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The verdict geometric quality library.

Description: Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of metrics. A metric is a real number assigned to one of these shapes depending on its particular vertex coordinates. These metrics are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. The geometric qualities of these regions is usually strongly tied to the accuracy these solvers are able to obtain in their approximations. The subroutines are written in C++ and have a simple C interface. Each metric may be evaluated individually or in combination. When multiple metrics are evaluated at once, they share common calculations to lower the cost of the evaluation.
Date: March 1, 2006
Creator: Knupp, Patrick Michael; Ernst, C.D. (Elemental Technologies, Inc., American Fork, UT); Thompson, David C. (Sandia National Laboratories, Livermore, CA); Stimpson, C.J. (Elemental Technologies, Inc., American Fork, UT) & Pebay, Philippe Pierre
Partner: UNT Libraries Government Documents Department
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Characterizations of Some Combinatorial Geometries

Description: We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.
Date: August 1992
Creator: Yoon, Young-jin
Partner: UNT Libraries
open access

The Torus Does Not Have a Hyperbolic Structure

Description: Several basic topics from Algebraic Topology, including fundamental group and universal covering space are shown. The hyperbolic plane is defined, including its metric and show what the "straight" lines are in the plane and what the isometries are on the plane. A hyperbolic surface is defined, and shows that the two hole torus is a hyperbolic surface, the hyperbolic plane is a universal cover for any hyperbolic surface, and the quotient space of the universal cover of a surface to the group of automorphisms on the covering space is equivalent to the original surface.
Date: August 1992
Creator: Butler, Joe R.
Partner: UNT Libraries
open access

Mapping the geometry of the F4 group

Description: In this paper, we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 Hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2 = F4/Spin(9), the octonionic projective plane, these results are a prerequisite for the study of E6, of which F4 is a (maximal) subgroup.
Date: May 28, 2007
Creator: Bernardoni, Fabio; Cacciatori, Sergio L; Scotti, Antonio & Cerchiai, Bianca L.
Partner: UNT Libraries Government Documents Department
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Motif based Hessian matrixfor ab initio geometry optimization ofnanostructures

Description: A simple method to estimate the atomic degree Hessian matrixof a nanosystem is presented. The estimated Hessian matrix, based on themotif decomposition of the nanosystem, can be used to accelerate abinitio atomic relaxations with speedups of 2 to 4 depending on the sizeof the system. In addition, the programing implementation for using thismethod in a standard ab initio package is trivial.
Date: April 5, 2006
Creator: Zhao, Zhengji; Wang, Lin-Wang & Meza, Juan
Partner: UNT Libraries Government Documents Department
open access

On the Euler angles for SU(N)

Description: In this paper we reconsider the problem of the Euler parametrization for the unitary groups. After constructing the generic group element in terms of generalized angles, we compute the invariant measure on SU(N) and then we determine the full range of the parameters, using both topological and geometrical methods. In particular, we show that the given parametrization realizes the group SU(N+1) as a fibration of U(N) over the complex projective space CP{sup n}. This justifies the interpretation of the parameters as generalized Euler angles.
Date: October 20, 2005
Creator: Cerchiai, Bianca L; Bertini, S. & Cacciatori, Sergio L.
Partner: UNT Libraries Government Documents Department
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Effect of channel geometry on the quenching of laminar flames

Description: Report presenting the effect of channel geometry on flame quenching, as calculated on the basis of average active particle chain lengths, is related among six different geometries: plane parallel plates of infinite extent, cylindrical tubes, rectangular slots, cylindrical annuli, and tubes of elliptical and equilaterally triangular shape. The results indicated that the observed variation of flame quenching as a function of quenching geometry may be successfully predicted for a range of pressures and for rich as well as lean propane-air flames.
Date: May 6, 1954
Creator: Berlad, A. L. & Potter, A. E., Jr.
Partner: UNT Libraries Government Documents Department
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Development of a Nodal Method for the Solution of the Neutron Diffusion Equation in General Cylindrical Geometry

Description: The usual strategy for solving the neutron diffusion equation in two or three dimensions by nodal methods is to reduce the multidimensional partial differential equation to a set of ordinary differential equations (ODEs) in the separate spatial coordinates. This reduction is accomplished by “transverse integration” of the equation.1 For example, in three-dimensional Cartesian coordinates, the three-dimensional equation is first integrated over x and y to obtain an ODE in z, then over x and z to obtain an ODE in y, and finally over y and z to obtain an ODE in x. Then the ODEs are solved to obtain onedimensional solutions for the neutron fluxes averaged over the other two dimensions. These solutions are found in regions (“nodes”) small enough for the material properties and cross sections in them to be adequately represented by average values. Because the solution in each node is an exact analytical solution, the nodes can be much larger than the mesh elements used in finite-difference solutions. Then the solutions in the different nodes are coupled by applying interface conditions, ultimately fixing the solutions to the external boundary conditions.
Date: April 1, 2002
Creator: Ougouag, Abderrafi Mohammed-El-Ami & Terry, William Knox
Partner: UNT Libraries Government Documents Department
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Voro++: a three-dimensional Voronoi cell library in C++

Description: Voro++ is a free software library for the computation of three dimensional Voronoi cells. It is primarily designed for applications in physics and materials science, where the Voronoi tessellation can be a useful tool in the analysis of densely-packed particle systems, such as granular materials or glasses. The software comprises of several C++ classes that can be modified and incorporated into other programs. A command-line utility is also provided that can use most features of the code. Voro++ makes use of a direct cell-by-cell construction, which is particularly suited to handling special boundary conditions and walls. It employs algorithms which are tolerant for numerical precision errors, and it has been successfully employed on very large particle systems.
Date: January 15, 2009
Creator: Rycroft, Chris
Partner: UNT Libraries Government Documents Department
open access

A SURFACE CRYSTALLOGRAPHY STUDY BY DYNAMICAL LEED OF THE (sqrt3xsqrt3)R30o CO STRUCTURE ON THE Rh(111) CRYSTAL SURFACE

Description: The atomic positions of the Rh(111) + ({radical}3 x {radical}3)R30{sup o} CO and CO{sub 2} surfaces are analyzed by dynamical LEED. The Rh(111) + ({radical}3 x {radical}3)R30{sup o} CO and CO{sub 2} systems produce identical I-V curves, confirming the dissociation of CO{sub 2} to CO on this surface. The adsorbed CO is found to stand perpendicular to the surface with the carbon end down at an atop site (that is, terminally bonded). The CO overlayer spacings are d{sub RhC} = 1.95 {+-} 0.1 {angstrom} and d{sub CD} = 1.07 {+-} 0.1 {angstrom}. This geometry yields a Zanazzi-Jona R-factor of 0.40 and a Pendry R-factor of 0.50.
Date: September 1, 1980
Creator: Koestner, R.J.; Van Hove, M.A. & Somorjai, G.A.
Partner: UNT Libraries Government Documents Department
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Predictions of Elliptic flow and nuclear modification factor from 200 GeV U+U collisions at RHIC

Description: Predictions of elliptic flow (v{sub 2}) and nuclear modification factor (R{sub AA}) are provided as a function of centrality in U + U collisions at {radical}s{sub NN} = 200 GeV. Since the {sup 238}U nucleus is naturally deformed, one could adjust the properties of the fireball, density and duration of the hot and dense system, for example, in high energy nuclear collisions by carefully selecting the colliding geometry. Within our Monte Carlo Glauber based approach, the v{sub 2} with respect to the reaction plane v{sub 2}{sup RP} in U + U collisions is consistent with that in Au + Au collisions, while the v{sub 2} with respect to the participant plane v{sub 2}{sup PP} increases {approx}30-60% at top 10% centrality which is attributed to the larger participant eccentricity at most central U + U collisions. The suppression of R{sub AA} increases and reaches {approx}0.1 at most central U + U collisions that is by a factor of 2 more suppression compared to the central Au + Au collisions due to large size and deformation of Uranium nucleus.
Date: July 7, 2010
Creator: Masui, Hiroshi; Mohanty, Bedangadas & Xu, Nu
Partner: UNT Libraries Government Documents Department
open access

Designing the Ideal Uranyl Ligand: a Sterically-Induced Speciation Change in Complexes with Thiophene-Bridged Bis(3-hydroxy-N-methylpyridin-2-one)

Description: Structural characterization of a mononuclear uranyl complex with a tetradentate, thiophene-linked bis(3-hydroxy-N-methylpyridin-2-one) ligand reveals the most planar coordination geometry yet observed with this ligand class. The introduction of ethylsulfanyl groups onto the thiophene linker disrupts this planar, conjugated ligand arrangement, resulting in the formation of dimeric (UO{sub 2}){sub 2}L{sub 2} species in which each ligand spans two uranyl centers. Relative energy calculations reveal that this tendency toward dimer formation is the result of steric interference between ethylsulfanyl substituents and linking amides.
Date: September 11, 2009
Creator: Szigethy, Geza & Raymond, Kenneth N.
Partner: UNT Libraries Government Documents Department
open access

Triangle: A Teaching Program of High School Geometry

Description: Among the early applications of computers, one can find frequent mention of intelligent instructional systems. Such intelligent instructional systems represent a new generation of learner-based computer aided instruction, preceded in time by the original frame-based systems and an intervening generation of expert-based CAI. The history of CAI is characterized by three generations: Frame-based CAI, Expert-based CAI and Learner-based CAI.
Date: August 1983
Creator: Chen, Yei-Huang
Partner: UNT Libraries
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