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.

Exponential asymptotics of free surface flow due to a line source

The steady problem of free surface flow due to a submerged line source is revisited for the case in which the fluid depth is finite and there is a stagnation point on the free surface directly above the source. Both the strength of the source and the fluid speed in the far field are measured by a dimensionless parameter, the Froude number. By applying techniques in exponential asymptotics, it is shown that there is a train of periodic waves on the surface of the fluid with an amplitude which is exponentially small in the limit that the Froude number vanishes. This study clarifies that periodic waves do form for flows due to a source, contrary to a suggestion by Chapman & Vanden-Broeck (2006, J. Fluid Mech., 567, 299--326). The exponentially small nature of the waves means they appear beyond all orders of the original power series expansion; this result explains why attempts at describing these flows using a finite number of terms in an algebraic power series incorrectly predict a flat free surface in the far field.

Timing and emplacement dynamics of newly recognised mass flow deposits at ~ 8–12 ka offshore Soufrière Hills volcano, Montserrat : how submarine stratigraphy can complement subaerial eruption histories

This contribution describes two mass movement deposits (total volume ~0.5 km3) identified in seven marine cores located 8 to 15 km offshore southern Montserrat, West Indies. The deposits were emplaced in the last 35 ka and have not previously been recognised in either the subaerial or distal submarine records. Age constraints, provided by radiocarbon dating, show that an explosive volcanic eruption occurred at ca 8–12 ka, emplacing a primary eruption-related deposit that overlies a large (~0.3 km3) reworked bioclastic and volcaniclastic flow deposit, formed from a shelf collapse between 8 and 35 ka. The origin of these deposits has been deduced through the correlation of marine sediment cores, component analysis and geochemical analysis. The 8–12 ka primary volcanic deposit was likely derived from a highly-erosive pyroclastic flow from the Soufrière Hills volcano that entered the ocean and mixed with the water column forming a water-supported density current. Previous investigations of the eruption record suggested that there was a hiatus in activity at the Soufrière Hills volcano between 16 and 6 ka. The ca 8–12 ka eruptive episode identified here shows that this hiatus was shorter than previously hypothesised, and thus highlights the importance of obtaining an accurate and completemarine record of events offshore from volcanic islands and incorporating such data into eruption history reconstructions. Comparisons with the submarine deposit characteristics of the 2003 dome collapse also suggests that the ~8–12 ka eruptive episode was more explosive than eruptions from the current eruptive episode.

Modelling the flow of juice through a mill

A juice flow model has been developed to estimate the juice expression at the four nips of a sixroller mill. An extended volumetric theory was applied to determine the juice expressed at each nip. The model was applied to a first and final mill, using typical mill settings and an empirical equation to estimate reabsorption. Results of using the model for typical heavy-duty pressure feeder settings show that most of the juice is expressed at the pressure feeder nip. Since the pressure feeders are remote from the mill, a significant portion of the juice is expressed before the bagasse enters the mill.

Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

An efficient numerical method to compute nonlinear solutions for two-dimensional steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996, J. Fluid Mech., 330, 339-347). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free-surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free-surface a priori while solving for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify eleven basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free-surface, given the free-surface shape itself.

Prediction of IBD based on population history for fine gene mapping

A novel multiple regression method (RM) is developed to predict identity-by-descent probabilities at a locus L (IBDL), among individuals without pedigree, given information on surrounding markers and population history. These IBDL probabilities are a function of the increase in linkage disequilibrium (LD) generated by drift in a homogeneous population over generations. Three parameters are sufficient to describe population history: effective population size (Ne), number of generations since foundation (T), and marker allele frequencies among founders (p). IBD L are used in a simulation study to map a quantitative trait locus (QTL) via variance component estimation. RM is compared to a coalescent method (CM) in terms of power and robustness of QTL detection. Differences between RM and CM are small but significant. For example, RM is more powerful than CM in dioecious populations, but not in monoecious populations. Moreover, RM is more robust than CM when marker phases are unknown or when there is complete LD among founders or Ne is wrong, and less robust when p is wrong. CM utilises all marker haplotype information, whereas RM utilises information contained in each individual marker and all possible marker pairs but not in higher order interactions. RM consists of a family of models encompassing four different population structures, and two ways of using marker information, which contrasts with the single model that must cater for all possible evolutionary scenarios in CM.

Candidate gene analysis for quantitative traits using the transmission disequilibrium test : the example of the melanocortin 4-receptor in pigs

Population-wide associations between loci due to linkage disequilibrium can be used to map quantitative trait loci (QTL) with high resolution. However, spurious associations between markers and QTL can also arise as a consequence of population stratification. Statistical methods that cannot differentiate between loci associations due to linkage disequilibria from those caused in other ways can render false-positive results. The transmission-disequilibrium test (TDT) is a robust test for detecting QTL. The TDT exploits within-family associations that are not affected by population stratification. However, some TDTs are formulated in a rigid-form, with reduced potential applications. In this study we generalize TDT using mixed linear models to allow greater statistical flexibility. Allelic effects are estimated with two independent parameters: one exploiting the robust within-family information and the other the potentially biased between-family information. A significant difference between these two parameters can be used as evidence for spurious association. This methodology was then used to test the effects of the fourth melanocortin receptor (MC4R) on production traits in the pig. The new analyses supported the previously reported results; i.e., the studied polymorphism is either causal of in very strong linkage disequilibrium with the causal mutation, and provided no evidence for spurious association.

Investigation into the noise map based on traffic flow prediction in the citywide road network

As one of the measures for decreasing road traffic noise in a city, the control of the traffic flow and the physical distribution is considered. To conduct the measure effectively, the model for predicting the traffic flow in the citywide road network is necessary. In this study, the existing model named AVENUE was used as a traffic flow prediction model. The traffic flow model was integrated with the road vehicles' sound power model and the sound propagation model, and the new road traffic noise prediction model was established. As a case study, the prediction model was applied to the road network of Tsukuba city in Japan and the noise map of the city was made. To examine the calculation accuracy of the noise map, the calculated values of the noise at the main roads were compared with the measured values. As a result, it was found that there was a possibility that the high accuracy noise map of the city could be made by using the noise prediction model developed in this study.

Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

Non-Newtonian natural convection flow along an isothermal horizontal circular cylinder using modified power-law model

Laminar two-dimensional natural convection boundary-layer flow of non-Newtonian fluids along an isothermal horizontal circular cylinder has been studied using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning as well as shear thickening fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively.

On the effective hydraulic conductivity and macrodispersivity for density-dependent groundwater flow

In this paper, semi-analytical expressions of the effective hydraulic conductivity ( KE) and macrodispersivity ( αE) for 3D steady-state density-dependent groundwater flow are derived using a stationary spectral method. Based on the derived expressions, we present the dependence of KE and αE on the density of fluid under different dispersivity and spatial correlation scale of hydraulic conductivity. The results show that the horizontal KE and αE are not affected by density-induced flow. However, due to gravitational instability of the fluid induced by density contrasts, both vertical KE and αE are found to be reduced slightly when the density factor ( γ ) is less than 0.01, whereas significant decreases occur when γ exceeds 0.01. Of note, the variation of KE and αE is more significant when local dispersivity is small and the correlation scale of hydraulic conductivity is large.

Image-based flow visualisation (IBFV) to enhance interpretation of complex flow patterns within a shallow tidal barrier estuary

We applied a texture-based flow visualisation technique to a numerical hydrodynamic model of the Pumicestone Passage in southeast Queensland, Australia. The quality of the visualisations using our flow visualisation tool, are compared with animations generated using more traditional drogue release plot and velocity contour and vector techniques. The texture-based method is found to be far more effective in visualising advective flow within the model domain. In some instances, it also makes it easier for the researcher to identify specific hydrodynamic features within the complex flow regimes of this shallow tidal barrier estuary as compared with the direct and geometric based methods.

Modelling the flow of cane constituents through the milling process of a raw sugar factory

This thesis reports on an investigation to develop an advanced and comprehensive milling process model of the raw sugar factory. Although the new model can be applied to both, the four-roller and six-roller milling units, it is primarily developed for the six-roller mills which are widely used in the Australian sugar industry. The approach taken was to gain an understanding of the previous milling process simulation model "MILSIM" developed at the University of Queensland nearly four decades ago. Although the MILSIM model was widely adopted in the Australian sugar industry for simulating the milling process it did have some incorrect assumptions. The study aimed to eliminate all the incorrect assumptions of the previous model and develop an advanced model that represents the milling process correctly and tracks the flow of other cane components in the milling process which have not been considered in the previous models. The development of the milling process model was done is three stages. Firstly, an enhanced milling unit extraction model (MILEX) was developed to access the mill performance parameters and predict the extraction performance of the milling process. New definitions for the milling performance parameters were developed and a complete milling train along with the juice screen was modelled. The MILEX model was validated with factory data and the variation in the mill performance parameters was observed and studied. Some case studies were undertaken to study the effect of fibre in juice streams, juice in cush return and imbibition% fibre on extraction performance of the milling process. It was concluded from the study that the empirical relations developed for the mill performance parameters in the MILSIM model were not applicable to the new model. New empirical relations have to be developed before the model is applied with confidence. Secondly, a soluble and insoluble solids model was developed using modelling theory and experimental data to track the flow of sucrose (pol), reducing sugars (glucose and fructose), soluble ash, true fibre and mud solids entering the milling train through the cane supply and their distribution in juice and bagasse streams.. The soluble impurities and mud solids in cane affect the performance of the milling train and further processing of juice and bagasse. New mill performance parameters were developed in the model to track the flow of cane components. The developed model is the first of its kind and provides some additional insight regarding the flow of soluble and insoluble cane components and the factors affecting their distribution in juice and bagasse. The model proved to be a good extension to the MILEX model to study the overall performance of the milling train. Thirdly, the developed models were incorporated in a proprietary software package "SysCAD’ for advanced operational efficiency and for availability in the ‘whole of factory’ model. The MILEX model was developed in SysCAD software to represent a single milling unit. Eventually the entire milling train and the juice screen were developed in SysCAD using series of different controllers and features of the software. The models developed in SysCAD can be run from macro enabled excel file and reports can be generated in excel sheets. The flexibility of the software, ease of use and other advantages are described broadly in the relevant chapter. The MILEX model is developed in static mode and dynamic mode. The application of the dynamic mode of the model is still under progress.

The ancient gene C12orf29 : an exploration of its role in the chordate body plan

The sheep (Ovis aries) is commonly used as a large animal model in skeletal research. Although the sheep genome has been sequenced there are still only a limited number of annotated mRNA sequences in public databases. A complementary DNA (cDNA) library was constructed to provide a generic resource for further exploration of genes that are actively expressed in bone cells in sheep. It was anticipated that the cDNA library would provide molecular tools for further research into the process of fracture repair and bone homeostasis, and add to the existing body of knowledge. One of the hallmarks of cDNA libraries has been the identification of novel genes and in this library the full open reading frame of the gene C12orf29 was cloned and characterised. This gene codes for a protein of unknown function with a molecular weight of 37 kDa. A literature search showed that no previous studies had been conducted into the biological role of C12orf29, except for some bioinformatics studies that suggested a possible link with cancer. Phylogenetic analyses revealed that C12orf29 had an ancient pedigree with a homologous gene found in some bacterial taxa. This implied that the gene was present in the last common eukaryotic ancestor, thought to have existed more than 2 billion years ago. This notion was further supported by the fact that the gene is found in taxa belonging to the two major eukaryotic branches, bikonts and unikonts. In the bikont supergroup a C12orf29-like gene was found in the single celled protist Naegleria gruberi, whereas in the unikont supergroup, encompassing the metazoa, the gene is universal to all chordate and, therefore, vertebrate species. It appears to have been lost to the majority of cnidaria and protostomes taxa; however, C12orf29-like genes have been found in the cnidarian freshwater hydra and the protostome Pacific oyster. The experimental data indicate that C12orf29 has a structural role in skeletal development and tissue homeostasis, whereas in silico analysis of the human C12orf29 promoter region suggests that its expression is potentially under the control of the NOTCH, WNT and TGF- developmental pathways, as well SOX9 and BAPX1; pathways that are all heavily involved in skeletogenesis. Taken together, this investigation provides strong evidence that C12orf29 has a very important role in the chordate body plan, in early skeletal development, cartilage homeostasis, and also a possible link with spina bifida in humans.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.