An analysis of the dense packing of disks : a computer simulated approach

This thesis is concerned with the analysis of dense packing of hard disks. The Voronoi diagram and the geometric neighbours were first computed. The average number of geometric neighbours of a disk is six. It is thus more efficient to choose structural neighbours from among the geometric neighbours than from among all other disks. Through the Monte Carlo simulation by Rosato et. al., disk configurations after pouring and subsequent shaking were provided for analysis. The mean number of geometric neighbours and the average coordination number were computed. The angular distribution of the structural neighbours was discussed. The packing fraction increases with number of shakes in a linear relationship. It seems to be packing into an ordered close packing after continued shaking. A configuration constrained by two rigid vertical walls was analyzed. It was found the packing fraction is smallest in the vicinity of the wall and increased asymptotically to the mean packing fraction when moving away from the wall

Embedded crack model: I. Basic formulation

The recently emerged idea of enriching standard nite element interpolations by strain or displacement discontinuities has triggered the development of powerful techniques that allow ecient modelling of regions with highly localized strains, e.g. of fracture zones in concrete, or shear bands in metals or soils. The present paper describes a triangular element with an embedded displacement discontinuity that represents a crack. The constitutive model is formulated within the framework of damage theory, with crack closure eects and friction on the crack faces taken into account. Numerical aspects of the implementation are discussed. In a companion paper, the embedded crack approach is combined with the more traditional smeared crack approach.\u

BEAM ELEMENT UNDER FINITE ROTATIONS

The present work focuses on the 2-D formulation of a nonlinear beam model for slender structures that can exhibit large rotations of the cross sections while remaining in the small-strain regime. Bernoulli-Euler hypothesis that plane sections remain plane and perpendicular to the deformed beam centerline is combined with a linear elastic stress-strain law. The formulation is based on the integrated form of equilibrium equations and leads to a set of three first-order differential equations for the displacements and rotation, which are numerically integrated using a special version of the shooting method. The element has been implemented into an open-source finite element code to ease computations involving more complex structures. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions

Concert recording 2018-03-02

[Track 1]. Quartet in A major, TWV 43:A1. Soave ; Allegro ; Andante ; Vivace / Georg Phillip Telemann -- [Track 2]. Du bist verflucht, o Shreckensstimmel, TWV 1:385. Aria: Du bist verflucht o Shreckensstimme ; Recitative: So ist\u27s: Seitdem bei Edens Baum des Baum des ersten Menschen erste Sunde ; Aria: Frohlocket, ihr seligen Kinder der Freien! / Telemann -- [Track 3]. Seele, lernce dich erkennen, TWV 1:1258. Aria: Seele, lerne dich erkennen! ; Recitative: Ein Vogelchen, dem noch die Glieder ; Aria: So will ich dich mit Freuden kussen / Telemann -- [Track 4]. Sonatae unarum fidium: Sonata no. 4 in D major. Ciaccona ; Variatio ; Sarabande ; Gigue ; Adagio e recitativo ; Allegro / Johann Heinrich Schmelzer -- [Track 5]. Auf ehernen Mauern, TWV 1:96. Aria; Auf ehernen Mauern, auf marmornen Grunden ; Recitative: So lange noch der Unbestand den Schuchternen ; Aria: Ja, ja, wiederholt nur eure Tucke? / Telemann -- [Track 6]. Nouveaux Quatuors: Quartet no. 6 in E minor, TWV 43:34. Prelude; tres vite ; Gay ; Vite ; Gracieusement ; Distrait ; Modere / Telemann

Impulsive waves in electrovac direct product spacetimes with Lambda

A complete family of non-expanding impulsive waves in spacetimes which are the direct product of two 2-spaces of constant curvature is presented. In addition to previously investigated impulses in Minkowski, (anti-)Nariai and Bertotti-Robinson universes, a new explicit class of impulsive waves which propagate in the exceptional electrovac Plebanski-Hacyan spacetimes with a cosmological constant Lambda is constructed. In particular, pure gravitational waves generated by null particles with an arbitrary multipole structure are described. The metrics are impulsive members of a more general family of the Kundt spacetimes of type II. The well-known pp-waves are recovered for Lambda=0.Comment: 6 pages, 1 figure, LaTeX 2e. To appear in Class. Quantum Gra

Complexity in Prefix-Free Regular Languages

We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next provide the tight bounds on state complexity of symmetric difference, and deterministic and nondeterministic state complexity of difference and cyclic shift of prefix-free languages.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Mathematics, Science and Technology Education: Their Place in the Nigeria National Transformation Agenda

ABSTRACT Mathematics, Science and Technology Education is indisputably recognised worldwide as essential tools for effecting national development. The developed economies of the world such as Japan, China, Germany and United State of America (U.S.A) have always accorded mathematics, science and technology high priority to the extent that 10% of their enormous Gross National Product (GNP) is spent on science and technology. In Nigeria however, in spite of the proliferation of universities, polytechnics and research institutes, less than 1% of GNP is budgeted for funding of science and technology. Hence, the transformation agenda of the Nigerian Government and its Vision 20:2020 would be a mirage except mathematics, science and technology takes the central and leadership role as the major driver of the nation's program. It is based on this that the research is focused on the implication of mathematics, science and technology on the national transformation agenda of the Federal Government of Nigeria. The research also highlights some missing links on how mathematics, science and technology can transform the economy and the challenges of the opportunity of using the skills and knowledge acquired in Mathematics, Science and Technology to bring about the most needed scientific and technological growth in Nigeria. The research recommends among others that the Nigerian Government should adequately fund mathematics, science and technology programs and research in higher institutions. The research concludes that the federal government should make it mandatory for the industrial sector to join international bodies in order to facilitate scientific and technological development by commercializing research results in mathematics, science and technology