Approximate Riemann solutions of the two-dimensional shallow-water equations

A finite-difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow-water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gasdynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. An extension to the two-dimensional equations with source terms, is included. The scheme is applied to a dam-break problem with cylindrical symmetry.

Solutions of a two-dimensional dam-break problem

Solutions of a two-dimensional dam break problem are presented for two tailwater/reservoir height ratios. The numerical scheme used is an extension of one previously given by the author [J. Hyd. Res. 26(3), 293–306 (1988)], and is based on numerical characteristic decomposition. Thus approximate solutions are obtained via linearised problems, and the method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations.

Microwave-assisted hydrogel synthesis: a new method for crosslinking polymers in aqueous solutions

It has been found that hydrogels may be formed by microwave irradiation of aqueous solutions containing appropriate combinations of polymers. This new method of hydrogel synthesis yields sterile hydrogels without the use of monomers, eliminating the need for the removal of unreacted species from the final product. Results for two particularly successful combinations, poly(vinyl alcohol) with either poly(acrylic acid) or poly(methylvinylether-alt-maleic anhydride), are presented. Irradiation using temperatures of 100–150 °C was found to yield hydrogels with large equilibrium swelling degrees of 500–1000 g g−1. Material leached from both types of hydrogel shows little cytotoxicity towards HT29 cells.

Analytical and numerical solutions describing the inward solidification of a binary melt

We present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature. The thermal and physical properties of the melt and solid are assumed to be identical. An asymptotic method, valid in the limit of large Stefan number is used to decompose the moving boundary problem for a pure substance into a hierarchy of fixed-domain diffusion problems. Approximate, analytical solutions are derived for the inward solidification of a slab and a sphere of a binary melt which are compared with numerical solutions of the unapproximated system. The solutions are found to agree within the appropriate asymptotic regime of large Stefan number and small time. Numerical solutions are used to demonstrate the dependence of the solidification process upon the level of impurity and other parameters. We conclude with a discussion of the solutions obtained, their stability and possible extensions and refinements of our study.

Linear viscoelasticity from molecular dynamics simulation of entangled polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation:  bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

A novel method for production of lipid hydroperoxide- or oxysterol-rich low-density lipoprotein

LDL oxidation may be important in atherosclerosis. Extensive oxidation of LDL by copper induces increased uptake by macrophages, but results in decomposition of hydroperoxides, making it more difficult to investigate the effects of hydroperoxides in oxidised LDL on cell function. We describe here a simple method of oxidising LDL by dialysis against copper ions at 4 degrees C, which inhibits the decomposition of hydroperoxides, and allows the production of LDL rich in hydroperoxides (626 +/- 98 nmol/mg LDL protein) but low in oxysterols (3 +/- 1 nmol 7-ketocholesterol/mg LDL protein), whilst allowing sufficient modification (2.6 +/- 0.5 relative electrophoretic mobility) for rapid uptake by macrophages (5.49 +/- 0.75 mu g I-125-labelled hydroperoxide-rich LDL vs. 0.46 +/- 0.04 mu g protein/mg cell protein in 18 h for native LDL). By dialysing under the same conditions, but at 37 degrees C, the hydroperoxides are decomposed extensively and the LDL becomes rich in oxysterols. This novel method of oxidising LDL with high yield to either a hydroperoxide- or oxysterol-rich form by simply altering the temperature of dialysis may provide a useful tool for determining the effects of these different oxidation products on cell function. (C) 2007 Elsevier Ireland Ltd. All rights reserved.

Layer-by-layer deposition of praseodymium oxide on tin-doped indium oxide (ITO) surface

Praseodymium oxide as a thin film of controllable layer is known to display many unique physiochemical properties, which can be useful to ceramic, semiconductive and sensor industries. Here in this short paper, we describe a new chemical method of depositing praseodymium oxide on tin-doped indium oxide (ITO) surface using a layer-by-layer approach. The process is carried out by dipping the ITO in solutions of adsorbable polycationic chitosan and alkaline praseodymium hydroxide Pr(OH)(3) alternatively in order to build up the well-defined multi-layers. XRD suggests that the predominant form of the oxide is Pr6O11, obtained after heat treatment of the deposited ITO in static air at 500 degrees C. Microscopic studies including AFM, TEM and SEM indicate that the deposited oxide particles are uniform in size and shape (cylindrical), mesoporous and the thickness of the film can be controlled. AC impedance measurements of the deposited materials also reveal that the oxide layers display a high electrical conductivity hence suitable for sensor uses. (c) 2006 Elsevier B.V. All rights reserved.

Sustainable building solutions: a review of lessons from the natural world

The realisation that much of conventional. modern architecture is not sustainable over the long term is not new. Typical approaches are aimed at using energy and materials more efficiently. However, by clearly understanding the natural processes and their interactions with human needs in view, designers can create buildings that are delightful. functional productive and regenerative by design. The paper aims to review the biomimetics literature that is relevant to building materials and design. Biomimetics is the abstraction of good design from Nature, an enabling interdisciplinary science. particularly interested in emerging properties of materials and structures as a result of their hierarchical organisation. Biomimetics provides ideas relevant to: graded functionality of materials (nano-scale), adaptive response (nano-, micro-. and macro-scales): integrated intelligence (sensing and actuation at all scales), architecture and additional functionality. There are many examples in biology where emergent response of plants and animals to temperature, humidity and other changes in their physical environments is based on relatively simple physical principles. However, the implementation of design solutions which exploit these principles is where inspiration for man-made structures should be. We analyse specific examples of sustainability from Nature and the benefits or value that these solutions have brought to different creatures. By doing this, we appreciate how the natural world fits into the world of sustainable buildings and how as building engineers we can value its true application in delivering sustainable building.

The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.

Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Numerical solution of some nonlocal, nonlinear dispersive wave equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

In this paper we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying `bulge', symmetric in the longitudinal direction. Extending the work in Biggs (2012), we first employ a WKBJ-type ansatz to identify the possible quasi-mode solutions which propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-on regions. We note that the expansions are nonuniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-on regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x = 0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

Principles and calibration of solid phase microextraction fibre (passive sampler) for measurements of airflow and air infiltration in dwellings

Tracer gas techniques have been the most appropriate experimental method of determining airflows and ventilation rates in houses. However, current trends to reduce greenhouse gas effects have prompted the need for alternative techniques, such as passive sampling. In this research passive sampling techniques have been used to demonstrate the potential to fulfil these requirements by using solutions of volatile organic compounds (VOCs) and solid phase microextraction (SPME) fibres. These passive sampling techniques have been calibrated against tracer gas decay techniques and measurements from a standard orifice plate. Two constant sources of volatile organic compounds were diffused into two sections of a humidity chamber and sampled using SPME fibres. From a total of four SPME fibres (two in each section), reproducible results were obtained. Emission rates and air movement from one section to the other were predicted using developed algorithms. Comparison of the SPME fibre technique with that of the tracer gas technique and measurements from an orifice plate showed similar results with good precision and accuracy. With these fibres, infiltration rates can be measured over grab samples in a time weighted averaged period lasting from 10 minutes up to several days. Key words: passive samplers, solid phase microextraction fibre, tracer gas techniques, airflow, air infiltration, houses.

Infrared absorption spectra, radiative efficiencies, and global warming potentials of perfluorocarbons: Comparison between experiment and theory

Experimentally and theoretically determined infrared spectra are reported for a series of straight-chain perfluorocarbons: C2F6, C3F8, C4F10, C5F12, C6F14, and C8F18. Theoretical spectra were determined using both density functional (DFT) and ab initio methods. Radiative efficiencies (REs) were determined using the method of Pinnock et al. (1995) and combined with atmospheric lifetimes from the literature to determine global warming potentials (GWPs). Theoretically determined absorption cross sections were within 10% of experimentally determined values. Despite being much less computationally expensive, DFT calculations were generally found to perform better than ab initio methods. There is a strong wavenumber dependence of radiative forcing in the region of the fundamental C-F vibration, and small differences in wavelength between band positions determined by theory and experiment have a significant impact on the REs. We apply an empirical correction to the theoretical spectra and then test this correction on a number of branched chain and cyclic perfluoroalkanes. We then compute absorption cross sections, REs, and GWPs for an additional set of perfluoroalkenes.

Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.