Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure

A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix to determine all the unknown CODs step by step. To deal with the interactions among cracks for multiple crack problems, all cracks in the problem are divided into two groups, namely the adjacent group and the far-field group, according to the distance to the current crack in consideration. The adjacent group contains cracks with relatively small distances but strong effects to the current crack, while the others, the cracks of far-field group are composed of those with relatively large distances. Correspondingly, the eigen COD of the current crack is computed in two parts. The first part is computed by using the fictitious tractions of adjacent cracks via the local Eshelby matrix derived from the traction boundary integral equations in discretized form, while the second part is computed by using those of far-field cracks so that the high computational efficiency can be achieved in the proposed approach. The numerical results of the proposed approach are compared not only with those using the dual boundary integral equations (D-BIE) and the BIE with numerical Green's functions (NGF) but also with those of the analytical solutions in literature. The effectiveness and the efficiency of the proposed approach is verified. Numerical examples are provided for the stress intensity factors of cracks, up to several thousands in number, in both the finite and infinite plates.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

Numerical solution of an optimal control model of dendritic cell treatment of a growing tumour

A new optimal control model of the interactions between a growing tumour and the host immune system along with an immunotherapy treatment strategy is presented. The model is based on an ordinary differential equation model of interactions between the growing tu- mour and the natural killer, cytotoxic T lymphocyte and dendritic cells of the host immune system, extended through the addition of a control function representing the application of a dendritic cell treat- ment to the system. The numerical solution of this model, obtained from a multi species Runge–Kutta forward-backward sweep scheme, is described. We investigate the effects of varying the maximum al- lowed amount of dendritic cell vaccine administered to the system and find that control of the tumour cell population is best effected via a high initial vaccine level, followed by reduced treatment and finally cessation of treatment. We also found that increasing the strength of the dendritic cell vaccine causes an increase in the number of natural killer cells and lymphocytes, which in turn reduces the growth of the tumour.

First flush analysis in urban catchments

The effectiveness of structural elements employed for stormwater mitigation such as bioretention basins and constructed wetlands depend on the compatibility between their design specifications and actual stormwater quality and quantity characteristics. These structural elements are commonly designed to accommodate the initial portion of runoff considering the occurrence of first flush. Therefore, the effectiveness of stormwater quality treatment primarily depends on the in-depth knowledge of the first flush phenomenon and the ability to provide appropriate treatment. The current scientific knowledge relating to first flush is limited primarily due to research investigations being undertaken based on lumped rainfall and runoff parameters. This paper presents the outcomes of an in-depth study undertaken of the first flush phenomenon using a set of indicators which are not only innovative, but is also able to accurately represent the characteristics of the different sectors in a runoff hydrograph. The analysis undertaken confirmed that pollutant wash-off during the initial 10% of runoff volume was critical for the occurrence of first flush. Typically first flush was found to last up to 40% of the runoff volume. The study outcomes provide new knowledge to enhance the effectiveness of structural stormwater treatment measures.

First flush behaviour in urban residential catchments

The current state of knowledge in relation to first flush does not provide a clear understanding of the role of rainfall and catchment characteristics in influencing this phenomenon. This is attributed to the inconsistent findings from research studies due to the unsatisfactory selection of first flush indicators and how first flush is defined. The research study discussed in this thesis provides the outcomes of a comprehensive analysis on the influence of rainfall and catchment characteristics on first flush behaviour in residential catchments. Two sets of first flush indicators are introduced in this study. These indicators were selected such that they are representative in explaining in a systematic manner the characteristics associated with first flush. Stormwater samples and rainfall-runoff data were collected and recorded from stormwater monitoring stations established at three urban catchments at Coomera Waters, Gold Coast, Australia. In addition, historical data were also used to support the data analysis. Three water quality parameters were analysed, namely, total suspended solids (TSS), total phosphorus (TP) and total nitrogen (TN). The data analyses were primarily undertaken using multi criteria decision making methods, PROMETHEE and GAIA. Based on the data obtained, the pollutant load distribution curve (LV) was determined for the individual rainfall events and pollutant types. Accordingly, two sets of first flush indicators were derived from the curve, namely, cumulative load wash-off for every 10% of runoff volume interval (interval first flush indicators or LV) from the beginning of the event and the actual pollutant load wash-off during a 10% increment in runoff volume (section first flush indicators or P). First flush behaviour showed significant variation with pollutant types. TSS and TP showed consistent first flush behaviour. However, the dissolved fraction of TN showed significant differences to TSS and TP first flush while particulate TN showed similarities. Wash-off of TSS, TP and particulate TN during the first 10% of the runoff volume showed no influence from corresponding rainfall intensity. This was attributed to the wash-off of weakly adhered solids on the catchment surface referred to as "short term pollutants" or "weakly adhered solids" load. However, wash-off after 10% of the runoff volume showed dependency on the rainfall intensity. This is attributed to the wash-off of strongly adhered solids being exposed when the weakly adhered solids diminish. The wash-off process was also found to depend on rainfall depth at the end part of the event as the strongly adhered solids are loosened due to impact of rainfall in the earlier part of the event. Events with high intensity rainfall bursts after 70% of the runoff volume did not demonstrate first flush behaviour. This suggests that rainfall pattern plays a critical role in the occurrence of first flush. Rainfall intensity (with respect to the rest of the event) that produces 10% to 20% runoff volume play an important role in defining the magnitude of the first flush. Events can demonstrate high magnitude first flush when the rainfall intensity occurring between 10% and 20% of the runoff volume is comparatively high while low rainfall intensities during this period produces low magnitude first flush. For events with first flush, the phenomenon is clearly visible up to 40% of the runoff volume. This contradicts the common definition that first flush only exists, if for example, 80% of the pollutant mass is transported in the first 30% of runoff volume. First flush behaviour for TN is different compared to TSS and TP. Apart from rainfall characteristics, the composition and the availability of TN on the catchment also play an important role in first flush. The analysis confirmed that events with low rainfall intensity can produce high magnitude first flush for the dissolved fraction of TN, while high rainfall intensity produce low dissolved TN first flush. This is attributed to the source limiting behaviour of dissolved TN wash-off where there is high wash-off during the initial part of a rainfall event irrespective of the intensity. However, for particulate TN, the influence of rainfall intensity on first flush characteristics is similar to TSS and TP. The data analysis also confirmed that first flush can occur as high magnitude first flush, low magnitude first flush or non existence of first flush. Investigation of the influence of catchment characteristics on first flush found that the key factors that influence the phenomenon are the location of the pollutant source, spatial distribution of the pervious and impervious surfaces in the catchment, drainage network layout and slope of the catchment. This confirms that first flush phenomenon cannot be evaluated based on a single or a limited set of parameters as a number of catchment characteristics should be taken into account. Catchments where the pollutant source is located close to the outlet, a high fraction of road surfaces, short travel time to the outlet, with steep slopes can produce high wash-off load during the first 50% of the runoff volume. Rainfall characteristics have a comparatively dominant impact on the wash-off process compared to the catchment characteristics. In addition, the pollutant characteristics also should be taken into account in designing stormwater treatment systems due to different wash-off behaviour. Analysis outcomes confirmed that there is a high TSS load during the first 20% of the runoff volume followed by TN which can extend up to 30% of the runoff volume. In contrast, high TP load can exist during the initial and at the end part of a rainfall event. This is related to the composition of TP available for the wash-off.

Study of the underlying electrochemistry of polycrystalline gold electrodes in aqueous solution and electrocatalysis by large amplitude Fourier transformed alternating current voltammetry

Polycrystalline gold electrodes of the kind that are routinely used in analysis and catalysis in aqueous media are often regarded as exhibiting relatively simple double-layer charging/discharging and monolayer oxide formation/ removal in the positive potential region. Application of the large amplitude Fourier transformed alternating current (FT-ac) voltammetric technique that allows the faradaic current contribution of fast electron-transfer processes to be emphasized in the higher harmonic components has revealed the presence of well-defined faradaic (premonolayer oxidation) processes at positive potentials in the double-layer region in acidic and basic media which are enhanced by electrochemical activation. These underlying quasi-reversible interfacial electron-transfer processes may mediate the course of electrocatalytic oxidation reactions of hydrazine, ethylene glycol, and glucose on gold electrodes in aqueous media. The observed responses support key assumptions associated with the incipient hydrous oxide adatom mediator (IHOAM) model of electrocatalysis.

Auto-inhibition of hydrogen gas evolution on gold in aqueous acid solution

It was demonstrated recently that dramatic changes in the redox behaviour of gold/aqueous solution interfaces may be observed following either cathodic or thermal electrode pretreatment. Further work on the cathodic pretreatment of gold in acid solution revealed that as the activity of the gold surface was increased, its performance as a substrate for hydrogen gas evolution under constant potential conditions deteriorated. The change in activity of the gold atoms at the interface, which was attributed to a hydrogen embrittlement process (the occurrence of the latter was subsequently checked by surface microscopy), was confirmed, as in earlier work, by the appearance of a substantial anodic peak at ca. 0.5 V (RHE) in a post-activation positive sweep. Changes in the catalytic activity of a metal surface reflect the fact that the structure (or topography), thermodynamic activity and electronic properties of a surface are dependent not only on pretreatment but also, in the case of the hydrogen evolution reaction, vary with time during the course of reaction. As will be reported shortly, similar (and often more dramatic) time-dependent behaviour was observed for hydrogen gas evolution on other metal electrodes.

The role of defects, or active states, in surface electrochemistry with particular reference to gold in neutral solution

Metastable, active, or nonequilibrium states due to the presence of abnormal structures and various types of defects are well known in metallurgy. The role of such states at gold surfaces in neutral aqueous media (an important electrode system in the microsensor area) was explored using cyclic voltammetry. It was demonstrated that, as postulated in earlier work from this laboratory, there is a close relationship between premonolayer oxidation, multilayer hydrous oxide reduction and electrocatalytic behaviour in the case of this and other metal electrode systems. Some of the most active, and therefore most important, entities at surfaces (e.g., metal adatoms) are not readily imageable or detectable by high resolution surface microscopy techniques. Cyclic voltammetry, however, provides significant, though not highly specific, information about such species. The main conclusion is that further practical and theoretical work on active states of metal surfaces is highly desirable as their behaviour is not simple and is of major importance in many electrocatalytic processes.

The formation of gold nanoparticles using hydroquinone as a reducing agent through a localized pH change upon addition of NaOH to a solution of HAuCl4

We demonstrate a rapid synthesis of gold nanoparticles using hydroquinone as a reducing agent under acidic conditions without the need for precursor seed particles. The nanoparticle formation process is facilitated by the addition of NaOH to a solution containing HAuCl4 and hydroquinone to locally change the pH; this enhances the reducing capability of hydroquinone to form gold nucleation centres, after which further growth of gold can take place through an autocatalytic mechanism. The stability of the nanoparticles is highly dependent on the initial solution pH, and both the concentration of added NaOH and hydroquinone present in solution. The gold nanoparticles were characterized by UV–visible spectroscopy, transmission electron microscopy, Fourier transform infrared spectroscopy, atomic force microscopy, dynamic light scattering, and zeta potential measurements. It was found that under optimal conditions that stable aqueous suspensions of 20 nm diameter nanoparticles can be achieved where benzoquinone, the oxidized product of hydroquinone, acts as a capping agent preventing nanoparticles aggregation.

The electrochemical corrosion behaviour of quaternary gold alloys when exposed to 3.5% NaCl solution

Lower carat gold alloys, specifically 9 carat gold alloys, containing less than 40 % gold, and alloying additions of silver, copper and zinc, are commonly used in many jewellery applications, to offset high costs and poor mechanical properties associated with pure gold. While gold is considered to be chemically inert, the presence of active alloying additions raises concerns about certain forms of corrosion, particularly selective dissolution of these alloys. The purpose of this study was to systematically study the corrosion behaviour of a series of quaternary gold–silver–copper–zinc alloys using dc potentiodynamic scanning in saline (3.5 % NaCl) environment. Full anodic/cathodic scans were conducted to determine the overall corrosion characteristics of the alloy, followed by selective anodic scans and subsequent morphological and compositional analysis of the alloy surface and corroding media to determine the extent of selective dissolution. Varying degrees of selective dissolution and associated corrosion rates were observed after anodic polarisation in 3.5 % NaCl, depending on the alloy composition. The corrosion behaviour of the alloys was determined by the extent of anodic reactions which induce (1) formation of oxide scales on the alloy surface and or (2) dissolution of Zn and Cu species. In general, the improved corrosion characteristics of alloy #3 was attributed to the composition of Zn/Cu in the alloy and thus favourable microstructure promoting the formation of protective oxide/chloride scales and reducing the extent of Cu and Zn dissolution.

A review of the removal of anions and oxyanions of the halogen elements from aqueous solution by layered double hydroxides

The application of layered double hydroxides (LDHs) and thermally activated LDHs for the removal of various fluorine (F-, BF-4), chlorine (Cl-,ClO-4), bromine (Br-, BrO-3) and iodine (I-, IO-3) species from aqueous solutions has been reviewed in this article. LDHs and thermally activated LDHs were able to significantly reduce the concentration of selected anions in laboratory scale experiments. The M2+:M3+ cation ratio of the LDH adsorbent was an important factor which influenced anion uptake. Though LDHs were able to remove some target anion species through anion exchange and surface adsorption thermal activation and reformation generally produced better results. The presence of competing anions including carbonate, phosphate and sulphate had a significant impact on uptake of the target anion as LDHs typically exhibit lower affinity towards monovalent anions compared to anions with multiple charges. The removal of fluoride and perchlorate from aqueous solution by a continuous flow system utilising fixed bed columns packed with LDH adsorbents has also been investigated. The adsorption capacity of the columns at breakpoint was heavily dependent on the flow rate and lower than result reported for the corresponding batch methods. There is still considerable scope for future research on numerous topics summarised in this article.

Observation of solution-induced corneal staining with fluorescein, rose bengal and lissamine green

Ever since sodium fluorescein (‘fluorescein’ [FL]) was first used to investigate the ocular surface over a century ago, the term ‘staining’ has been taken to mean the presence of ocular surface fluorescence [1]. This term has not been necessarily taken to infer any particular mechanism of causation, and indeed, can be attributed to a variety of possible aetiologies [2]. In recent times, there has been considerable interest in a form of ocular surface fluorescence seen in association with the use of certain combinations of soft contact lenses and multipurpose solutions. The first clinical account of this phenomenon was reported by Jones et al. [3], which was followed by a more formal investigation by the same author in 2002 [4]. Jones et al described this appearance as a ‘classic solution-based toxicity reaction’. Subsequently, this appearance has come to be known as ‘solution-induced corneal staining’ or more recently by the acronym ‘SICS’ [5]. The term SICS is potentially problematic in that from a cell biology point of view, there is an inference that ‘staining’ means the entry of a dye into corneal epithelial cells. Morgan and Maldonado-Codina [2] noted there was no foundation of solid scientific literature underpinning our understanding of the true basic causative mechanisms of this phenomenon; since that time, further work has been published in this field [6] and [7] but questions still remain about the precise aetiology of this phenomenon...