GHP: a maple package for performing calculations in the Geroch-Held-Penrose formalism

We present a new symbolic algebra package, written for Maple, for performing computations in the Geroch-Held-Penrose formalism. We demonstrate the essential features and capabilities of our package by investigating Petrov-D vacuum solutions of Einstein's field equations.

Quasiclassical trajectory calculations of collisional energy transfer in propane systems: multiple direct-encounter hard-sphere model

Quasiclassical trajectory calculations of collisional energy transfer from highly vibrationally excited propane + rare gas systems are reported. This work extends our hard-sphere model (A. Linhananta and K. F. Lim, Phys. Chem. Chem. Phys., 2000, 2, 1385) to examine the variation of the internal energy during collisions with a rare bath gas. This was accomplished by recording the vibrational and rotational energy of propane after each atom–atom encounter during trajectory simulations of propane + rare gas systems. This provides detailed information of the energy flow during a collision. It was found that collisions with small number of encounters transfer energy efficiently, whereas those with many encounters do not. Detailed analyses reveal that the former collisions arise from trajectories with high initial impact parameter, whereas the latter have small initial impact parameter. The reason behind this is the dependence of collision energy transfer (CET) of large polyatomic molecules on their shape. This is connected to the well-known role of rotational energy transfer (RET) as a gateway for CET.

Fluorination-induced magnetism in boron nitride nanotubes from ab initio calculations

Ab initio calculations were conducted to investigate the electronic structures and magnetic properties of fluorinated boron nitride nanotube (F-BNNT). It was found that the chemisorption of F atoms on the B atoms of BNNT can induce spontaneous magnetization, whereas no magnetism can be produced when the B and N atoms are equally fluorinated. This provides a different approach to tune the magnetic properties of BNNTs as well as a synthetic route toward metal-free magnetic materials.

C-BN single-walled nanotubes from hybrid connection of BN/C nanoribbons : prediction by ab initio density functional calculations

We demonstrated for the first time by ab initio density functional calculation and molecular dynamics simulation that C0.5(BN)0.5 armchair single-walled nanotubes (NT) are gapless semiconductors and can be spontaneously formed via the hybrid connection of graphene/BN Nanoribbons (GNR/BNNR) at room temperature. The direct synthesis of armchair C0.5(BN)0.5 via the hybrid connection of GNR/BNNR is predicted to be both thermodynamically and dynamically stable. Such novel armchair C0.5(BN)0.5 NTs possess enhanced conductance as that observed in GNRs. Additionally, the zigzag C0.5(BN)0.5 SWNTs are narrow band gap semiconductors, which may have potential application for light emission. In light of recent experimental progress and the enhanced degree of control in the synthesis of GNRs and BNNR, our results highlight an interesting avenue for synthesizing a novel specific type of C0.5(BN)0.5 nanotube (gapless or narrow direct gap semiconductor), with potentially important applications in BNC-based nanodevices.

Ab initio calculations, Raman and NMR investigation of the plastic crystal di-methyl pyrrolidinium iodide

Above 110 °C the symmetric di-methyl-pyrrolidinium iodide salt forms a plastic crystal phase of interest in the area of new electrolyte materials. In this study ab initio calculations of this material has been conducted in order to assign the vibrational spectra. Raman spectroscopy measurements on the solid salt as well as on the salt dissolved in different solvents has been performed and these have been compared to the theoretical spectra. Furthermore, Raman spectra as a function of temperature have been recorded to investigate possible changes in inter-ionic interaction and/or structure through the phase transition. 1H NMR linewidth measurements as a function of temperature showed a large decrease in linewidth above 100 °C, attributed here to an increase in mobility in agreement with a previously reported phase transition at ~110 °C.

Understanding decimal numbers : a foundation for correct calculations

This paper reports on the effectiveness of an intervention designed to improve nursing students’ conceptual understanding of decimal numbers. Results of recent intervention studies have indicated some success at improving nursing students’ numeracy through practice in applying procedural rules for calculation and working in real or simulated practical contexts. However, in this we identified a fundamental problem: a significant minority of students had an inadequate understanding of decimal numbers. The intervention aimed to improve nursing students’ basic understanding of the size of decimal numbers, so that, firstly, calculation rules are more meaningful, and secondly, students can interpret decimal numbers (whether digital output or results of calculations) sensibly. A well-researched, time-efficient diagnostic instrument was used to identify individuals with an inadequate understanding of decimal numbers. We describe a remedial intervention that resulted in significant improvement on a delayed post-intervention test. We conclude that nurse educators should consider diagnosing and, as necessary, plan for remediation of students’ foundational understanding of decimal numbers before teaching procedural rules.

High-pressure structural transitions of Sc2O3 by X-ray diffraction, raman spectra, and ab initio calculations

The high-pressure behavior of scandium oxide (Sc₂O₃) has been investigated by angle-dispersive synchrotron powder X-ray diffraction and Raman spectroscopy techniques in a diamond anvil cell up to 46.2 and 42 GPa, respectively. An irreversible structural transformation of Sc₂O₃ from the cubic phase to a monoclinic high-pressure phase was observed at 36 GPa. Subsequent ab initio calculations for Sc₂O₃ predicted the phase transition from the cubic to monoclinic phase but at a much lower pressure. The same calculations predicted a second phase transition at 77 GPa from the monoclinic to hexagonal phase.

A tabular approach to titration calculations

Titrations are common laboratory exercises in high school and university chemistry courses, because they are easy, relatively inexpensive, and they illustrate a number of fundamental chemical principles. While students have little difficulty with calculations involving a single titration step, there is a significant leap in conceptual difficulty when “scaling-up” to more involved titration calculations with two or more steps. Currently, there is no alternative approach for students who are unable to follow the standard textbook method for titration calculations. This paper presents a new method of setting out the titration calculations, which helps these weaker students to better organize the data. The connection between the new method and current models of learning is discussed to explain why the tabular approach is successful for students who have difficulty following the standard textbook method.