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 Use of a Nitroxide Probe in DMSO to Capture Radicals in Particulate Pollution

A profluorescent nitroxide was used to evaluate the oxidative potential of pollution derived from a compression ignition engine fuelled with biodiesel. The reaction products responsible for the observed fluorescence increase when a DMSO solution of nitroxide was exposed to biodiesel exhaust were determined by using HPLC/MS. The main fluorescent species was identified as a methanesulfonamide adduct arising from the reaction of the nitroxide with DMSO-derived sulfoxyl radicals.

Distribution of organic-rich sediments through the Phanerozoic

It is commonly assumed that rates of accumulation of organic-rich strata have varied through geologic time with some periods that were particularly favorable for accumulation of petroleum source rocks or coals. A rigorous analysis of the validity of such an assumption requires consideration of the basic fact that although sedimentary rocks have been lost through geologic time to erosion and metamorphism. Consequently, their present-day global abundance decreases with their geologic age. Measurements of the global abundance of coal-bearing strata suggest that conditions for coal accumulation were exceptionally favorable during the late Carboniferous. Strata of this age constitute 21% of the world's coal-bearing strata. Global rates of coal accumulation appear to have been relatively constant since the end of the Carboniferous, with the exception of the Triassic which contains only 1.75% of the world's coal-bearing strata. Estimation of the global amount of discovered oil by age of the source rock show that 58% of the world's oil has been sourced from Cretaceous or younger strata and 99% from Silurian or younger strata. Although most geologic periods were favourable for oil source-rock accumulation the mid-Permian to mid-Jurassic appears to have been particularly unfavourable accounting for less than 2% of the world's oil. Estimation of the global amount of discovered natural gas by age of the source rock show that 48% of the world's oil has been sourced from Cretaceous or younger strata and 99% from Silurian or younger strata. The Silurian and Late Carboniferous were particularly favourable for gas source-rock accumulation respectively accounting for 12.9% and 6.9% of the world's gas. By contrast, Permian and Triassic source rocks account for only 1.7% of the world's natural gas. Rather than invoking global climatic or oceanic events to explain the relative abundance of organic rich sediments through time, examination of the data suggests the more critical control is tectonic. The majority of coals are associated with foreland basins and the majority of oil-prone source rocks are associated with rifting. The relative abundance of these types of basin through time determines the abundance and location of coals and petroleum source rocks.

Organic and acquisitive growth : re-examining, testing and extending Penrose’s growth theory

The Theory of the Growth of The Firm by Edith Penrose, first published in 1959, is a seminal contribution to the field of management. Penrose's intention was to create a theory of firm growth which was logically consistent and empirically tractable (Buckley and Casson, 2007). Much attention, however, has been focused on her unintended contribution to the resource-based view (henceforth RBV) (e.g. Kor and Mahoney, 2004; Lockett and Thompson, 2004) rather than her firm growth theory. We feel that this is unfortunate because despite a rapidly growing body of empirical work, conceptual advancement in growth studies has been limited (Davidsson and Wiklund, 2000; Davidsson et ai., 2006; Delmar, 1997; Storey, 1994). The growth literature frequently references Penrose's work, but little explicit testing of her ideas has been undertaken. This is surprising given that Penrose's work remains the most comprehensive theory of growth to date. One explanation is that she did not formality present her arguments, favouring verbal exposition over formalized models (Lockett, 2005; Lockett and Thompson, 2004). However, the central propositions and conclusions of her theory can be operationalized and empirically tested.

Effects of pH on pretreatment of sugarcane bagasse using aqueous imidazolium ionic liquids

Pretreatments of sugarcane bagasse for saccharification using different acid-catalysed imidazolium IL solutions (containing 20% water) at 130 °C for 30 min were investigated. At the same solution pH, pretreatment effectiveness in terms of glucan digestibility, delignification and xylan removal were similar for aqueous 1-butyl-3-methylimidazolium methane sulfonate (BMIMCH3SO3), 1-butyl-3-methylimidazolium methyl sulfate (BMIMCH3SO4), 1-ethyl-3-methylimidazolium chloride (EMIMCl) and 1-butyl-3-methylimidazolium chloride (BMIMCl). Decreasing solution pH of aqueous IL systems from 6.0 to 0.4 increased bagasse delignification and xylan removal, and as a result, improved glucan digestibility. The glucan digestibilities for bagasse samples pretreated by IL solutions with pH ≤ 0.9 were > 90% after 72 h of enzymatic hydrolysis. Without pH adjustment, the effectiveness of these aqueous IL solutions (except BMIMCH3SO3 because of its low natural pH of 0.9) to deconstruct the biomass was poor and the glucan digestibilities of pretreated bagasse samples were < 20%. These results show that pretreatment effectiveness of aqueous imidazolium ILs can simply be estimated from solution pH rather than hydrogen bond basicity (β) of the IL solution.

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.

Blocking layer optimisation of poly(3-hexylthiopene)based solid state dye sensitized solar cells

The optimisation study of the fabrication of a compact TiO2 blocking layer (via Spray Pyrolysis Deposition) for poly (3-hexylthiopene) (P3HT) for Solid State Dye Sensitized Solar Cells (SDSCs) is reported. We used a novel spray TiO2 precursor solution composition obtained by adding acetylacetone to a conventional formulation (Diisopropoxytitanium bis (acetylacetonate) in ethanol). By Scanning Electron Microscopy a TiO2 layer with compact morphology and thickness of around 100 nmis shown. Through a Tafel plot analysis an enhancement of the device diode-like behaviour induced by the acetylacetone blocking layer respect to the conventional one is observed. Significantly, the device fabricatedwith the acetylacetone blocking layer shows an overall increment of the cell performance with respect to the cellwith the conventional one (DJsc/Jsc = +13.8%, DFF/FF = +39.7%, DPCE/PCE = +55.6%). A conversion efficiency optimumis found for 15 successive spray cycles where the diode-like behaviour of the acetylacetone blocking layer is more effective. Over three batches of cells (fabricated with P3HT and dye D35) an average conversion efficiency value of 3.9% (under a class A sun simulator with 1 sun A.M. 1.5 illumination conditions) was measured. From the best cell we fabricated a conversion efficiency value of 4.5% was extracted. This represents a significant increment with respect to previously reported values for P3HT/dye D35 based SDSCs.

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.

Fabrication and mechanical and thermal behaviour of graphene oxide/epoxy nanocomposites

Bulk amount of graphite oxide was prepared by oxidation of graphite using the modified Hummers method and its ultrasonication in organic solvents yielded graphene oxide (GO). X-ray diffraction (XRD) pattern, X-ray photoelectron (XPS), Raman and Fourier transform infrared (FTIR) spectroscopy indicated the successful preparation of GO. XPS survey spectrum of GO revealed the presence of 66.6 at% C and 30.4 at% O. Scanning electron microscopy (SEM) and Transmission electron microscopy (TEM) images of the graphene oxide showed that they consist of a large amount of graphene oxide platelets with a curled morphology containing of a thin wrinkled sheet like structure. AFM image of the exfoliated GO signified that the average thickness of GO sheets is ~1.0 nm which is very similar to GO monolayer. GO/epoxy nanocomposites were prepared by typical solution mixing technique and influence of GO on mechanical and thermal properties of nanocomposites were investigated. As for the mechanical behaviour of GO/epoxy nanocomposites, 0.5 wt% GO in the nanocomposite achieved the maximum increase in the elastic modulus (~35%) and tensile strength (~7%). The TEM analysis provided clear image of microstructure with homogeneous dispersion of GO in the polymer matrix. The improved strength properties of GO/epoxy nanocomposites can be attributed to inherent strength of GO, the good dispersion and the strong interfacial interactions between the GO sheets and the polymer matrix. However, incorporation of GO showed significant negative effect on composite glass transition temperature (Tg). This may arise due to the interference of GO on curing reaction of epoxy.

Analysis of organic aerosols collected on filters by Aerosol Mass Spectrometry for source identification

Aerosol mass spectrometers (AMS) are powerful tools in the analysis of the chemical composition of airborne particles, particularly organic aerosols which are gaining increasing attention. However, the advantages of AMS in providing on-line data can be outweighed by the difficulties involved in its use in field measurements at multiple sites. In contrast to the on-line measurement by AMS, a method which involves sample collection on filters followed by subsequent analysis by AMS could significantly broaden the scope of AMS application. We report the application of such an approach to field studies at multiple sites. An AMS was deployed at 5 urban schools to determine the sources of the organic aerosols at the schools directly. PM1 aerosols were also collected on filters at these and 20 other urban schools. The filters were extracted with water and the extract run through a nebulizer to generate the aerosols, which were analysed by an AMS. The mass spectra from the samples collected on filters at the 5 schools were found to have excellent correlations with those obtained directly by AMS, with r2 ranging from 0.89 to 0.98. Filter recoveries varied between the schools from 40 -115%, possibly indicating that this method provides qualitative rather than quantitative information. The stability of the organic aerosols on Teflon filters was demonstrated by analysing samples stored for up to two years. Application of the procedure to the remaining 20 schools showed that secondary organic aerosols were the main source of aerosols at the majority of the schools. Overall, this procedure provides accurate representation of the mass spectra of ambient organic aerosols and could facilitate rapid data acquisition at multiple sites where AMS could not be deployed for logistical reasons.

First measurements of source apportionment of organic aerosols in the Southern Hemisphere

An Aerodyne Aerosol Mass Spectrometer was deployed at five urban schools to examine spatial and temporal variability of organic aerosols (OA) and positive matrix factorization (PMF) used for the first time in the Southern Hemisphere to apportion the sources of the OA across an urban area. The sources identified included hydrocarbon-like OA (HOA), biomass burning OA (BBOA) and oxygenated OA (OOA). At all sites, the main source was OOA, which accounted for 62–73% of the total OA mass and was generally more oxidized compared to those reported in the Northern Hemisphere. This suggests that there are differences in aging processes or regional sources in the two hemispheres. Unlike HOA and BBOA, OOA demonstrated instructive temporal variations but not spatial variation across the urban area. Application of cluster analysis to the PMF-derived sources offered a simple and effective method for qualitative comparison of PMF sources that can be used in other studies.