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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 geometri… more
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 ch… more
Date: August 1992
Creator: Yoon, Young-jin
Partner: UNT Libraries
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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… more
Date: May 28, 2007
Creator: Bernardoni, Fabio; Cacciatori, Sergio L; Scotti, Antonio & Cerchiai, Bianca L.
Partner: UNT Libraries Government Documents Department
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… more
Date: August 1992
Creator: Butler, Joe R.
Partner: UNT Libraries
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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 … more
Date: October 20, 2005
Creator: Cerchiai, Bianca L; Bertini, S. & Cacciatori, Sergio L.
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… more
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+… more
Date: January 15, 2009
Creator: Rycroft, Chris
Partner: UNT Libraries Government Documents Department
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Calculation of Average Flux in Moderator of Water Lattices by Means of a Relaxation Method

Description: The following report concerns the application of a relaxation mesh method for the determination of the average flux within the moderator of a light water moderated, 1.027 per cent U-235, hexagonal lattice with a volume ratio (V_H2O + V_Al)/V_Uranium of 4:1. It was hoped that the calculation would enable one to determine any differences in flux which might result from the fact that the unit cell is a hexagon instead of a cylinder. Because we were primarily interested in the effect due to geometr… more
Date: March 24, 1953
Creator: Oleksa, S. & Mozer, B.
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 pressure… more
Date: May 6, 1954
Creator: Berlad, A. L. & Potter, A. E., Jr.
Partner: UNT Libraries Government Documents Department
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The generation of hexahedral meshes for assembly geometries: A survey

Description: The finite element method is being used today to model component assemblies in a wide variety of application areas, including structural mechanics, fluid simulations, and others. Generating hexahedral meshes for these assemblies usually requires the use of geometry decomposition, with different meshing algorithms applied to different regions. While the primary motivation for this approach remains the lack of an automatic, reliable all-hexahedral meshing algorithm, requirements in mesh quality a… more
Date: February 14, 2000
Creator: TAUTGES,TIMOTHY J.
Partner: UNT Libraries Government Documents Department
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Final Report: Geometry and Elementary Particle Physics

Description: The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is… more
Date: March 4, 2008
Creator: Singer, Isadore M.
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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Geometric Imagery

Description: It was those problems and possibilities I wished to explore in my problem in lieu of thesis. While the simple, geometric images were very satisfying to that part of myself that craves order and rationality, it was all too easy to make work that was dull and uninteresting. I wanted to find a way to produce rich, sensuous, engaging work using only simple geometric forms.
Date: May 1996
Creator: Dodd, Guthrie McRae
Partner: UNT Libraries
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