shallow water equations derived out of the depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of Boussinesq-type equations obtained by an expansion in the nondimensional parameters for nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a linear vertical interpolation of the nonhydrostatic pressure, whereas the second system's derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure. In this case the analytical dispersion relations do not coincide. We show that the nonhydrostatic correction with a quadratic vertical interpolation yields an equation set equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case of a horizontal bottom. Now, both systems yield the same analytical dispersion relation according up to the first order with the reference dispersion relation of the linear wave theory. The adjusted model is also compared to other Boussinesq-type equations. The numerical model with the nonhydrostatic correction for the shallow water equations uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element space discretization. The numerical dispersion relations are computed and compared by employing a testcase of a standing wave in a closed basin. All numerical values match their theoretical expectations. This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support given by Geir K. Petersen from the University of Oslo.
Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
NASA Astrophysics Data System (ADS)
Neumeyer, S.; Sorokin, V. S.; Thomsen, J. J.
2017-01-01
We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing-Mathieu equation with appended quadratic nonlinearity is considered as the model system, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic nonlinearities may generate additional amplitude-frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi-stability in the amplitude-phase characteristics are predicted, supporting previously reported experimental observations.
Synthesis of tetrahedral quasi-type-II CdSe-CdS core-shell quantum dots.
Sugunan, Abhilash; Zhao, Yichen; Mitra, Somak; Dong, Lin; Li, Shanghua; Popov, Sergei; Marcinkevicius, Saulius; Toprak, Muhammet S; Muhammed, Mamoun
2011-10-21
Synthesis of colloidal nanocrystals of II-VI semiconductor materials has been refined in recent decades and their size dependent optoelectronic properties have been well established. Here we report a facile synthesis of CdSe-CdS core-shell heterostructures using a two-step hot injection process. Red-shifts in absorption and photoluminescence spectra show that the obtained quantum dots have quasi-type-II alignment of energy levels. The obtained nanocrystals have a heterostructure with a large and highly faceted tetrahedral CdS shell grown epitaxially over a spherical CdSe core. The obtained morphology as well as high resolution electron microscopy confirms that the tetrahedral shell have a zinc blende crystal structure. A phenomenological mechanism for the growth and morphology of the nanocrystals is discussed.
Bruno, Rosaria; Vallejo, Julia; Marino, Nadia; De Munno, Giovanni; Krzystek, J; Cano, Joan; Pardo, Emilio; Armentano, Donatella
2017-02-20
A family of tetrahedral mononuclear Co(II) complexes with the cytosine nucleobase ligand is used as the playground for an in-depth study of the effects that the nature of the ligand, as well as their noninnocent distortions on the Co(II) environment, may have on the slow magnetic relaxation effects. Hence, those compounds with greater distortion from the ideal tetrahedral geometry showed a larger-magnitude axial magnetic anisotropy (D) together with a high rhombicity factor (E/D), and thus, slow magnetic relaxation effects also appear. In turn, the more symmetric compound possesses a much smaller value of the D parameter and, consequently, lacks single-ion magnet behavior.
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.
Hepburn, Iain; Cannon, Robert; De Schutter, Erik
2013-01-01
We describe a novel method for calculating the quasi-static electrical potential on tetrahedral meshes, which we call E-Field. The E-Field method is implemented in STEPS, which performs stochastic spatial reaction-diffusion computations in tetrahedral-based cellular geometry reconstructions. This provides a level of integration between electrical excitability and spatial molecular dynamics in realistic cellular morphology not previously achievable. Deterministic solutions are also possible. By performing the Rallpack tests we demonstrate the accuracy of the E-Field method. Efficient node ordering is an important practical consideration, and we find that a breadth-first search provides the best solutions, although principal axis ordering suffices for some geometries. We discuss potential applications and possible future directions, and predict that the E-Field implementation in STEPS will play an important role in the future of multiscale neural simulations.
Hepburn, Iain; Cannon, Robert; De Schutter, Erik
2013-01-01
We describe a novel method for calculating the quasi-static electrical potential on tetrahedral meshes, which we call E-Field. The E-Field method is implemented in STEPS, which performs stochastic spatial reaction-diffusion computations in tetrahedral-based cellular geometry reconstructions. This provides a level of integration between electrical excitability and spatial molecular dynamics in realistic cellular morphology not previously achievable. Deterministic solutions are also possible. By performing the Rallpack tests we demonstrate the accuracy of the E-Field method. Efficient node ordering is an important practical consideration, and we find that a breadth-first search provides the best solutions, although principal axis ordering suffices for some geometries. We discuss potential applications and possible future directions, and predict that the E-Field implementation in STEPS will play an important role in the future of multiscale neural simulations. PMID:24194715
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.
Integrability of Quadratic Non-autonomous Quantum Linear Systems
NASA Astrophysics Data System (ADS)
Lopez, Raquel
The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is
NASA Astrophysics Data System (ADS)
Han, Yifeng; Ye, Xuanhong; Zhu, Hong; Li, Yuexiang; Kuang, Xiaojun
2017-03-01
Ba6Na2M2Mn2O17 (M=Nb, Ta) oxides were synthesized by high-temperature solid-state reaction. The compounds adopt 6-layer perovskite-related structure (referred to as 6C) in P 3 ̅m1, analogous to Ba6Na2Nb2P2O17. The 6C structure consists of cubic (c) BaO3 layers and pseudo-cubic (c') oxygen-vacancy-ordered BaO2 layers stacked according to a sequence of c'ccccc. Ordering of oxygen vacancies in oxygen-deficient c'-BaO2 layers leads to two successive isolated tetrahedral layers, which stabilize an unusual +5 oxidation state for Mn cations in the tetrahedral sites. In Ba6Na2M2Mn2O17, these two Mn5+O4 layers are sandwiched by two single octahedral NaO6 layers that connected by two successive octahedral NbO6 layers, forming alternative 2:1-ordered (Ba3NaM2O9)- and (Ba3NaMn2O8)+ perovskite-like units along the stacking direction. The Mn5+O4 tetrahedral units act as a turquoise chromophore in Ba6Na2M2Mn2O17, making these two compounds potential turquoise-coloring materials for the cool pigments.
Ghose, J.; Murthy, K.S.R.C.
1996-09-01
In studies of CO oxidation on substituted copper chromite spinel oxide catalyst decreases as the Cu{sup 2+} content of the catalyst decreases, either by substitution with a divalent ion, i.e., Cu{sub 1-x} Mg{sub x} [Cr{sub 2}]O{sub 4}, or by reduction of Cu{sup 2+} to Cu{sup 1+}. Crystallographic studies have shown that Cu[Cr{sub 2}]O{sub 4} changes from normal to partially inverse when Cr{sup 3+} is replaced by Al{sup 3+}. Thus, in aluminum-substituted copper chromite catalysts, copper is present on both tetrahedral and octahedral sites of the spinel lattice, i.e., Cu{sub 1-x}Al{sub x} [Cu{sub x}Cr{sub 2-(x+y)}Al{sub y}]O{sub 4}. ESCA studies have shown that upon Al substitution some of the tetrahedral Cu{sup 2+} ions are reduced to Cu{sup 1+} and this causes a reduction in the catalytic activity of the catalysts. The present work was taken up to compare the activity of Cu{sup 2+} on tetrahedral sites with that on octahedral sites of the spinel oxide catalysts. For this, CO oxidation studies were carried out on the inverse spinel CuFe{sub 2}O{sub 4} and on the normal spinel CuRh{sub 2}O{sub 4} catalysts. 7 refs., 1 fig.
Anderson, K.S.; Sammons, R.D.; Leo, G.C.; Sikorski, J.A. ); Benesi, A.J.; Johnson, K.A. )
1990-02-13
Direct observation of the tetrahedral intermediate in the EPSP synthase reaction pathway was provided by {sup 13}C NMR by examining the species bound to the enzyme active site under internal equilibrium conditions and using (2-{sup 13}C)PEP as a spectroscopic probe. The tetrahedral center of the intermediate bound to the enzyme gave a unique signal appearing at 104 ppm. Separate signals were observed for free EPSP and EPSP bound to the enzyme in a ternary complex with phosphate. These peak assignments account for the quantitation of the species bound to the enzyme and liberated upon quenching with either triethylamine or base. A comparison of quenching with acid, base, or triethylamine was conducted. After long times of incubation during the NMR measurement, a signal at 107 ppm appeared. The compound giving rise to this resonance was isolated and identified as an EPSP ketal. The rate of formation of the EPSP ketal was very slow establishing that it is a side product of the normal enzymatic reaction. To look for additional signals that might arise from a covalent adduct which has been postulated to arise from reaction of enzyme with PEP, and NMR experiment was performed with an analogue of S3P lacking the 4- and 5-hydroxyl groups. All of these results reaffirm identification of the tetrahedral species as the only observable intermediate in the EPSP synthase reaction.
Gong K.; Vukmirovic M.B.; Ma C.; Zhu Y.; Adzic R.R.
2011-11-01
We synthesized the Pt monolayer shell-Pd tetrahedral core electrocatalysts that are notable for their high activity and stable performance. A small number of low-coordination sites and defects, and high content of the (1 1 1)-oriented facets on Pd tetrahedron makes them a suitable support for a Pt monolayer to obtain an active O{sub 2} reduction reaction (ORR) electrocatalyst. The surfactants, used to control size and shape of Pd tetrahedral nanoparticles, are difficult to remove and cause adverse effects on the ORR. We describe a simple and noninvasive method to synthesize high-purity tetrahedral Pd nanocrystals (TH Pd) by combining a hydrothermal route and CO adsorption-induced removal of surfactants. Poly(vinylpyrrolidone) (PVP), used as a protecting and reducing agent in hydrothermal reactions, is strongly bonded to the surface of the resulting nanocrystals. We demonstrate that PVP was displaced efficiently by adsorbed CO. A clean surface was achieved upon CO stripping at a high potential (1.0 V vs RHE). It played a decisive role in improving the activity of the Pt monolayer/TH Pd electrocatalyst for the ORR. Furthermore, the results demonstrate a versatile method for removal of surfactants from various nanoparticles that severely limited their applications.
NASA Astrophysics Data System (ADS)
Zhao, Jie; Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
2017-01-01
We develop a multidimensionally constrained relativistic Hartree-Bogoliubov (MDC-RHB) model in which the pairing correlations are taken into account by making the Bogoliubov transformation. In this model, the nuclear shape is assumed to be invariant under the reversion of x and y axes; i.e., the intrinsic symmetry group is V4 and all shape degrees of freedom βλ μ with even μ are included self-consistently. The RHB equation is solved in an axially deformed harmonic oscillator basis. A separable pairing force of finite range is adopted in the MDC-RHB model. The potential energy curves of neutron-rich even-even Zr isotopes are calculated with relativistic functionals DD-PC1 and PC-PK1 and possible tetrahedral shapes in the ground and isomeric states are investigated. The ground state shape of 110Zr is predicted to be tetrahedral with both functionals and so is that of 112Zr with the functional DD-PC1. The tetrahedral ground states are caused by large energy gaps around Z =40 and N =70 when β32 deformation is included. Although the inclusion of the β30 deformation can also reduce the energy around β20=0 and lead to minima with pear-like shapes for nuclei around 110Zr, these minima are unstable due to their shallowness.
Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential
NASA Astrophysics Data System (ADS)
Leonenko, N. N.; Ruiz-Medina, M. D.
2006-07-01
The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.
Octahedral-tetrahedral equilibrium and solvent exchange of cobalt(II) ions in primary alkylamines.
Aizawa, Sen-ichi; Funahashi, Shigenobu
2002-08-26
The enthalpy differences (Delta H degrees ) of the equilibrium between the octahedral and tetrahedral solvated cobalt(II) complexes were obtained in some primary alkylamines such as propylamine (pa, 36.1 +/- 2.3 kJ mol(-1)), n-hexylamine (ha, 34.9 +/- 1.0 kJ mol(-1)), 2-methoxyethylamine (meea, 44.8 +/- 3.1 kJ mol(-1)), and benzylamine (ba, 50.1 +/- 3.6 kJ mol(-1)) by the spectrophotometric method. The differences in the energy levels between the two geometries of the cobalt(II) complexes in the spherically symmetric field (Delta E(spher)) were estimated from the values of Delta H degrees by offsetting the ligand field stabilization energies. It was indicated that the value of Delta E(spher) is the decisive factor in determining the value of Delta H degrees and is largely dependent on the electronic repulsion between the d-electrons and the donor atoms and the interelectronic repulsion in the d orbitals. The comparison between activation enthalpies (Delta H(++)) for the solvent exchange reactions of octahedral cobalt(II) ions in pa and meea revealed that the unexpectedly large rate constant and small Delta H(++) in pa are attributed to the strong electronic repulsion in the ground state and removal of the electronic repulsion in the dissociative transition state, which can give the small Delta E(spher) between the ground and transition states. Differences in the solvent exchange rates and the DeltaH(++) values of the octahedral metal(II) ions in some other solvents are discussed in connection with the electronic repulsive factors.
NASA Astrophysics Data System (ADS)
Paiva Fonseca, Gabriel; Landry, Guillaume; White, Shane; D'Amours, Michel; Yoriyaz, Hélio; Beaulieu, Luc; Reniers, Brigitte; Verhaegen, Frank
2014-10-01
Accounting for brachytherapy applicator attenuation is part of the recommendations from the recent report of AAPM Task Group 186. To do so, model based dose calculation algorithms require accurate modelling of the applicator geometry. This can be non-trivial in the case of irregularly shaped applicators such as the Fletcher Williamson gynaecological applicator or balloon applicators with possibly irregular shapes employed in accelerated partial breast irradiation (APBI) performed using electronic brachytherapy sources (EBS). While many of these applicators can be modelled using constructive solid geometry (CSG), the latter may be difficult and time-consuming. Alternatively, these complex geometries can be modelled using tessellated geometries such as tetrahedral meshes (mesh geometries (MG)). Recent versions of Monte Carlo (MC) codes Geant4 and MCNP6 allow for the use of MG. The goal of this work was to model a series of applicators relevant to brachytherapy using MG. Applicators designed for 192Ir sources and 50 kV EBS were studied; a shielded vaginal applicator, a shielded Fletcher Williamson applicator and an APBI balloon applicator. All applicators were modelled in Geant4 and MCNP6 using MG and CSG for dose calculations. CSG derived dose distributions were considered as reference and used to validate MG models by comparing dose distribution ratios. In general agreement within 1% for the dose calculations was observed for all applicators between MG and CSG and between codes when considering volumes inside the 25% isodose surface. When compared to CSG, MG required longer computation times by a factor of at least 2 for MC simulations using the same code. MCNP6 calculation times were more than ten times shorter than Geant4 in some cases. In conclusion we presented methods allowing for high fidelity modelling with results equivalent to CSG. To the best of our knowledge MG offers the most accurate representation of an irregular APBI balloon applicator.
The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry
NASA Astrophysics Data System (ADS)
Noya, Eva G.; Vega, Carlos; Doye, Jonathan P. K.; Louis, Ard A.
2010-06-01
The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values of the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centered-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centered-cubic crystal becomes more stable than the body-centered-cubic crystal, and at higher temperatures, a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centered-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centered-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centered-cubic crystal and between the fluid and the diamond crystal show that at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles.
Simple shearing flow of dry soap foams with TCP structure[Tetrahedrally Close-Packed
REINELT,DOUGLAS A.; KRAYNIK,ANDREW M.
2000-02-16
The microrheology of dry soap foams subjected to large, quasistatic, simple shearing deformations is analyzed. Two different monodisperse foams with tetrahedrally close-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Laves (C15). The elastic-plastic response is evaluated by calculating foam structures that minimize total surface area at each value of strain. The minimal surfaces are computed with the Surface Evolver program developed by Brakke. The foam geometry and macroscopic stress are piecewise continuous functions of strain. The stress scales as T/V{sup 1/3} where T is surface tension and V is cell volume. Each discontinuity corresponds to large changes in foam geometry and topology that restore equilibrium to unstable configurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a small increase in strain changes the energy profile in the neighborhood of a foam structure from a local minimum to a saddle point, which can lead to symmetry-breaking bifurcations. In general, the new foam topology associated with each stable solution branch results from a cascade of local topology changes called T1 transitions. Each T1 cascade produces different cell neighbors, reduces surface energy, and provides an irreversible, film-level mechanism for plastic yield behavior. Stress-strain curves and average stresses are evaluated by examining foam orientations that admit strain-periodic behavior. For some orientations, the deformation cycle includes Kelvin cells instead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and can even cause strain localization.
The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry.
Noya, Eva G; Vega, Carlos; Doye, Jonathan P K; Louis, Ard A
2010-06-21
The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values of the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centered-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centered-cubic crystal becomes more stable than the body-centered-cubic crystal, and at higher temperatures, a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centered-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centered-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centered-cubic crystal and between the fluid and the diamond crystal show that at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles.
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.
Peltola, Emilia; Wester, Niklas; Holt, Katherine B; Johansson, Leena-Sisko; Koskinen, Jari; Myllymäki, Vesa; Laurila, Tomi
2017-02-15
We hypothesize that by using integrated carbon nanostructures on tetrahedral amorphous carbon (ta-C), it is possible to take the performance and characteristics of these bioelectrodes to a completely new level. The integrated carbon electrodes were realized by combining nanodiamonds (NDs) with ta-C thin films coated on Ti-coated Si-substrates. NDs were functionalized with mixture of carboxyl and amine groups NDandante or amine NDamine, carboxyl NDvox or hydroxyl groups NDH and drop-casted or spray-coated onto substrate. By utilizing these novel structures we show that (i) the detection limit for dopamine can be improved by two orders of magnitude [from 10µM to 50nM] in comparison to ta-C thin film electrodes and (ii) the coating method significantly affects electrochemical properties of NDs and (iii) the ND coatings selectively promote cell viability. NDandante and NDH showed most promising electrochemical properties. The viability of human mesenchymal stem cells and osteoblastic SaOS-2 cells was increased on all ND surfaces, whereas the viability of mouse neural stem cells and rat neuroblastic cells was improved on NDandante and NDH and reduced on NDamine and NDvox. The viability of C6 cells remained unchanged, indicating that these surfaces will not cause excess gliosis. In summary, we demonstrated here that by using functionalized NDs on ta-C thin films we can significantly improve sensitivity towards dopamine as well as selectively promote cell viability. Thus, these novel carbon nanostructures provide an interesting concept for development of various in vivo targeted sensor solutions.
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.
Tetrahedral Clusters of GaMo 4S 8-Type Compounds: A Metal Bonding Analysis
NASA Astrophysics Data System (ADS)
Le Beuze, A.; Loirat, H.; Zerrouki, M. C.; Lissillour, R.
1995-11-01
Extended Hückel tight binding calculations have been performed on ligated as well as on ligand-free Mo4 and Mo6 extended frames, in order to analyze the metal-metal bonding within the clusters and particularly the appreciable changes of the metal-metal bond lengths through the M4 tetrahedral units contained in GaM4X8 (M = Mo, Nb, V, Ta; X = S, Se, Te), Mo4S4Y4 (Y = Cl, Br, I). A comparison with the M6 octahedral units of the M Mo6X8 (M = Pb, Ag, La; X = S, Se) series is made. By means of DOS, COOP curves, and overlap populations, results clearly display the strong reorganization of the electronic structure of the bare metal clusters network while the ligand interactions occur, inducing a strong reduction of the strength of the metal-metal bonds. We outline the relationship between the metal-metal bond lengths and various parameters such as the valence electron count (VEC) per cluster and the nature of the ligands. Our results indicate that the two series M4 and M6 differ: M-M bond lengths are unaffected by the VEC in the regular M4 cluster, whereas some M-M bond lengths undergo a significant change when the VEC increases in the distorded M6 clusters. Likewise, it is worthy to note that metal d orbitals have a more significant effect in M4 cluster series. In contrast, the metal-ligand covalency induces similar elongations of metal-metal bonds in the two series.
Importance of Tetrahedral Iron during Microbial Reduction of Clay Mineral NAu-2
NASA Astrophysics Data System (ADS)
Shi, B.; Wu, L.; Liu, K.; Smeaton, C. M.; Li, W.; Beard, B. L.; Johnson, C.; Roden, E. E.; Van Cappellen, P.
2015-12-01
Transformations between Fe(II) and Fe(III) in ferruginous clay minerals significantly impact the physicochemical properties of soils and sediments, such as the ion exchange capacity and redox potential. An increasing number of studies have focused on clay minerals that undergo redox changes, however, none have so far addressed Fe isotope fractionation during these processes. In this study, Fe isotope fractionations were determined during microbial reduction of Fe(III) in nontronite NAu-2 with different concentrations of lactate. No secondary Fe-bearing minerals, including Fe oxides, were detected by SEM in over 100 days of incubation, suggesting that the measured fractionations only reflected the net isotope effect associated with the clay minerals. The initial reduction likely started from edge sites, and the reductive dissolution released aqueous Fe(II). Basal plane sorbed Fe(II) was detectable after the extent of Fe reduction exceeded 5% and extensive electron transfer and isotope exchange had occurred between basal plane sorbed Fe(II) and structural Fe(III). With lower concentrations of the lactate(40 mM), the maximum Fe isotope fractionation was larger (∆56Febasal Fe(II)-structure Fe(III)= -4.37‰), consistent with greater adsorption than in systems with more lactate. After the Fe in reactive sites was all reduced, isotope exchange between Fe(II) and structural Fe(III) was inhibited due to blockage of electron transfer pathways by the collapse of the clay layers. The results agree with another study in our group on microbial reduction of NAu-1, despite both the smaller extent of reduction (~10% vs. 22% max bioreduction for NAu-1 and NAu-2, respectively) and smaller isotope fractionation factor than for NAu-2. We speculate that tetrahedral Fe in NAu-2 may have accelerated the electron transfer between Fe atoms, thus inducing a higher extent of reduction and a larger Fe isotope fractionation compared to NAu-1.
Longitudinal force distribution using quadratically constrained linear programming
NASA Astrophysics Data System (ADS)
Klomp, M.
2011-12-01
In this paper, a new method is presented for the optimisation of force distribution for combined traction/braking and cornering. In order to provide a general, simple and flexible problem formulation, the optimisation is addressed as a quadratically constrained linear programming (QCLP) problem. Apart from fast numerical solutions, different driveline configurations can be included in the QCLP problem in a very straightforward fashion. The optimisation of the distribution of the individual wheel forces using the quasi-steady-state assumption is known to be useful for the study of the influence of particular driveline configurations on the combined lateral and longitudinal grip envelope of a particular vehicle-driveline configuration. The addition of the QCLP problem formulation makes another powerful tool available to the vehicle dynamics analyst to perform such studies.
A quadratic-shaped-finger comb parametric resonator
NASA Astrophysics Data System (ADS)
Guo, Congzhong; Fedder, Gary K.
2013-09-01
A large-stroke (8 µm) parametric resonator excited by an in-plane ‘shaped-finger’ electrostatic comb drive is fabricated using a 15 µm thick silicon-on-insulator microelectromechanical systems (SOI-MEMS) process. A quadratic capacitance-engagement response is synthesized by engineering a custom-shaped comb finger profile. A folded-flexure suspension allows lateral motion while constraining rotational modes. The excitation of the nonlinear parametric resonance is realized by selecting an appropriate combination of the linear and cubic electrostatic stiffness coefficients through a specific varying-gap comb-finger design. The large-amplitude parametric resonance promotes high signal-to-noise ratio for potential use in sensitive chemical gravimetric sensors, strain gauges, and mode-matched gyroscope applications.
Consultant-Guided Search Algorithms for the Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Iordache, Serban
Consultant-Guided Search (CGS) is a recent swarm intelligence metaheuristic for combinatorial optimization problems, inspired by the way real people make decisions based on advice received from consultants. Until now, CGS has been successfully applied to the Traveling Salesman Problem. Because a good metaheuristic should be able to tackle efficiently a large variety of problems, it is important to see how CGS behaves when applied to other classes of problems. In this paper, we propose an algorithm for the Quadratic Assignment Problem (QAP), which hybridizes CGS with a local search procedure. Our experimental results show that CGS is able to compete in terms of solution quality with one of the best Ant Colony Optimization algorithms, the MAX-MIN Ant System.
Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories
NASA Astrophysics Data System (ADS)
Adamson, L. N. C.; Osbaldestin, A. H.
2014-03-01
We present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisation approach for quadratic irrational trajectories. Depending on the nature of the barrier, this leads to either self-similar or chaotic behaviour. In the self-similar case we give an analysis of the half barrier and present a detailed calculation of the locations, asymptotic heights and signs of the main peaks in the autocorrelation function. Then we consider arbitrary barriers, illustrating that typically these give rise to chaotic correlations of the autocorrelation function which we further represent by showing the invariant sets associated with these correlations. Our main ingredient here is a functional recurrence which has been previously derived and used in work on the Harper equation, strange non-chaotic attractors and a quasi-periodically forced two-level system.
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.
Repopulation Kinetics and the Linear-Quadratic Model
NASA Astrophysics Data System (ADS)
O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.
2009-08-01
The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.
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.
Cosmology for quadratic gravity in generalized Weyl geometry
Jiménez, Jose Beltrán; Heisenberg, Lavinia; Koivisto, Tomi S.
2016-04-26
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.
Nonlinear equality constraints in feasible sequential quadratic programming
Lawrence, C.; Tits, A.
1994-12-31
In this talk we show that convergence of a feasible sequential quadratic programming algorithm modified to handle smooth nonlinear equality constraints. The modification of the algorithm to incorporate equality constraints is based on a scheme proposed by Mayne and Polak and is implemented in fsqp/cfsqp, an optimization package that generates feasible iterates. Nonlinear equality constraints are treated as {open_quotes}{<=}-type constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function which penalizes negative values. For example, the problem minimize f(x) s.t. h(x) = 0, with h(x) a scalar, is replaced by minimize f(x) - ch(x) s.t. h(x) {<=} 0. The modified problem is equivalent to the original problem when c is large enough (but finite). Such a value is determined automatically via iterative adjustments.
Qualitative analysis of certain generalized classes of quadratic oscillator systems
Bagchi, Bijan Ghosh, Samiran Pal, Barnali Poria, Swarup
2016-02-15
We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56, 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ, the other points to a centre for λ < 0 but a saddle λ > 0. On the other hand, the second potential reveals only a center for both the signs of λ from a linear stability analysis. We carry out our study by extending Quesne’s scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term fcosωt.
Adiabatic theory, Liapunov exponents, and rotation number for quadratic Hamiltonians
NASA Astrophysics Data System (ADS)
Delyon, François; Foulon, Patrick
1987-11-01
We consider the adiabatic problem for general time-dependent quadratic Hamiltonians and develop a method quite different from WKB. In particular, we apply our results to the Schrödinger equation in a strip. We show that there exists a first regular step (avoiding resonance problems) providing one adiabatic invariant, bounds on the Liapunov exponents, and estimates on the rotation number at any order of the perturbation theory. The further step is shown to be equivalent to a quantum adiabatic problem, which, by the usual adiabatic techniques, provides the other possible adiabatic invariants. In the special case of the Schrödinger equation our method is simpler and more powerful than the WKB techniques.
Confidence set inference with a prior quadratic bound
NASA Technical Reports Server (NTRS)
Backus, George E.
1988-01-01
In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.
Blind deconvolution estimation of fluorescence measurements through quadratic programming
NASA Astrophysics Data System (ADS)
Campos-Delgado, Daniel U.; Gutierrez-Navarro, Omar; Arce-Santana, Edgar R.; Skala, Melissa C.; Walsh, Alex J.; Jo, Javier A.
2015-07-01
Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.
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.
Hamilton, Tamara D; Bucar, Dejan-Kresimir; MacGillivray, Leonard R
2007-04-28
An achiral ligand, synthesized in the solid state via a coded hydrogen bond-directed organic synthesis, self-assembles with Cu(II) ions to form a chiral tetrahedral capsule that hosts an anion as a guest.
NASA Astrophysics Data System (ADS)
Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.
2014-11-01
By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.
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.
ERIC Educational Resources Information Center
Ozaltun Celik, Aytug; Bukova Guzel, Esra
2017-01-01
The quadratic function is an important concept for calculus but the students at high school have many difficulties related to this concept. It is important that the teaching of the quadratic function is realized considering the students' thinking. In this context, the aim of this study conducted through a qualitative case study is to reveal the…
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2012-01-01
In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…
ERIC Educational Resources Information Center
Ellis, Amy B.; Grinstead, Paul
2008-01-01
This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…
ERIC Educational Resources Information Center
Strickland, Tricia K.; Maccini, Paula
2013-01-01
The current study focuses on the effects of incorporating multiple visual representations on students' conceptual understanding of quadratic expressions embedded within area word problems and students' procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the…
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.
Stoddard, Mary Caswell; Prum, Richard O
2008-06-01
We use a tetrahedral color space to describe and analyze male plumage color variation and evolution in a clade of New World buntings--Cyanocompsa and Passerina (Aves: Cardinalidae). The Goldsmith color space models the relative stimulation of the four retinal cones, using the integrals of the product of plumage reflectance spectra and cone sensitivity functions. A color is represented as a vector defined by the relative stimulation of the four cone types--ultraviolet, blue, green, and red. Color vectors are plotted in a tetrahedral, or quaternary, plot with the achromatic point at the origin and the ultraviolet/violet channel along the Z-axis. Each color vector is specified by the spherical coordinates theta, phi, and r. Hue is given by the angles theta and phi. Chroma is given by the magnitude of r, the distance from the achromatic origin. Color vectors of all distinct patches in a plumage characterize the plumage color phenotype. We describe the variation in color space occupancy of male bunting plumages, using various measures of color contrast, hue contrast and diversity, and chroma. Comparative phylogenetic analyses using linear parsimony (in MacClade) and generalized least squares (GLS) models (in CONTINUOUS) with a molecular phylogeny of the group document that plumage color evolution in the clade has been very dynamic. The single best-fit GLS evolutionary model of plumage color variation over the entire clade is a directional change model with no phylogenetic correlation among species. However, phylogenetic innovations in feather color production mechanisms--derived pheomelanin and carotenoid expression in two lineages--created new opportunities to colonize novel areas of color space and fostered the explosive differentiation in plumage color. Comparison of the tetrahedral color space of Goldsmith with that of Endler and Mielke demonstrates that both provide essentially identical results. Evolution of avian ultraviolet/violet opsin sensitivity in relation
Zhou, B B; Chong, A; Wise, F W; Bache, M
2012-07-27
Cascaded nonlinearities have attracted much interest, but ultrafast applications have been seriously hampered by the simultaneous requirements of being near phase matching and having ultrafast femtosecond response times. Here we show that in strongly phase-mismatched nonlinear frequency conversion crystals the pump pulse can experience a large and extremely broadband self-defocusing cascaded Kerr-like nonlinearity. The large cascaded nonlinearity is ensured through interaction with the largest quadratic tensor element in the crystal, and the strong phase mismatch ensures an ultrafast nonlinear response with an octave-spanning bandwidth. We verify this experimentally by showing few-cycle soliton compression with noncritical cascaded second-harmonic generation: Energetic 47 fs infrared pulses are compressed in a just 1-mm long bulk lithium niobate crystal to 17 fs (under 4 optical cycles) with 80% efficiency, and upon further propagation an octave-spanning supercontinuum is observed. Such ultrafast cascading is expected to occur for a broad range of pump wavelengths spanning the near- and mid-IR using standard nonlinear crystals.
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.
Memetic algorithms for the unconstrained binary quadratic programming problem.
Merz, Peter; Katayama, Kengo
2004-12-01
This paper presents a memetic algorithm, a highly effective evolutionary algorithm incorporating local search for solving the unconstrained binary quadratic programming problem (BQP). To justify the approach, a fitness landscape analysis is conducted experimentally for several instances of the BQP. The results of the analysis show that recombination-based variation operators are well suited for the evolutionary algorithms with local search. Therefore, the proposed approach includes--besides a highly effective randomized k-opt local search--a new variation operator that has been tailored specially for the application in the hybrid evolutionary framework. The operator is called innovative variation and is fundamentally different from traditional crossover operators, since new genetic material is included in the offspring which is not contained in one of the parents. The evolutionary heuristic is tested on 35 publicly available BQP instances, and it is shown experimentally that the algorithm is capable of finding best-known solutions to large BQPs in a short time and with a high frequency. In comparison to other approaches for the BQP, the approach appears to be much more effective, particularly for large instances of 1000 or 2500 binary variables.
A Neurodynamic Optimization Approach to Bilevel Quadratic Programming.
Qin, Sitian; Le, Xinyi; Wang, Jun
2016-08-19
This paper presents a neurodynamic optimization approach to bilevel quadratic programming (BQP). Based on the Karush-Kuhn-Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). It is proved that the global solution of the MPCC is the minimal one of the optimal solutions to multiple convex optimization subproblems. A recurrent neural network is developed for solving these convex optimization subproblems. From any initial state, the state of the proposed neural network is convergent to an equilibrium point of the neural network, which is just the optimal solution of the convex optimization subproblem. Compared with existing recurrent neural networks for BQP, the proposed neural network is guaranteed for delivering the exact optimal solutions to any convex BQP problems. Moreover, it is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time. Finally, three numerical examples are elaborated to substantiate the efficacy of the proposed approach.
Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube
NASA Astrophysics Data System (ADS)
Mittelmann, Hans; Peng, Jiming; Wu, Xiaolin
2009-07-01
In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs. Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.
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.
Quadratic Fermi node in a 3D strongly correlated semimetal
Kondo, Takeshi; Nakayama, M.; Chen, R.; ...
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
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).
Two simple approximations to the distributions of quadratic forms.
Yuan, Ke-Hai; Bentler, Peter M
2010-05-01
Many test statistics are asymptotically equivalent to quadratic forms of normal variables, which are further equivalent to T = sigma(d)(i=1) lambda(i)z(i)(2) with z(i) being independent and following N(0,1). Two approximations to the distribution of T have been implemented in popular software and are widely used in evaluating various models. It is important to know how accurate these approximations are when compared to each other and to the exact distribution of T. The paper systematically studies the quality of the two approximations and examines the effect of the lambda(i) and the degrees of freedom d by analysis and Monte Carlo. The results imply that the adjusted distribution for T can be as good as knowing its exact distribution. When the coefficient of variation of the lambda(i) is small, the rescaled statistic T(R) = dT/(sigma(d)(i=1) lambda(i)) is also adequate for practical model inference. But comparing T(R) against chi2(d) will inflate type I errors when substantial differences exist among the lambda(i), especially, when d is also large.
The Quadratic Spinor Lagrangian, Axial Torsion Current and Generalizations
NASA Astrophysics Data System (ADS)
Da Rocha, R.; Pereira, J. G.
We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field — Weyl, Majorana, flagpole, or flag-dipole spinor fields — yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.
Bright nonlocal quadratic solitons induced by boundary confinement
NASA Astrophysics Data System (ADS)
Zheng, Yizhou; Gao, Yan; Wang, Jing; Lv, Fang; Lu, Daquan; Hu, Wei
2017-01-01
Under the Dirichlet boundary conditions, a family of bright quadratic solitons exists in the regime where the second harmonic can be regarded as the refractive index of the fundamental wave with an oscillatory nonlocal response. By simplifying the governing equations into the Snyder-Mitchell mode, the approximate analytical solutions are obtained. Taking them as the initial guess and using a numerical code, we found two branches of bright solitons, of which the beam width increases (branch I) and decreases (branch II) with the increase of the sample size, respectively. If the nonlocality is fixed and the sample size is varied, the soliton width varies piecewise and approximately periodically. In each period, solitons only exist in a small range of sample size. Single-hump fundamental wave solitons with the same beam width in narrower samples can be, if the second harmonics are connected smoothly, jointed to be a multihump soliton in a wider sample whose size is the sum of those for the narrower ones. The dynamical simulation shows that the found solitons are unstable.
Monitoring bioeroding sponges: using rubble, Quadrat, or intercept surveys?
Schönberg, C H L
2015-04-01
Relating to recent environmental changes, bioerosion rates of calcium carbonate materials appear to be increasing worldwide, often driven by sponges that cause bioerosion and are recognized bioindicators for coral reef health. Various field methods were compared to encourage more vigorous research on bioeroding sponges and their inclusion in major monitoring projects. The rubble technique developed by Holmes et al. (2000) had drawbacks often due to small specimen sizes: it was time-costly, generated large variation, and created a biased impression about dominant species. Quadrat surveys were most rapid but overestimated cover of small specimens. Line intercepts are recommended as easiest, least spatially biased, and most accurate, especially when comparing results from different observers. Intercepts required fewer samples and provided the best statistical efficiency, evidenced by better significances and test power. Bioeroding sponge abundances and biodiversities are influenced by water depth, sediment quality, and most importantly by availability of suitable attached substrate. Any related data should thus be standardized to amount of suitable substrate to allow comparison between different environments, concentrating on dominant, easily recognized species to avoid bias due to experience of observers.
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.; 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.
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.
Mechanical cooling in single-photon optomechanics with quadratic nonlinearity
NASA Astrophysics Data System (ADS)
Gu, Wen-ju; Yi, Zhen; Sun, Li-hui; Xu, Da-hai
2015-08-01
In the paper we study the nonlinear mechanical cooling processes in an intrinsic quadratically optomechanical coupling system without linearizing the optomechanical interaction. We apply scattering theory to calculate the transition rates between different mechanical Fock states using the resolvent of the Hamiltonian, which allows for a direct identification of the underlying physical processes, where only even-phonon transitions are permitted and odd-phonon transitions are forbidden. We verify the feasibility of the approach by comparing the steady-state mean phonon number obtained from transition rates with the simulation of the full quantum master equation, and also discuss the analytical results in the weak coupling limit that coincide with two-phonon mechanical cooling processes. Furthermore, to evaluate the statistical properties of steady mechanical state, we respectively apply the Mandel Q parameter to show that the oscillator can be in nonclassical mechanical states, and the phonon number fluctuations F to display that the even-phonon transitions favor suppressing the phonon number fluctuations compared to the linear coupling optomechanical system.
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
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)
Kaarour, A.; Ouardi, O.; Meskine, M.
2015-03-01
The use of tensor models adapted to tetrahedral molecules such CH4, SiH4, GeH4... that use mathematical tools (group theory, irreducible tensor operators) and the characteristics of symmetrical molecules, gives good results. Starting from an experimental spectrum, we can calculate some parameters of the Hamiltonian and consequently the energy levels. Once the line positions are determined, we calculate the parameters of the dipole moment of these molecules and consequently the rovibrational intensities. Both software STDS and SPVIEW, we determined the parameters of the Hamiltonian and those of the dipole moment.
Structural study of GeS2 glass: Reverse Monte Carlo modelling for edge-sharing tetrahedral network
NASA Astrophysics Data System (ADS)
Itoh, Keiji
2017-04-01
The pulsed neutron diffraction and reverse Monte Carlo (RMC) modelling methods were used to investigate the structure of GeS2 glass. The high-resolution real-space neutron data shows that there is a negligible amount of chemical disorder in the structure of GeS2 glass. The RMC modelling was done by fitting to the neutron total structure factor with constraints for the edge- and corner-sharing tetrahedral configurations as well as the nearest neighbour coordination numbers. Two different structure models (two-dimensional layer network and three-dimensional random network) were examined and both the models reproduced the experimental data.
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
NASA Astrophysics Data System (ADS)
Jenkins, D. M.; Lei, J.
2013-12-01
The sodium content in the M4 site of amphibole (BNa) was calibrated by Brown (1977, J Petrol, 18, 53-72) in a study that continues to be highly cited to this day. This study, based on empirical observations of amphibole compositional changes in the presence of the buffering assemblage plagioclase, chlorite, epidote, iron oxide, and water, demonstrated a systematic variation in the BNa and tetrahedral Al (TAl) content with pressure. Recent experimental work in this lab aimed at defining the extent of miscibility along the tremolite-glaucophane and hornblende-glaucophane joins in the Na2O-CaO-MgO-Al2O3-SiO2-H2O system has provided some additional information on the cation mixing along these joins. These joins also serve as the chemically-simplified framework of the BNa versus TAl correlation reported by Brown (1977). There are now sufficient, though still a bare minimum, of experimentally-confirmed mixing data for sodium-rich amphiboles to test this correlation and for quantifying the pressure-temperature (P-T) dependence of amphibole compositions in metamafic rocks relevant to subduction zones. From experimental results obtained over the range of 500-800°C, 1.5-2.0 GPa, and using a variety of amphibole synthesis and re-equilibration methods, the following set of asymmetric formalism (ASF) macroscopic interaction and mixing parameters have been derived that can be used with THERMOCALC dataset 55: Wtrgl = 70 kJ, Wglts = Wtrts =20 kJ, α(tr) = 1.0, α(ts) = 1.2, and α(gl) = 0.52. Using a fixed MORB bulk composition, the composition of amphiboles within the P-T stability field of the buffering assemblage were calculated for the above chemical system with FeO added (i.e., NCFMASH) over the range of 0.2 - 2.0 GPa and 400 - 700°C. The following main observations can be made. First, the empirical amphibole compositions at low TAl and high BNa contents are well modeled by the miscibility gap in the amphibole ternary sub-system tremolite
The fifteen theorem for universal Hermitian lattices over imaginary quadratic fields
NASA Astrophysics Data System (ADS)
Kim, Byeong Moon; Kim, Ji Young; Park, Poo-Sung
2010-04-01
We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields Q(√{-m}) for all m . For each imaginary quadratic field Q(√{-m}) , we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13, 14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneeberger's fifteen theorem and ours is the number 13. In addition, we determine the minimal rank of universal Hermitian lattices for all imaginary quadratic fields.
Peng, Haowei; Ndione, Paul F.; Ginley, David S.; ...
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
NASA Astrophysics Data System (ADS)
Peng, Haowei; Ndione, Paul F.; Ginley, David S.; Zakutayev, Andriy; Lany, Stephan
2015-04-01
Transition metal oxides play important roles as contact and electrode materials, but their use as active layers in solar energy conversion requires achieving semiconducting properties akin to those of conventional semiconductors like Si or GaAs. In particular, efficient bipolar carrier transport is a challenge in these materials. Based on the prediction that a tetrahedral polymorph of MnO should have such desirable semiconducting properties, and the possibility to overcome thermodynamic solubility limits by nonequilibrium thin-film growth, we exploit both structure-property and composition-structure relationships to design and realize novel wurtzite-structure Mn1 -xZnxO alloys. At Zn compositions above x ≈0.3 , thin films of these alloys assume the tetrahedral wurtzite structure instead of the octahedral rocksalt structure of MnO, thereby enabling semiconductor properties that are unique among transition metal oxides, i.e., a band gap within the visible spectrum, a band-transport mechanism for both electron and hole carriers, electron doping, and a band lineup suitable for solar hydrogen generation. A proof of principle is provided by initial photo-electrocatalytic device measurements, corroborating, in particular, the predicted favorable hole-transport properties of these alloys.
Gustin, Léa; Hosaka, Yoshiteru; Tassel, Cédric; Aharen, Tomoko; Shimakawa, Yuichi; Kageyama, Hiroshi; Wiley, John B
2016-11-07
Synthesis, characterization, and thermal modification of the new layered perovskite FeLa2Ti3O10 have been studied. FeLa2Ti3O10 was prepared by ion exchange of the triple-layered Ruddlesden-Popper phase Li2La2Ti3O10 with FeCl2 at 350 °C under static vacuum. Rietveld refinement on synchrotron X-ray diffraction data indicates that the new phase is isostructural with CoLa2Ti3O10, where Fe(II) cations occupy slightly compressed/flattened interlayer tetrahedral sites. Magnetic measurements on FeLa2Ti3O10 display Curie-Weiss behavior at high temperatures and a spin-glass transition at lower temperatures (<30 K). Thermal treatment in oxygen shows that FeLa2Ti3O10 undergoes a significant cell contraction (Δc ≈ -2.7 Å) with a change in the oxidation state of iron (Fe(2+) to Fe(3+)); structural analysis and Mössbauer studies indicate that upon oxidation the local iron environment goes from tetrahedral to octahedral coordination with some deintercalation of iron as Fe2O3 to produce Fe0.67La2Ti3O10.
Scheiner, S; Kleier, D A; Lipscomb, W N
1975-01-01
The charge relay ststem and its role in the acylation of serine proteinases is studied using the partial retention of diatomic differential overlap (PRDDO) technique to perform approximate ab initio molecular orbital calculations on a model of the enzyme-substrate complex. The aspartate in the charge relay system is seen to act as the ultimate proton acceptor during the charging of the serine nucleophile. A projection of the potential energy surface is obtained in a subspace corresponding to this charge transfer and to the coupled motions of active site residues and the substrate. These results together with extended basis set results for cruder models suggest that a concerted transfer of protons from Ser-195 to His-57 and from His-57 to Asp-102 occurs with an energy barrier of 20-25 kcal/mole (84-105 kJ/mole). The subsequent nucleophilic attack on the scissile peptide linkage by the charged serine is then seen to proceed energetically downhill to the tetrahedral intermediate. The formation of the tetrahedral intermediate from the Michaelis complex is calculated to be nearly thermoneutral. PMID:1058476
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.
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
Moments for general quadratic densities in n dimensions
Furman, Miguel A.
2002-03-20
We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.
Gravity waves from non-minimal quadratic inflation
Pallis, Constantinos; Shafi, Qaisar
2015-03-12
We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio 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.
Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid
ERIC Educational Resources Information Center
Brilleslyper, Michael A.
2004-01-01
Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.
Detection of spatial variations in temporal trends with a quadratic function.
Moraga, Paula; Kulldorff, Martin
2016-08-01
Methods for the assessment of spatial variations in temporal trends (SVTT) are important tools for disease surveillance, which can help governments to formulate programs to prevent diseases, and measure the progress, impact, and efficacy of preventive efforts already in operation. The linear SVTT method is designed to detect areas with unusual different disease linear trends. In some situations, however, its estimation trend procedure can lead to wrong conclusions. In this article, the quadratic SVTT method is proposed as alternative of the linear SVTT method. The quadratic method provides better estimates of the real trends, and increases the power of detection in situations where the linear SVTT method fails. A performance comparison between the linear and quadratic methods is provided to help illustrate their respective properties. The quadratic method is applied to detect unusual different cervical cancer trends in white women in the United States, over the period 1969 to 1995.
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.
Zhang, Xin; Zhang, Xu; Johnson, Jacob A.; Chen, Yu-Sheng; Zhang, Jian
2016-06-24
Two non-interpenetrated zirconium metal–organic frameworks (Zr-MOFs), NPF-200 and NPF-201, were synthesized via the assembly of elongated tetrahedral linkers with Zr_{6} and Zr_{8} clusters. They represent the first examples of MOFs to have the β-UH_{3}-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.
Models of quadratic quantum algebras and their relation to classical superintegrable systems
Kalnins, E. G.; Miller, W.; Post, S.
2009-05-15
We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.
Flight Control System Design by Quadratic Stabilization with Partial Pole Placement
NASA Astrophysics Data System (ADS)
Satoh, Atsushi; Sugimoto, Kenji
The most fundamental requirements for flight control system are ensuring robust stability and improving flying quality. Quadratic stabilization is a powerful technique ensuring robust stability against parameter change of aircraft due to flight condition. Furthermore, flying quality requirements are regarded as eigenstructure assignment specifications. This paper proposes a new design method of feedback gain which simultaneously achieves quadratic stabilization and partial pole placement. This design method is reduced to a numerical optimization problem including linear matrix inequality (LMI) constraints.
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.
Optimal Control Using Pontryagin's Maximum Principle in a Linear Quadratic Differential Game
NASA Astrophysics Data System (ADS)
Khakestari, Marzieh; Ibragimov, Gafurjan; Suleiman, Mohamed
This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.
Sequential design of discrete linear quadratic regulators via optimal root-locus techniques
NASA Technical Reports Server (NTRS)
Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar
1989-01-01
A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.
Controller design for nonlinear quadratic Markov jumping systems with input saturation
NASA Astrophysics Data System (ADS)
Chen, Fu; Xu, Shengyuan; Zou, Yun; Xu, Huiling
2014-01-01
This paper deals with the controller design problem of nonlinear quadratic Markov jumping systems with input saturation. Both mode-dependent and mode-independent state feedback controllers are designed. By using the concept of domain of attraction in mean square sense, sufficient conditions for stochastic stabilisation for nonlinear quadratic systems are derived in terms of linear matrix inequalities. Certain existing results are improved. Simulation examples are presented to illustrate the effectiveness of the proposed technique.
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
Robust and reliable control via quadratic Lyapunov functions
NASA Astrophysics Data System (ADS)
Alt, Terry Robert
In this dissertation we present a new approach to design robust and reliable controllers. Our results are used to find control laws for systems that are subject to (1) real polytopic and norm bounded uncertainties, (2) actuator and sensor variations and (3) actuator and sensor failure. In addition, we present conditions that can be added to the control design problem to constrain the controller to be stable or strictly positive real, further strengthening the robustness and reliability of the control design. The basic framework relies on the use of quadratic Lyapunov functions to accommodate potentially time varying uncertainty. Conditions are derived that, when satisfied, allow a robust control design to be obtained by performing two convex optimizations. These controllers recover the performance robustness of either state feedback or full information controllers. Sufficient conditions are presented that remove the non-convexity in terms of the control design variables. This allows a robust control design to be obtained by solving a set of linear matrix inequalities. These general robustness results are then applied to the reliability problem. Actuator and sensor variations are modeled using real polytopic uncertainties. It is shown that under some simplifying assumptions the state feedback problem reduces to a single linear matrix inequality. It also shows that the Riccati equations for standard LQR and Hsb{infty} need only a slight modification to obtain a control law that is reliable with respect to actuator variability. For the output feedback case, convex conditions are presented that yield controllers which are reliable to actuator and sensor variations. Utilizing the simultaneous Lyapunov function approach, we further extend these results to include actuator or sensor failure. Additionally, when applicable, stronger reliability guaranties may be obtained by constraining the controller to be strictly positive real. This guarantees stability for positive real
NASA Astrophysics Data System (ADS)
Chen, T. H.; Wang, K. X.; Luo, W. L.; Yuan, Z. Y.; Wang, J. Z.; Ding, D. T.; Li, H. X.; Hu, C.
1996-04-01
For the zeolite offretite, a formula is proposed which includes the framework Si/Al ratio ( R), the partitioning ratio of Al over two crystallographically non-equivalent tetrahedral sites ( r) and intensities of the observed peaks in the 29Si MAS NMR spectrum. By this formula, the framework Si/Al ratio of offretite can be estimated from the 29Si MAS NMR spectrum. Combined with chemical analysis of the Si/Al ratio, Al partitioning in two kinds of T sites can also be deduced. It is concluded that the T B sites are favored by Al atoms in parent offretites and Al atoms at T B sites can more easily be substituted isomorphously by Si when treated with (NH 4) 2SiF 6. The formula proposed here is based only on experiments and may be used to testify some statistical models of Al distributions in offretites.
Morra, Elena; Giamello, Elio; Chiesa, Mario
2014-06-10
Transition-metal ions with open-shell configurations hold promise in the development of novel coordination chemistry and potentially unprecedented redox catalysis. Framework-substituted Ti(3+) ions with tetrahedral coordination are generated by reductive activation of titanium silicalite-1 with triethylaluminum, an indispensable co-catalyst for heterogeneous Ziegler-Natta polymerization catalysts. Continuous-wave and pulse electron paramagnetic resonance methods are applied to unravel details on the local environment of the reduced transition metal-ions, which are shown to be part of the silica framework by detection of (29)Si hyperfine interactions. The chemical accessibility of the reduced sites is probed using ammonia as probe molecule. Evidence is found for the coordination of a single ammonia molecule. Comparison to similar systems, such as TiAlPO-5, reveals clear differences in the coordination chemistry of the reduced Ti sites in the two solids, which may be understood considering the different electronic properties of the solid frameworks.
Argent, Stephen P; Adams, Harry; Riis-Johannessen, Thomas; Jeffery, John C; Harding, Lindsay P; Ward, Michael D
2006-01-11
Two new types of coordination cage have been prepared and structurally characterized: [M16(mu-L1)24]X32 are based on a tetra-capped truncated tetrahedral core and have a bridging ligand L1 along each of the 24 edges; [M12(mu-L1)12(mu3-L2)4]X24 are based on a cuboctahedral core which is supported by a combination of face-capping ligands L2 and edge-bridging ligands L1. The difference between the two illustrates how combinations of ligands with different coordination modes can generate coordination cages which are not available using one ligand type on its own.
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
Structural and Thermal Properties of Elementary and Binary Tetrahedral Semiconductor Nanoparticles
NASA Astrophysics Data System (ADS)
Omar, M. S.
2016-01-01
We report an equation free from fitting parameters as a direct calculation of size-dependent mean bond length for group IV and compounds from the III-V and II-VI binary groups. Size-dependent melting temperature and thermal expansion are also investigated for some materials forming the groups mentioned above. The empirical relation, which is obtained from fitting experimental data of melting enthalpy, is used to recalculate their values as well as entropy. The nanosize dependence of lattice thermal expansion for elements forming group IV is analyzed according to the hard sphere model, while mean ionicity is used for groups III-V and II-VI.
NASA Astrophysics Data System (ADS)
Jing, Longfei; Jiang, Shaoen; Kuang, Longyu; Zhang, Lu; Li, Liling; Lin, Zhiwei; Li, Hang; Zheng, Jianhua; Hu, Feng; Huang, Yunbao; Huang, Tianxuan; Ding, Yongkun
2017-04-01
A tetrahedral hohlraum with four half-cylindrical cavities (FHCH) is proposed to balance tradeoffs among the drive symmetry, coupling efficiency, and plasma filling of the hohlraum performance for indirectly driven inertial confinement fusion. The peak drive symmetry in the FHCH with a cavity-to-capsule ratio (CCR) of 2.2 is comparable to those in the spherical hohlraum of CCR = 4.5 with six laser entrance holes (6LEHs-Sph.) ((Lan et al 2014 Phys. Plasmas 21 010704) and three-axis cylindrical hohlraum (6LEHs-Cyls.) of CCR = 2.0 (Kuang et al 2016 Sci. Rep. 6 34636), and the filling time of plasma is close to the ones in the 6LEHs-Cyls. and the ignition target Rev5-CH of the national ignition campaign, and about half of that in the 6LEHs-Sph. In particular, the coupling efficiency is about 19% and 16% higher than those of the 6LEHs-Sph. and 6LEHs-Cyls., respectively. Besides, preliminary study indicates that the FHCH has a robust symmetry to uncertainties of power imbalance and pointing errors of laser beams. Furthermore, utilizing the FHCH, the feasibility of a tetrahedral indirect drive approach on the national ignition facility and hybrid indirect–direct drive approach with the laser arrangement designed specially for 6LEHs-Sph. or 6LEHs-Cyls., is also envisioned. Therefore, the proposed hohlraum configuration merits consideration as an alternative route to indirect-drive ignition.
Vaidya, Shefali; Tewary, Subrata; Singh, Saurabh Kumar; Langley, Stuart K; Murray, Keith S; Lan, Yanhua; Wernsdorfer, Wolfgang; Rajaraman, Gopalan; Shanmugam, Maheswaran
2016-10-03
A family of mononuclear tetrahedral cobalt(II) thiourea complexes, [Co(L1)4](NO3)2 (1) and [Co(Lx)4](ClO4)2 where x = 2 (2), 3 (3), 4 (4) (where L1 = thiourea, L2 = 1,3-dibutylthiourea, L3 = 1,3-phenylethylthiourea, and L4 = 1,1,3,3-tetramethylthiourea), has been synthesized using a rationally designed synthetic approach, with the aim of stabilizing an Ising-type magnetic anisotropy (-D). On the basis of direct-current, alternating-current, and hysteresis magnetic measurements and theoretical calculations, we have identified the factors that govern the sign and magnitude of D and ultimately the ability to design a single-ion magnet for a tetrahedral cobalt(II) ion. To better understand the magnetization relaxation dynamics, particularly for complexes 1 and 2, dilution experiments were performed using their diamagnetic analogues, which are characterized by single-crystal X-ray diffraction with the general molecular formulas of [Zn(L1)4](NO3)2 (5) and [Zn(L2)4](ClO4)2 (6). Interestingly, intermolecular interactions are shown to play a role in quenching the quantum tunneling of magnetization in zero field, as evidenced in the hysteresis loop of 1. Complex 2 exhibits the largest Ueff value of 62 cm(-1) and reveals open hysteresis loops below 4 K. Furthermore, the influence of the hyperfine interaction on the magnetization relaxation dynamics is witnessed in the hysteresis loops, allowing us to determine the electron/nuclear spin S(Co) = (3)/2/I(Co) = (7)/2 hyperfine coupling constant of 550 MHz, a method ideally suited to determine the hyperfine coupling constant of highly anisotropic metal ions stabilized with large D value, which are otherwise hard to determine by conventional methods such as electron paramagnetic resonance.
Strečka, Jozef; Rojas, Onofre; Verkholyak, Taras; Lyra, Marcelo L
2014-02-01
The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model.
NASA 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.
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
Statistical power of latent growth curve models to detect quadratic growth.
Diallo, Thierno M O; Morin, Alexandre J S; Parker, Philip D
2014-06-01
Latent curve models (LCMs) have been used extensively to analyze longitudinal data. However, little is known about the power of LCMs to detect nonlinear trends when they are present in the data. For this study, we utilized simulated data to investigate the power of LCMs to detect the mean of the quadratic slope, Type I error rates, and rates of nonconvergence during the estimation of quadratic LCMs. Five factors were examined: the number of time points, growth magnitude, interindividual variability, sample size, and the R (2)s of the measured variables. The results showed that the empirical Type I error rates were close to the nominal value of 5 %. The empirical power to detect the mean of the quadratic slope was affected by the simulation factors. Finally, a substantial proportion of samples failed to converge under conditions of no to small variation in the quadratic factor, small sample sizes, and small R (2) of the repeated measures. In general, we recommended that quadratic LCMs be based on samples of (a) at least 250 but ideally 400, when four measurement points are available; (b) at least 100 but ideally 150, when six measurement points are available; (c) at least 50 but ideally 100, when ten measurement points are available.
Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu
2014-01-27
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.
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.
NASA Astrophysics Data System (ADS)
Helser, Terry L.
2003-04-01
This puzzle uses the symbols of 39 elements to spell the names of 25 animals found in zoos. Underlined spaces and the names of the elements serve as clues. To solve the puzzle, students must find the symbols that correspond to the elemental names and rearrange them into the animals' names.
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.
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.
Chang, Weng-Long
2012-03-01
Assume that n is a positive integer. If there is an integer such that M (2) ≡ C (mod n), i.e., the congruence has a solution, then C is said to be a quadratic congruence (mod n). If the congruence does not have a solution, then C is said to be a quadratic noncongruence (mod n). The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithm's submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.
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.
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.
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.
High-order Finite Element Analysis of Boundary Layer Flows
NASA Astrophysics Data System (ADS)
Zhang, Alvin; Sahni, Onkar
2014-11-01
Numerical analysis of boundary layer flows requires careful approximations, specifically the use of a mesh with layered and graded elements near the (viscous) walls. This is referred to as a boundary layer mesh, which for complex geometries is composed of triangular elements on the walls that are inflated or extruded into the volume along the wall-normal direction up to a desired height while the rest of the domain is filled with unstructured tetrahedral elements. Linear elements with C0 inter-element continuity are employed and in some situations higher order C0 elements are also used. However, these elements only enforce continuity whereas high-order smoothness is not attained as will be the case with C1 inter-element continuity and higher. As a result, C0 elements result in a poor approximation of the high-order boundary layer behavior. To achieve greater inter-element continuity in boundary layer region, we employ B-spline basis functions along the wall-normal direction (i.e., only in the layered portion of the mesh). In the rest of the fully unstructured mesh, linear or higher order C0 elements are used as appropriate. In this study we demonstrate the benefits of finite-element analysis based on such higher order and continuity basis functions for boundary layer flows.
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
NASA Astrophysics Data System (ADS)
Bicken, Gurcan
This dissertation deals with the analysis and identification of quadratic non-linearities in hydrodynamic transport problems arising in engineering and science. As representative application areas, homogenous oscillations of electron and ion plasmas in a 1-D periodic domain and the forced voltage-current dynamics of a semiconductor device are considered. The time series data obtained from numerical solutions of the associated hydrodynamic equations are used for the spectral analysis of the quadratic nonlinearities in these respective systems. More specifically, electron plasma oscillations are analyzed using power spectra and cross-bicoherency spectra to gain insight into the quadratic interactions predicted by a simple model of the energy transfer that cascades from lower modes to higher modes within a small amplitude range of oscillations. The efficiency of the bicoherency function in detecting the quadratic wave interactions from the complex time series of the mode amplitudes is observed. The difference in the modal interactions for isentropic and isothermal plasma models are investigated based on numerical 'experiments' simulating the modal dynamics in each case. Furthermore, the concentration oscillations of cold ion plasmas in a Lagrangian frame are analyzed for different Debye lengths. The detailed effects of linear and nonlinear mechanisms in the hydrodynamic model on the power spectra of the oscillations are investigated. Second-order Volterra models are considered for approximating the dynamics of input-output systems with quadratic nonlinear terms. The linear and quadratic kernels of the Volterra model are estimated using multi- tone inputs and least-squares minimization. The implications of the non-orthogonality of the model are investigated in detail. To circumvent the negative effects of non-orthogonality on the accuracy of the kernel estimation, an 'odd-even' separation technique is utilized in the kernel estimation. This approach for estimating an
NASA Astrophysics Data System (ADS)
Kortan, Victoria Ramaker
It has become increasingly apparent that the future of electronic devices can and will rely on the functionality provided by single or few dopant atoms. The most scalable physical system for quantum technologies, i.e. sensing, communication and computation, are spins in crystal lattices. Diamond is an excellent host crystal offering long room temperature spin coherence times and there has been exceptional experimental work done with the nitrogen vacancy center in diamond demonstrating many forms of spin control. Transition metal dopants have additional advantages, large spin-orbit interaction and internal core levels, that are not present in the nitrogen vacancy center. This work explores the implications of the internal degrees of freedom associated with the core d levels using a tight-binding model and the Koster-Slater technique. The core d levels split into two separate symmetry states in tetrahedral bonding environments and result in two levels with different wavefunction spatial extents. For 4 d semiconductors, e.g. GaAs, this is reproduced in the tight-binding model by adding a set of d orbitals on the location of the transition metal impurity and modifying the hopping parameters from impurity to its nearest neighbors. This model does not work in the case of 3d semiconductors, e.g. diamond, where there is no physical reason to drastically alter the hopping from 3 d dopant to host and the difference in wavefunction extent is not as pronounced. In the case of iron dopants in gallium arsenide the split symmetry levels in the band gap are responsible for a decrease in tunneling current when measured with a scanning tunneling microscope due to interference between two elastic tunneling paths and comparison between wavefunction measurements and tight-binding calculations provides information regarding material parameters. In the case of transition metal dopants in diamond there is less distinction between the symmetry split d levels. When considering pairs of
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
Parameter estimation of optical fringes with quadratic phase using the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Lu, Ming-Feng; Zhang, Feng; Tao, Ran; Ni, Guo-Qiang; Bai, Ting-Zhu; Yang, Wen-Ming
2015-11-01
Optical fringes with a quadratic phase are often encountered in optical metrology. Parameter estimation of such fringes plays an important role in interferometric measurements. A novel method is proposed for accurate and direct parameter estimation using the fractional Fourier transform (FRFT), even in the presence of noise and obstacles. We take Newton's rings fringe patterns and electronic speckle pattern interferometry (ESPI) interferograms as classic examples of optical fringes that have a quadratic phase and present simulation and experimental results demonstrating the performance of the proposed method.
A Branch and Bound Based Heuristic for Solving the Quadratic Assignment Problem,
1981-10-01
the Quadratic Assignment Problem M. S. Bazaraa and 0. Kirca FDRC-81-13 V Contract N~o. N00014-8O-k-0709 A Branch and Bound Based Heuristic for...Solving the Quadratic Assignment Problem M. S. Bazaraa and 0. Kirca Abstract I\\ .... In this paper a branch and bound algorithm is proposed for solving the...concept of branch and bound or im- plicit enumeration, as in the works of Gilmore (1962), Lawler (1963), Craves and Whinston (1970), Bazaraa and Elshafei
A new one-layer neural network for linear and quadratic programming.
Gao, Xingbao; Liao, Li-Zhi
2010-06-01
In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective function is convex on the set defined by equality constraints. Compared with existing one-layer neural networks for quadratic programming problems, the proposed neural network has the least neurons and requires weak stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.
Design of variable-weight quadratic congruence code for optical CDMA
NASA Astrophysics Data System (ADS)
Feng, Gang; Cheng, Wen-Qing; Chen, Fu-Jun
2015-09-01
A variable-weight code family referred to as variable-weight quadratic congruence code (VWQCC) is constructed by algebraic transformation for incoherent synchronous optical code division multiple access (OCDMA) systems. Compared with quadratic congruence code (QCC), VWQCC doubles the code cardinality and provides the multiple code-sets with variable code-weight. Moreover, the bit-error rate (BER) performance of VWQCC is superior to those of conventional variable-weight codes by removing or padding pulses under the same chip power assumption. The experiment results show that VWQCC can be well applied to the OCDMA with quality of service (QoS) requirements.
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.
NASA Technical Reports Server (NTRS)
Fleming, P.
1983-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.
NASA Astrophysics Data System (ADS)
Bai, Zheng-Jian; Yang, Jin-Ku; Datta, Biswa Nath
2016-12-01
In this paper, we consider the robust partial quadratic eigenvalue assignment problem in vibration by active feedback control. Based on the receptance measurements and the system matrices, we propose an optimization method for the robust and minimum norm partial quadratic eigenvalue assignment problem. We provide a new cost function and the closed-loop eigenvalue sensitivity and the feedback norms can be minimized simultaneously. Our method is also extended to the case of time delay between measurements of state and actuation of control. Numerical tests demonstrate the effectiveness of our method.
NASA Astrophysics Data System (ADS)
Shafii, M. A.; Fitriyani, D.; Tongkukut, S. H. J.; Abdullah, A. G.
2017-03-01
To solve the integral neutron transport equation using collision probability (CP) method usually requires flat flux (FF) approach. In this research, it has been carried out in the cylindrical nuclear fuel cell with the spatial of mesh with quadratic flux approach. This means that the neutron flux at any region of the nuclear fuel cell is forced to follow the pattern of a quadratic function. The mechanism may be referred to as the process of non-flat flux (NFF) approach. The parameters that calculated in this study are the k-eff and the distribution of neutron flux. The result shows that all parameters are in accordance with the result of SRAC.
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.
Sequential design of linear quadratic state regulators via the optimal root-locus techniques
NASA Technical Reports Server (NTRS)
Shieh, L. S.; Dib, H. M.; Yates, R. E.
1988-01-01
The use of well-known root-locus techniques for sequentially finding the weighting matrices and the linear quadratic state regulators of multivariable control systems in the frequency domain is considered. This sequential design method permits the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system; it also allows some optimal closed-loop poles to be placed in a specific region of the complex plane. In addition, it provides a design procedure for determining the weighting matrices and linear quadratic state regulators for the optimal control of multivariable systems in the frequency domain.
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.
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
Design of linear quadratic regulators with eigenvalue placement in a specified region
NASA Technical Reports Server (NTRS)
Shieh, Leang-San; Zhen, Liu; Coleman, Norman P.
1990-01-01
Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.
Zhang, X.; Yu, L.; Zakutayev, A.; Zunger, A.
2012-04-10
Electronic structure theory has recently been used to propose hypothetical compounds in presumed crystal structures, seeking new useful functional materials. In some cases, such hypothetical materials are metastable, albeit with technologically useful long lifetimes. Yet, in other cases, suggested hypothetical compounds may be significantly higher in energy than their lowest-energy crystal structures or competing phases, making their synthesis and eventual device-stability questionable. By way of example, the focus here is on the family of 1:1:1 compounds ABX called 'filled tetrahedral structure' (sometimes called Half-Heusler) in the four groups with octet electron count: I-I-VI (e.g., CuAgSe), I-II-V (e.g., AgMgAs), I-III-IV (e.g., LiAlSi), and II-II-IV (e.g., CaZnSn). First-principles thermodynamics is used to sort the lowest-energy structure and the thermodynamic stability of the 488 unreported hypothetical ABX compounds, many of which were previously proposed to be useful technologically. It is found that as many as 235 of the 488 are unstable with respect to decomposition (hence, are unlikely to be viable technologically), whereas other 235 of the unreported compounds are predicted to be thermodynamically stable (hence, potentially interesting new materials). 18 additional materials are too close to determine. The electronic structures of these predicted stable compounds are evaluated, seeking potential new material functionalities.
Liang, Le; Li, Jiang; Li, Qian; Huang, Qing; Shi, Jiye; Yan, Hao; Fan, Chunhai
2014-07-21
DNA is typically impermeable to the plasma membrane due to its polyanionic nature. Interestingly, several different DNA nanostructures can be readily taken up by cells in the absence of transfection agents, which suggests new opportunities for constructing intelligent cargo delivery systems from these biocompatible, nonviral DNA nanocarriers. However, the underlying mechanism of entry of the DNA nanostructures into the cells remains unknown. Herein, we investigated the endocytotic internalization and subsequent transport of tetrahedral DNA nanostructures (TDNs) by mammalian cells through single-particle tracking. We found that the TDNs were rapidly internalized by a caveolin-dependent pathway. After endocytosis, the TDNs were transported to the lysosomes in a highly ordered, microtubule-dependent manner. Although the TDNs retained their structural integrity within cells over long time periods, their localization in the lysosomes precludes their use as effective delivery agents. To modulate the cellular fate of the TDNs, we functionalized them with nuclear localization signals that directed their escape from the lysosomes and entry into the cellular nuclei. This study improves our understanding of the entry into cells and transport pathways of DNA nanostructures, and the results can be used as a basis for designing DNA-nanostructure-based drug delivery nanocarriers for targeted therapy.
Beaujean, Pierre-Philippe J; Mohamed, Asif I; Warin, Raphael
2007-01-01
Acoustic communications and positioning are vital aspects of unmanned underwater vehicle operations. The usage of separate units on each vehicle has become an issue in terms of frequency bandwidth, space, power, and cost. Most vehicles rely on acoustic modems transmitting frequency-hopped multiple frequency-shift keyed sequences for command-and-control operations, which can be used to locate the vehicle with a good level of accuracy without requiring extra signal transmission. In this paper, an ultrashort baseline acoustic positioning technique has been designed, simulated, and tested to locate an acoustic modem source in three dimensions using a tetrahedral, half-wavelength acoustic antenna. The position estimation is performed using the detection sequence contained in each message, which is a series of frequency-hopped pulses. Maximum likelihood estimation of azimuth and elevation estimation is performed using a varying number of pulse and various signal-to-noise ratios. Simulated and measured position estimation error match closely, and indicate that the accuracy of this system improves dramatically as the number of pulses processed increases, given a fixed signal-to-noise ratio.
NASA Astrophysics Data System (ADS)
Iyer, Ajai; Kaskela, Antti; Novikov, Serguei; Etula, Jarkko; Liu, Xuwen; Kauppinen, Esko I.; Koskinen, Jari
2016-05-01
Single walled carbon nanotube networks (SWCNTNs) were coated by tetrahedral amorphous carbon (ta-C) to improve the mechanical wear properties of the composite film. The ta-C deposition was performed by using pulsed filtered cathodic vacuum arc method resulting in the generation of C+ ions in the energy range of 40-60 eV which coalesce to form a ta-C film. The primary disadvantage of this process is a significant increase in the electrical resistance of the SWCNTN post coating. The increase in the SWCNTN resistance is attributed primarily to the intrinsic stress of the ta-C coating which affects the inter-bundle junction resistance between the SWCNTN bundles. E-beam evaporated carbon was deposited on the SWCNTNs prior to the ta-C deposition in order to protect the SWCNTN from the intrinsic stress of the ta-C film. The causes of changes in electrical resistance and the effect of evaporated carbon thickness on the changes in electrical resistance and mechanical wear properties have been studied.
Wang, Z J
2012-12-06
The overriding objective for this project is to develop an efficient and accurate method for capturing strong discontinuities and fine smooth flow structures of disparate length scales with unstructured grids, and demonstrate its potentials for problems relevant to DOE. More specifically, we plan to achieve the following objectives: 1. Extend the SV method to three dimensions, and develop a fourth-order accurate SV scheme for tetrahedral grids. Optimize the SV partition by minimizing a form of the Lebesgue constant. Verify the order of accuracy using the scalar conservation laws with an analytical solution; 2. Extend the SV method to Navier-Stokes equations for the simulation of viscous flow problems. Two promising approaches to compute the viscous fluxes will be tested and analyzed; 3. Parallelize the 3D viscous SV flow solver using domain decomposition and message passing. Optimize the cache performance of the flow solver by designing data structures minimizing data access times; 4. Demonstrate the SV method with a wide range of flow problems including both discontinuities and complex smooth structures. The objectives remain the same as those outlines in the original proposal. We anticipate no technical obstacles in meeting these objectives.
NASA Astrophysics Data System (ADS)
Xu, Zhijun; Schneeloch, J. A.; Wen, Jinsheng; Božin, E. S.; Granroth, G. E.; Winn, B. L.; Feygenson, M.; Birgeneau, R. J.; Gu, Genda; Zaliznyak, I. A.; Tranquada, J. M.; Xu, Guangyong
2016-03-01
It has recently been demonstrated that dynamical magnetic correlations measured by neutron scattering in iron chalcogenides can be described with models of short-range correlations characterized by particular choices of four-spin plaquettes, where the appropriate choice changes as the parent material is doped towards superconductivity. Here we apply such models to describe measured maps of magnetic scattering as a function of two-dimensional wave vectors obtained for optimally superconducting crystals of FeTe1 -xSex . We show that the characteristic antiferromagnetic wave vector evolves from that of the bicollinear structure found in underdoped chalcogenides (at high temperature) to that associated with the stripe structure of antiferromagnetic iron arsenides (at low temperature); these can both be described with the same local plaquette, but with different interplaquette correlations. While the magnitude of the low-energy magnetic spectral weight is substantial at all temperatures, it actually weakens somewhat at low temperature, where the charge carriers become more itinerant. The observed change in spin correlations is correlated with the dramatic drop in the electronic scattering rate and the growth of the bulk nematic response upon cooling. Finally, we also present powder neutron diffraction results for lattice parameters in FeTe1 -xSex indicating that the tetrahedral bond angle tends to increase towards the ideal value upon cooling, in agreement with the increased screening of the crystal field by more itinerant electrons and the correspondingly smaller splitting of the Fe 3 d orbitals.
NASA Astrophysics Data System (ADS)
Xu, Guangyong; Xu, Zhijun; Schneeloch, John; Wen, Jinsheng; Bozin, Emil; Winn, Barry; Feygenson, M.; Birgeneau, R. J.; Gu, Genda; Zaliznyak, Igor; Tranquada, John
We will present neutron scattering measurements of low energy magnetic excitations from superconducting FeTe1-xSex samples. A model with short-range correlated spin plaquettes characterized by particular antiferromagnetic wave vectors is used to describe the measured magnetic scattering data in the (HK0) plane. We show that the characteristic antiferromagnetic wave vector evolves from that characteristic of the bicollinear structure characteristic of FeTe1-xSex (at high temperature) to that associated with the stripe structure of antiferromagnetic iron arsenides (at low temperature). We also present powder neutron diffraction results for lattice parameters in FeTe1-xSex indicating that the tetrahedral bond angle tends to increase towards the ideal value on cooling, with a corresponding reduction in crystal-field splitting of the Fe 3d orbitals. We suggest that the thermal change in spin correlations implies a relative change among the exchange couplings, and that this is associated with changes in orbital occupancies. Finally, while the magnitude of the low energy magnetic spectral weight is substantial at all temperatures, it actually weakens somewhat at low temperature, where the charge carriers become more itinerant.
NASA Astrophysics Data System (ADS)
Chua, Daniel H. C.; Hsieh, Jovan; Gao, Xingyu; Qi, Dongchen; Chen, Shi; Varghese, Binni; Sow, Chorng Haur; Wee, A. T. S.; Lu, Jiong; Loh, Kian Ping; Yu, Xiaojiang; Moser, Herbert O.
2009-07-01
This paper reports a comprehensive experimental study on the effects of hydrogen microwave plasma treatment on nonhydrogenated high sp3 content tetrahedral amorphous carbon (ta-C) film. In this study, a surface C-H dipole layer was first observed by high resolution electron energy loss spectroscopy, showing the presence of C-H bonding states. This resulted in the enhancement of electron field emission of the plasma treated films by largely lowering the turn-on field. Thermal stability tests using in situ ultraviolet photoelectron spectroscopy confirm that the C-H dipole layer not only reduces the work function of the films, it is extremely stable in both ambient and vacuum conditions and can sustain up to 600 °C annealing in vacuum. Atomic force microscopy studies also show minimal modifications to the surface morphology, leading to the conclusion that the C-H dipole layer is responsible for lowering the work function. This has improved the electron emission properties which can lead to potential applications such as electron emission displays.
NASA Astrophysics Data System (ADS)
Do, Dat T.; Mahanti, S. D.
2014-04-01
An interesting class of tetrahedrally coordinated ternary compounds has attracted considerable interest because of their potential as good thermoelectrics. These compounds, denoted as I3-V-VI4, contain three monovalent-I (Cu, Ag), one nominally pentavalent-V (P, As, Sb, Bi), and four hexavalent-VI (S, Se, Te) atoms; and can be visualized as ternary derivatives of the II-VI zincblende or wurtzite semiconductors, obtained by starting from four unit cells of (II-VI) and replacing four type II atoms by three type I and one type V atoms. We find that nominally pentavalent-V atoms are effectively trivalent and their lone (ns2) pairs play an active role in opening up a gap. The lowest conduction band is a strongly hybridized anti-bonding combination of the lone pair and chalcogen (VI) p-states. The magnitude of the gap is sensitive to the nature of the exchange interaction (local vs non-local) and the V-VI distance. We also find that the electronic structure near the gap can be reproduced extremely well within a local theory if one can manipulate the position of the filled d bands of Cu and Ag by an effectively large U.
Xu, X M; Ridout, M S
2000-07-01
ABSTRACT The spatiotemporal spread of plant diseases was simulated using a stochastic model to study the effects of initial conditions (number of plants initially infected and their spatial pattern), spore dispersal gradient, and size and shape of sampling quadrats on statistics describing the spatiotemporal dynamics of epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance mu (units of distance). A total of 54 different quadrat types, including 23 distinct sizes ranging from 4 to 144 plants, were used to sample the simulated epidemics. A symmetric form of the binary power law with two parameters (alpha, beta) was fitted to the sampled epidemic data using each of the 54 quadrats for each replicate simulation run. The alpha and beta estimates were highly correlated positively with each other, and their estimates were comparable to those estimated from observed epidemics. Intraclass correlation (kappa) was calculated for each quadrat type; kappa decreased exponentially with increasing quadrat size. An asymmetric form of the binary power law with three parameters (alpha (1), beta(1), beta(2)) was used to relate kappa to the disease incidence (p); beta1 was highly correlated to beta: beta1 approximately beta - 1. In general, initial conditions and quadrat size affected alpha, beta, alpha(1), beta(1), and beta(2) greatly. The parameter estimates increased as quadrat size increased, and the relationships were described well by a linear regression model on the logarithm of quadrat size with the slope or intercept parameters dependent on initial conditions and mu. Compared with initial conditions and quadrat size, the overall effects of mu and quadrat shape were generally small, although within each quadrat size and initial condition they could be substantial. Quadrat shape had the greatest effect when the quadrat was long and thin. The relationship of the index of dispersion (D) to p and quadrat size was
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…
NASA Astrophysics Data System (ADS)
Kim, C. W.; Song, S. R.; Hwang, W.; Park, H. C.; Han, K. S.
1994-01-01
The quadratic failure criterion, which is intended to predict fracture, may be used as an object function for optimal stacking sequence design of laminated plate. However, calculations using a symmetric laminated plate demonstrate that Tsai-Wu theory may give incorrect optimum predictions under uniaxial loading.
2012-02-09
several optimization models and algorithm design for problems from computer vision and learning , research on sparse solutions in quadratic optimization...following papers: [9] L. Mukherjee, V. Singh, J. Peng and C. Hinrichs. Learning kernels for variants of normalized cuts: Convex relaxations and...are very small gaps compared to state-of-the-art knowledge in comunications . Table 1. Bounds for adjacency matrix
A tutorial on the LQG/LTR method. [Linear Quadratic Gaussian/Loop Transfer Recovery
NASA Technical Reports Server (NTRS)
Athans, M.
1986-01-01
In this paper the so-called Linear-Quadratic-Gaussian method with Loop-Transfer-Recovery is surveyed. The objective is to provide a pragmatic exposition, with special emphasis on the step-by-step characteristics for designing multivariable feedback control systems.
NASA Technical Reports Server (NTRS)
Wong, P.-K.; Stein, G.; Athans, M.
1979-01-01
Strong sufficient conditions are derived for the robustness of optimal linear-quadratic (LQ) regulators to large parameter perturbations. In particular, it is shown that under certain conditions LQ designs remain stable in the presence of actuator channel failures. The general results can be specialized to provide insight into the gain margin, gain reduction, and phase margin properties of optimal LQ regulators.
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.
Becker, R
2006-03-03
The goal is to examine the dependence of the plastic flow direction as a function of strain increment for a generalized quadratic flow potential; and from that, extract a scheme for constructing a plastic flow direction for a more general class of yield and flow surfaces.
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…
Quadratic partial eigenvalue assignment problem with time delay for active vibration control
NASA Astrophysics Data System (ADS)
Pratt, J. M.; Singh, K. V.; Datta, B. N.
2009-08-01
Partial pole assignment in active vibration control refers to reassigning a small set of unwanted eigenvalues of the quadratic eigenvalue problem (QEP) associated with the second order system of a vibrating structure, by using feedback control force, to suitably chosen location without altering the remaining large number of eigenvalues and eigenvectors. There are several challenges of solving this quadratic partial eigenvalue assignment problem (QPEVAP) in a computational setting which the traditional pole-placement problems for first-order control systems do not have to deal with. In order to these challenges, there has been some work in recent years to solve QPEVAP in a computationally viable way. However, these works do not take into account of the practical phenomenon of the time-delay effect in the system. In this paper, a new "direct and partial modal" approach of the quadratic partial eigenvalue assignment problem with time-delay is proposed. The approach works directly in the quadratic system without requiring transformation to a standard state-space system and requires the knowledge of only a small number of eigenvalues and eigenvectors that can be computed or measured in practice. Two illustrative examples are presented in the context of active vibration control with constant time-delay to illustrate the success of our proposed approach. Future work includes generalization of this approach to a more practical complex time-delay system and extension of this work to the multi-input problem.
Assessment Guidelines for Ant Colony Algorithms when Solving Quadratic Assignment Problems
NASA Astrophysics Data System (ADS)
See, Phen Chiak; Yew Wong, Kuan; Komarudin, Komarudin
2009-08-01
To date, no consensus exists on how to evaluate the performance of a new Ant Colony Optimization (ACO) algorithm when solving Quadratic Assignment Problems (QAPs). Different performance measures and problems sets are used by researchers to evaluate their algorithms. This paper is aimed to provide a recapitulation of the relevant issues and suggest some guidelines for assessing the performance of new ACO algorithms.
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.
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…
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.
Magraner, Eric; Bertaux, Nicolas; Réfrégier, Philippe
2008-12-01
An approach for point target detection in the presence of speckle fluctuations with nonhomogeneous backgrounds is proposed. This approach is based on an automatic selection between the standard constant background model and a quadratic model for the logarithm of the background values. An improvement of the regulation of the false alarm probability in nonhomogeneous backgrounds is demonstrated.
Sun, Zhihua; Luo, Junhua; Zhang, Shuquan; Ji, Chengmin; Zhou, Lei; Li, Shenhui; Deng, Feng; Hong, Maochun
2013-08-14
Exceptional nonlinear optical (NLO) switching behavior, including an extremely large contrast (on/off) of ∼35 and high NLO coefficients, is displayed by a solid-state reversible quadratic NLO switch. The favorable results, induced by very fast molecular motion and anionic ordering, provides impetus for the design of a novel second-harmonic-generation switch involving molecular motion.
Variational viewpoint of the quadratic Markov measure field models: theory and algorithms.
Rivera, Mariano; Dalmau, Oscar
2012-03-01
We present a framework for image segmentation based on quadratic programming, i.e., by minimization of a quadratic regularized energy linearly constrained. In particular, we present a new variational derivation of the quadratic Markov measure field (QMMF) models, which can be understood as a procedure for regularizing model preferences (memberships or likelihoods). We also present efficient optimization algorithms. In the QMMFs, the uncertainty in the computed regularized probability measure field is controlled by penalizing Gini's coefficient, and hence, it affects the convexity of the quadratic programming problem. The convex case is reduced to the solution of a positive definite linear system, and for that case, an efficient Gauss-Seidel (GS) scheme is presented. On the other hand, we present an efficient projected GS with subspace minimization for optimizing the nonconvex case. We demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two-class segmentation, as well as the simultaneous estimation of segmentation and (parametric and nonparametric) generative models. We present extensions to the original formulation for including color and texture clues, as well as imprecise user scribbles in an interactive framework.
First Report of Soybean Pest, Euschistus quadrator (Hempitera: Pentatomidae) in Mississippi
Technology Transfer Automated Retrieval System (TEKTRAN)
Here we report on the first state and county record of Euschistus quadrator Ralston (Hemiptera: Pentatomidae) in Washington County, Mississippi. The species has been documented from Honduras to Virginia primarily on soybeans, cotton, various row crops, fruit, and non-crop hosts. The local impact...
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…
NASA Astrophysics Data System (ADS)
Khaneja, Navin
2017-03-01
In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system. This article is part of the themed issue 'Horizons of cybernetical physics'.
Khaneja, Navin
2017-03-06
In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system.This article is part of the themed issue 'Horizons of cybernetical physics'.
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…
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…
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.
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.
The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; Um, Chung IN; George, T. F.
1994-01-01
The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.
Solution to Projectile Motion with Quadratic Drag and Graphing the Trajectory in Spreadsheets
ERIC Educational Resources Information Center
Benacka, Jan
2010-01-01
This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and…
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 Method for Selecting between Linear and Quadratic Classification Models in Discriminant Analysis.
ERIC Educational Resources Information Center
Meshbane, Alice; Morris, John D.
A method for comparing the cross validated classification accuracies of linear and quadratic classification rules is presented under varying data conditions for the k-group classification problem. With this method, separate-group as well as total-group proportions of correct classifications can be compared for the two rules. McNemar's test for…
The Maraner effect as a particular case of the quadratic Sagnac effect
NASA Astrophysics Data System (ADS)
Malykin, G. B.; Pozdnyakova, V. I.
2016-12-01
The quadratic Sagnac effect consists in a Michelson interferometer (MI) being located on a rotating base with a phase difference in its arms arising, the value of which depends on the orientation of the MI arms relative to the rotating base and on the angle of its rotation. This phase difference is caused by different values of the Newtonian (nonrelativistic) scalar gravitational potential of Coriolis forces acting on different MI arms, which leads to time dilation and varies with change in the angle of MI rotation. Distributions of the scalar gravitational potential of Coriolis forces over different parts of MI arms are considered. Allowance for this distribution makes it possible to calculate a value of the certain effect that is a higher approximation of the quadratic Sagnac effect. This effect is shown to be the Maraner effect known earlier, which also leads to a change in the phase difference of MI arms, but differs in value from the quadratic Sagnac effect. Consequently, the Maraner effect is a particular case of the quadratic Sagnac effect. Numerical estimations are performed.
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…
NASA Astrophysics Data System (ADS)
Biryukov, V. A.; Muratov, M. V.; Petrov, I. B.; Sannikov, A. V.; Favorskaya, A. V.
2015-10-01
Seismic responses from fractured geological layers are mathematically simulated by applying the grid-characteristic method on unstructured tetrahedral meshes with the use of high-performance computer systems. The method is intended for computing complicated spatial dynamical processes in complex heterogeneous media and is characterized by exact formulation of contact conditions. As a result, it can be applied to the simulation of seismic exploration problems, including in regions with a large number of inhomogeneities, examples of which are fractured structures. The use of unstructured tetrahedral meshes makes it possible to specify geological cracks of various shapes and spatial orientations. As a result, problems are solved in a formulation maximally close to an actual situation. A cluster of computers is used to improve the accuracy of the computation by optimizing its duration.
Hartley, D. J.; Riedinger, L. L.; Janssens, R. V. F.; Majola, S. N. T.; Riley, M. A.; Allmond, J. M.; Beausang, C. W.; Carpenter, M. P.; Chiara, C. J.; Cooper, N.; Curien, D.; Gall, B. J. P.; Garrett, P. E.; Kondev, F. G.; Kulp, W. D.; Lauritsen, T.; McCutchan, E. A.; Miller, D.; Miller, S.; Piot, J.; Redon, N.; Sharpey-Schafer, J. F.; Simpson, J.; Stefanescu, I.; Wang, X.; Werner, V.; Wood, J. L.; Yu, C. -H.; Zhu, S.; Dudek, J.
2017-01-01
An experiment populating low/medium-spin states in ^{156}Dy was performed to investigate the possibility of tetrahedral symmetry in this nucleus. In particular, focus was placed on the low-spin, negative-parity states since recent theoretical studies suggest that these may be good candidates for this high-rank symmetry. The states were produced in the ^{148}Nd(^{12}C,4 n) reaction and the Gammasphere array was utilized to detect the emitted rays. B(E 2) /B(E1) ratios of transition probabilities from the low-spin, negative-parity bands were determined and used to interpret whether these structures are best associated with tetrahedral symmetry or, as previously assigned, to octupole vibrations. Additionally, several other negative-parity structures were observed to higher spin and two new sequences were established
Be3(AsO4)2 2H2O, a New Berylloarsenate Phase Containing Bridged Tetrahedral 3-Rings
1994-04-15
CsH(ZnPO 4 )2 and NaH(ZnPO 4 )2 contain "bridged" 3-rings as part of anionic layers sandwiching cesium and sodium cations (9). Finally, the novel...0 have been found in the layered, anionic zincophosphate phases CsH(ZnPO 4 )2 and NaH(ZnP0 4 )2 (9). However, the precise nature of the tetrahedral
Self-Assembly of a Giant Tetrahedral 3 d-4 f Single-Molecule Magnet within a Polyoxometalate System.
Ibrahim, Masooma; Mereacre, Valeriu; Leblanc, Nicolas; Wernsdorfer, Wolfgang; Anson, Christopher E; Powell, Annie K
2015-12-14
A giant tetrahedral heterometallic polyoxometalate (POM) [Dy30 Co8 Ge12 W108 O408 (OH)42 (OH2 )30 ](56-) , which shows single-molecule magnet (SMM) behavior, is described. This hybrid contains the largest number of 4f ions of any polyoxometalate (POM) reported to date and is the first to incorporate two different 3d-4f and 4f coordination cluster assemblies within same POM framework.
Mohanty, Debasish; Li, Jianlin; Abraham, Daniel P.; Huq, Ashfia; Payzant, E. Andrew; Wood, David L.; Daniel, Claus
2014-09-30
Discovery of high-voltage layered lithium-and manganese-rich (LMR) composite oxide electrode has dramatically enhanced the energy density of current Li-ion energy storage systems. However, practical usage of these materials is currently not viable because of their inability to maintain a consistent voltage profile (voltage fading) during subsequent charge-discharge cycles. This report rationalizes the cause of this voltage fade by providing the evidence of layer to spinel-like (LSL) structural evolution pathways in the host Li_{1.2}Mn_{0.55}Ni_{0.15}Co_{0.1}O_{2} LMR composite oxide. By employing neutron powder diffraction, and temperature dependent magnetic susceptibility, we show that LSL structural rearrangement in LMR oxide occurs through a tetrahedral cation intermediate via: i) diffusion of lithium atoms from octahedral to tetrahedral sites of the lithium layer [(Li_{Li}oct →Li_{Li}tet] which is followed by the dispersal of the lithium ions from the adjacent octahedral site of the metal layer to the tetrahedral sites of lithium layer [Li_{TM} oct → Li_{Li}tet]; and ii) migration of Mn from the octahedral sites of the transition metal layer to the permanent octahedral site of lithium layer via tetrahedral site of lithium layer [Mn_{TM}oct Mn_{Li}tet Mn_{Li}oct)]. The findings opens the door to the potential routes to mitigate this atomic restructuring in the high-voltage LMR composite oxide cathodes by manipulating the composition/structure for practical use in high-energy-density lithium-ion batteries.
Mohanty, Debasish; Li, Jianlin; Abraham, Daniel P.; ...
2014-09-30
Discovery of high-voltage layered lithium-and manganese-rich (LMR) composite oxide electrode has dramatically enhanced the energy density of current Li-ion energy storage systems. However, practical usage of these materials is currently not viable because of their inability to maintain a consistent voltage profile (voltage fading) during subsequent charge-discharge cycles. This report rationalizes the cause of this voltage fade by providing the evidence of layer to spinel-like (LSL) structural evolution pathways in the host Li1.2Mn0.55Ni0.15Co0.1O2 LMR composite oxide. By employing neutron powder diffraction, and temperature dependent magnetic susceptibility, we show that LSL structural rearrangement in LMR oxide occurs through a tetrahedral cationmore » intermediate via: i) diffusion of lithium atoms from octahedral to tetrahedral sites of the lithium layer [(LiLioct →LiLitet] which is followed by the dispersal of the lithium ions from the adjacent octahedral site of the metal layer to the tetrahedral sites of lithium layer [LiTM oct → LiLitet]; and ii) migration of Mn from the octahedral sites of the transition metal layer to the permanent octahedral site of lithium layer via tetrahedral site of lithium layer [MnTMoct MnLitet MnLioct)]. The findings opens the door to the potential routes to mitigate this atomic restructuring in the high-voltage LMR composite oxide cathodes by manipulating the composition/structure for practical use in high-energy-density lithium-ion batteries.« less