Realization of the transformation operator in the Jansen—Byers brown perturbation theory for exchange interactions

We obtain the general form and exhibit simple expressions for the transformation operator in the Jansen—Byers Brown exchange perturbation theory, without the use of an orthonormalization process.     

Characterizing student mathematics teachers’ levels of understanding in spherical geometry

This article presents an exploratory study aimed at the identification of students’ levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, task-based interviews were held with eight student mathematics teachers at particular times through the course to determine the spherical geometry learning levels. After identifying the properties of spherical geometry levels, we developed Understandings in Spherical Geometry Test to test whether or not the levels form hierarchy, and 58 student mathematics teachers took the test. The outcomes seemed to support our theoretical perspective that there are some understanding levels in spherical geometry that progress through a hierarchical order as van Hiele levels in Euclidean geometry.     

Polarization-independent unidirectional light transmission by an annular photonic crystal prism

Unidirectional transmission of light irrespective of its polarization by a two-dimensional annular photonic crystal in the form of a right prism is numerically demonstrated. Band structure of the crystal obtained through the plane-wave expansion method reveals a directional band gap along a principal axis, leading to prohibition of wave transmission in the reverse direction. In the forward direction, however, transmission of waves is facilitated by circumventing the directional band gap due to altered surface orientation. Polarization-independent unidirectional light transmission is demonstrated through finite-difference time-domain simulations. Unidirectional operation is enhanced and the polarization independence is established through the introduction of an anti-reflection coating layer, which increases the forward transmittances for both polarizations up to 0.44, such that a contrast ratio of 0.96 is attained at a free-space wavelength of 1.55 μm. Although polarization independence deteriorates, unidirectionality is preserved between 1.45 μm and 1.60 μm, provided that the angle of incidence remains between ?5° and +5°. Device performance is also influenced by the transverse source size, where leakage in the reverse direction may be suffered if the source width is beyond a critical value.     

Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.     

Acoustic beam splitting in a sonic crystal around a directional band gap

Beam splitting upon refraction in a triangular sonic crystal composed of aluminum cylinders in air is experimentally and numerically demonstrated to occur due to finite source size,which facilitates circumvention of a directional band gap.Experiments reveal that two distinct beams emerge at crystal output,in agreement with the numerical results obtained through the finite-element method.Beam splitting occurs at sufficiently-small source sizes comparable to lattice periodicity determined by the spatial gap width in reciprocal space.Split beams propagate in equal amplitude,whereas beam splitting is destructed for oblique incidence above a critical incidence angle.     

A self-consistent boundary element, parametric dislocation dynamics formulation of plastic flow in finite volumes

We present a self-consistent formulation of 3-D parametric dislocation dynamics (PDD) with the boundary element method (BEM) to describe dislocation motion, and hence microscopic plastic flow in finite volumes. We develop quantitative measures of the accuracy and convergence of the method by considering a comparison with known analytical solutions. It is shown that the method displays absolute convergence with increasing the number of quadrature points on the dislocation loop and the surface mesh density. The error in the image force on a screw dislocation approaching a free surface is shown to increase as the dislocation approaches the surface, but is nevertheless controllable. For example, at a distance of one lattice parameter from the surface, the relative error is less than 5% for a surface mesh with an element size of 1000×2000 (in units of lattice parameter), and 64 quadrature points. The Eshelby twist angle in a finite-length cylinder containing a coaxial screw dislocation is also used to benchmark the method. Finally, large scale 3-D simulation results of single slip behavior in cylindrical microcrystals are presented. Plastic flow characteristics and the stress-strain behavior of cylindrical microcrystals under compression are shown to be in agreement with experimental observations. It is shown that the mean length of dislocations trapped at the surface is the dominant factor in determining the size effects on hardening of single crystals. The influence of surface image fields on the flow stress is finally explored. It is shown that the flow stress is reduced by as much as 20% for small single crystals of size less than .     

Thermal analysis of thin layer boilover

A mathematical model is developed to simulate the thin layer boilover phenomenon. This model takes into account convective currents as well as conduction and radiation absorption through the fuel layer and is resolved numerically employing a scheme of Runge–Kutta, combined with the numerical method of lines. Solutions of the model showed a good agreement with the experimental data, both from this work and by other authors, demonstrating the importance of the convective currents. The model provided velocities of these currents, of the same order of magnitude as the values reported in the technical literature. Thickness of the remaining fuel and the interface temperature are correctly calculated by the model, allowing the prediction of the time required for the boilover to start.     

Design of Sol-Gel Coating Media for Ink-Jet Printing

Image transfer and storage is rapidly becoming one of the most important technologies in the communication age. Ink-jet printing by which multicolor images are transferred onto paper and transparencies is a major branch of this technology. In this technology electronic image transfer capabilities are often limited by the shortcomings in the materials used. The coating designed to receive the ink determines the ink-dry time, edge acuity or patterns, color fidelity, as well as light and water fastness of the print. These in turn govern the speed, resolution and quality of the image transferred. Chemical, structural and process parameters involved in the design of a transparent, single layer sol-gel coating media for ink-jet printing are discussed. Design goals include quick drying of the print, water resistance, edge acuity without bleeding, UV protection of color dyes, and being printer nonspecific.     

Electrochemical Determination of Copper(II) in Water Samples Using a Novel Ion-Selective Electrode Based on a Graphite Oxide–Imprinted Polymer Composite

A novel copper(II)-selective electrode based on graphite oxide/imprinted polymer composite was developed for the electrochemical monitoring of copper(II) (Cu²⁺) ions. The electrode exhibited highly selective potentiometric response to Cu²⁺ with respect to common alkaline, alkaline earth and heavy metal cations. The composite composition studies indicated that the most suitable composite composition performing the most promising potentiometric properties was 20.0% ionophore (Cu²⁺-ion imprinted polymer), 10.0% paraffin oil, 5.0% multiwalled carbon nanotubes, and 65.0% graphite oxide. The fabricated electrode exhibited a linear response to Cu²⁺ over the concentration range of 1.0?×?10^??6–1.0?×?10^??1?M (correlation coefficient of 0.9998) with a sensitivity of 26.1?±?0.9?mV decade^??1. The detection limit of the fabricated electrode was determined to be 4.0?×?10^??7?M. The electrode worked well in the pH range of 4.0–8.0. The electrode had stable, reversible and fast potentiometric response (3?s). In addition, the electrode had a lifetime of more than 1 year. The analytical applications of the proposed electrode were performed using as an indicator electrode for the potentiometric titration of Cu²⁺ with ethylene diamine tetraacetic acid solution and for the determination of Cu²⁺ of spiked river, dam, and tap water samples. The obtained results for potentiometric titration and water samples were satisfactory.     

Focusing with two-dimensional angular-symmetric circular acoustic lenses

Focusing properties of an acoustic lens based on a modified triangular sonic crystal slab whose columns are aligned on concentric arcs of equal radial distance are investigated. Capability of focusing normally-incident plane waves is demonstrated by means of Finite Element Method. Focusing mechanisms are discussed on the basis of band structures and equifrequency contours considering a model where triangular lattice is elongated along ΓK direction. Focusing behavior of the proposed lens is argued to arise from negative refractions at the air-lens interfaces accompanied by index guiding in its interiors. Wavelength-order confinement in the transverse direction is observed. Double focusing is attributed to geometrical effects and contribution of self guiding is discussed. Possibility of occurrence of birefraction at the input face of the lens together with positive refraction at the output face is also discussed.