A shock capturing scheme for steady, supercritical, free-surface flow

Abstract A finite difference scheme is presented for the solution of the two-dimensional shallow water equations in steady, supercritical flow. The scheme incorporates numerical characteristic decomposition, is shock capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supercritical in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

An algorithm for the shallow water equations with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations in a generalised coordinate system. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme has good jump capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for flow past a circular obstruction.

The physical pendulum in an advanced undergraduate course in mechanics

The physical pendulum treated with a Hamiltonian formulation is a natural topic for study in a course in advanced classical mechanics. For the past three years, we have been offering a series of problem sets studying this system numerically in our third-year undergraduate courses in mechanics. The problem sets investigate the physics of the pendulum in ways not easily accessible without computer technology and explore various algorithms for solving mechanics problems. Our computational physics is based on Mathematica with some C communicating with Mathematica, although nothing in this paper is dependent on that choice. We have nonetheless found this system, and particularly its graphics, to be a good one for use with undergraduates.

Memory-based Embodied Cognition: a computational architecture

At its most fundamental, cognition as displayed by biological agents (such as humans) may be said to consist of the manipulation and utilisation of memory. Recent discussions in the field of cognitive robotics have emphasised the role of embodiment and the necessity of a value or motivation for autonomous behaviour. This work proposes a computational architecture – the Memory-Based Cognitive (MBC) architecture – based upon these considerations for the autonomous development of control of a simple mobile robot. This novel architecture will permit the exploration of theoretical issues in cognitive robotics and animal cognition. Furthermore, the biological inspiration of the architecture is anticipated to result in a mobile robot controller which displays adaptive behaviour in unknown environments.

A groove-ploughing theory for the production of mega-scale glacial lineations, and implications for ice-stream mechanics

Mega-scale glacial lineations (MSGLs) are longitudinally aligned corrugations (ridge-groove structures 6-100 km long) in sediment produced subglacially. They are indicators of fast flow and a common signature of ice-stream beds. We develop a qualitative theory that accounts for their formation, and use numerical modelling, and observations of ice-stream beds to provide supporting evidence. Ice in contact with a rough (scale of 10-10(3) m) bedrock surface will mimic the form of the bed. Because of flow acceleration and convergence in ice-stream onset zones, the ice-base roughness elements experience transverse strain, transforming them from irregular bumps into longitudinally aligned keels of ice protruding downwards. Where such keels slide across a soft sedimentary bed, they plough through the sediments, carving elongate grooves, and deforming material up into intervening ridges. This explains MSGLs and has important implications for ice-stream mechanics. Groove ploughing provides the means to acquire new lubricating sediment and to transport large volumes of it downstream. Keels may provide basal drag in the force budget of ice streams, thereby playing a role in flow regulation and stability We speculate that groove ploughing permits significant ice-stream widening, thus facilitating high-magnitude ice discharge.

Accessing biodiversity resources in computational environments from workflow applications

In the Biodiversity World (BDW) project we have created a flexible and extensible Web Services-based Grid environment for biodiversity researchers to solve problems in biodiversity and analyse biodiversity patterns. In this environment, heterogeneous and globally distributed biodiversity-related resources such as data sets and analytical tools are made available to be accessed and assembled by users into workflows to perform complex scientific experiments. One such experiment is bioclimatic modelling of the geographical distribution of individual species using climate variables in order to predict past and future climate-related changes in species distribution. Data sources and analytical tools required for such analysis of species distribution are widely dispersed, available on heterogeneous platforms, present data in different formats and lack interoperability. The BDW system brings all these disparate units together so that the user can combine tools with little thought as to their availability, data formats and interoperability. The current Web Servicesbased Grid environment enables execution of the BDW workflow tasks in remote nodes but with a limited scope. The next step in the evolution of the BDW architecture is to enable workflow tasks to utilise computational resources available within and outside the BDW domain. We describe the present BDW architecture and its transition to a new framework which provides a distributed computational environment for mapping and executing workflows in addition to bringing together heterogeneous resources and analytical tools.

Selectivity of bis(calix[4]diquinone) ionophores towards metal ions in solvent dimethylsulfoxide: a molecular mechanics and molecular dynamics study

Molecular modelling studies have been carried out on two bis(calix[4]diqu(inone) ionophores, each created from two (calix[4]diquinone)arenes bridged at their bottom rims via alkyl chains (CH2)(n), 1: n = 3, 2; n = 4, in order to understand the reported selectivity of these ligands towards different sized metal ions such as Na+, K+, Rb+, and Cs+ in dmso solution. Conformational. analyses have been carried out which show that in the lowest energy conformations of the two macrocycles, the individual calix[4]diquinones exhibit a combination of partial cone, 1,3-alternate and cone conformations. The interactions of these alkali metals with the macrocycles have been studied in the gas phase and in a periodic box of solvent dmso by molecular mechanics and molecular dynamics calculations. Molecular mechanics calculations have been carried out on the mode of entry of the ions into the macrocycles and suggest that this is likely to occur from the side of the central cavity, rather than through the main axis of the calix[4]diquinones. There are energy barriers of ca. 19 kcal mol(-1) for this entry path in the gas phase, but in solution no energy barrier is found. Molecular dynamics simulations show that in both 1 and 2, though particularly in the latter macrocycle, one or two solvent molecules are bonded to the metal throughout the course of the simulation, often to the exclusion, of one or more of the ether oxygen atoms. By contrast the carbonyl oxygen atoms remain bonded to the metal atoms throughout with bond lengths that remain significantly less than those to the ether oxygen atoms. Free energy perturbation studies have been carried out in dmso and indicate that for 1, the selectivity follows the order Rb+ approximate to K+ > Cs+ >> Na+, which is partially in agreement with the experimental results. The energy differences are small and indeed the ratio between stability constants found for Cs+ and K+ complexes is only 0.60, showing that 1 has only a slight preference for K+. For the larger receptor 2, which is better suited to metal complexation, the binding affinity follows the pattern Cs+ >> Rb+ >> K+ >> Na+, with energy differences of 5.75, 2.61, 2.78 kcal mol(-1) which is perfectly consistent with experimental results.

Design, synthesis and computational modelling of aromatic tweezer-molecules as models for chain-folding polymer blends

Novel 'tweezer-type' complexes that exploit the interactions between pi-electron-rich pyrenyl groups and pi-electron deficient diimide units have been designed and synthesised. The component molecules leading to complex formation were accessed readily from commercially available starting materials through short and efficient syntheses. Analysis of the resulting complexes, using the visible charge-transfer band, revealed association constants that increased sequentially from 130 to 11,000 M-1 as increasing numbers of pi-pi-stacking interactions were introduced into the systems. Computational modelling was used to analyse the structures of these complexes, revealing low-energy chain-folded conformations for both components, which readily allow close, multiple pi-pi-stacking and hydrogen bonding to be achieved. In this paper, we give details of our initial studies of these complexes and outline how their behaviour could provide a basis for designing self-healing polymer blends for use in adaptive coating systems. (C) 2008 Elsevier Ltd. All rights reserved.

Quantum mechanics studies of the tautomers of dlhydrodiacetylformoin, an important Maillard intermediate and the synthesis of furaneol

Conformational analyses have been carried out on the acyclic and cyclic forms of dihydrodiacetylformoin, an important Maillard intermediate and precursor for furaneol. For the acyclic forms, the 2,5-dicarbonyl isomers have the lowest energy, while for the cyclic forms, the 3-carbonyl are favoured over the 4-carbonyl isomers. The likely path for cyclisation is investigated and it is shown that the favoured path is dependent upon the relative chiralities of the carbon atoms and in particular that the reaction proceeds more readily if C2 and C3 have different chiralities. After cyclisation, the reaction path to produce furaneol proceeds via the loss of a water molecule. This reaction has been studied with a model including two water molecules and a hydroxide anion and shows relatively low-energy barriers. (C) 2008 Published by Elsevier B.V.