Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Workable solutions : the intersubjective careers of women with families

This chapter considers to what degree the careers of women with young families, both in and out of paid employment, are lived as contingent, intersubjective projects pursued across time and space, in the social condition of growing biographical possibilities and uneven social/ideological change. Their resolutions of competing priorities by engaging in various permutations of home-work and paid work are termed ‘workable solutions’, with an intentional play on the double sense of ‘work’ – firstly as labour, thus being able to perform work, whether paid or not; secondly as in being able to make things work or function in the family unit’s best interests, however defined.

Numerical solutions of stochastic differential equations – implementation and stability issues

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.

A generic framework and runtime environment for development and evaluation of behavioral biometrics solutions

Increasing use of computerized systems in our daily lives creates new adversarial opportunities for which complex mechanisms are exploited to mend the rapid development of new attacks. Behavioral Biometrics appear as one of the promising response to these attacks. But it is a relatively new research area, specific frameworks for evaluation and development of behavioral biometrics solutions could not be found yet. In this paper we present a conception of a generic framework and runtime environment which will enable researchers to develop, evaluate and compare their behavioral biometrics solutions with repeatable experiments under the same conditions with the same data.

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.

Neutralization of acid sulfate solutions using bauxite refinery residues and its derivatives

This investigation has shown that by transforming free caustic in red mud (RM) to Bayer hydrotalcite (during the seawater neutralization (SWN) process) enables a more controlled release mechanism for the neutralization of acid sulfate soils. The formation of hydrotalcite has been confirmed by X-ray diffraction (XRD) and differential thermalgravimetric analysis (DTG), while the dissolution of hydrotalcite and sodalite has been observed through XRD, DTG, pH plots, and ICP-OES. Coupling of all techniques enabled three neutralization mechanisms to be determined: (1) free alkali, (2) hydrotalcite dissolution, and (3) sodalite dissolution. The mechanisms are determined on the basis of ICP-OES and kinetic information. When the mass of RM or SWN-RM is greater than 0.08 g/50 mL, the pH of solution increases to a suitable value for plant life with aluminum leaching kept at a minimum. To obtain a neutralization pH greater than 6 in 10 min, the following ratio of bauxite residue (g) in 50 mL with a known iron sulfate (Fe2(SO4)3) concentration can be determined as follows: 0.04 g:50 mL:0.1 g/L of Fe2(SO4)3.

Laboratory and pilot scale pretreatment of sugarcane bagasse by acidified aqueous glycerol solutions

Pretreatment of sugarcane bagasse with acidified aqueous glycerol solution was evaluated at both laboratory and pilot scales. Laboratory scale pretreatment (4.00 g dry mass in 40.00 g liquid) with glycerol solutions containing ≤ 20 wt% water and 1.2 wt% HCl at 130 °C for 60 min resulted in biomass having glucan digestibilities of ≥ 88%. Comparable glucan enzymatic digestibility of 90% was achieved with bagasse pretreated at pilot scale (10 kg dry mass in 60 kg liquid) using a glycerol solution containing 0.4 wt% HCl and 17 wt% water at 130 °C for 15 min. We attribute more efficient pretreatment at pilot scale (despite shorter reaction time and reduced acid content) to improved mixing and heat transfer in a horizontal reactor. Pretreatment of sugarcane bagasse with acid-catalysed glycerol solutions likely produces glycerol-glycosides, which together with hydrolysed lignin are potential substrates for the production of biopolymers.

Aspects of the kinetics and solubility of silica and calcium oxalate composites in sugar solutions

Fouling of industrial surfaces by silica and calcium oxalate can be detrimental to a number of process streams. Solution chemistry plays a large roll in the rate and type of scale formed on industrial surfaces. This study is on the kinetics and thermodynamics of SiO2 and calcium oxalate composite formation in solutions containing Mg2+ ions, trans-aconitic acid and sucrose, to mimic factory sugar cane juices. The induction time (ti) of silicic acid polymerization is found to be dependent on the sucrose concentration and SiO2 supersaturation ratio (SS). Generalized kinetic and solubility models are developed for SiO2 and calcium oxalate in binary systems using response surface methodology. The role of sucrose, Mg, trans-aconitic acid, a mixture of Mg and trans-aconitic acid, SiO2 SS ratio and Ca in the formation of com- posites is explained using the solution properties of these species including their ability to form complexes.

Analysis of regionally enhanced GPS orbit and clock solutions and contribution to improvement of real-time precise point positioning

This work experimentally examines the performance benefits of a regional CORS network to the GPS orbit and clock solutions for supporting real-time Precise Point Positioning (PPP). The regionally enhanced GPS precise orbit solutions are derived from a global evenly distributed CORS network added with a densely distributed network in Australia and New Zealand. A series of computational schemes for different network configurations are adopted in the GAMIT-GLOBK and PANDA data processing. The precise GPS orbit results show that the regionally enhanced solutions achieve the overall orbit improvements with respect to the solutions derived from the global network only. Additionally, the orbital differences over GPS satellite arcs that are visible by any of the five Australia-wide CORS stations show a higher percentage of overall improvements compared to the satellite arcs that are not visible from these stations. The regional GPS clock and Uncalibrated Phase Delay (UPD) products are derived using the PANDA real time processing module from Australian CORS networks of 35 and 79 stations respectively. Analysis of PANDA kinematic PPP and kinematic PPP-AR solutions show certain overall improvements in the positioning performance from a denser network configuration after solution convergence. However, the clock and UPD enhancement on kinematic PPP solutions is marginal. It is suggested that other factors, such as effects of ionosphere, incorrectly fixed ambiguities, may be the more dominating, deserving further research attentions.

Estimating the effects of ambient temperature on mortality : methodological challenges and proposed solutions

The health impacts of exposure to ambient temperature have been drawing increasing attention from the environmental health research community, government, society, industries, and the public. Case-crossover and time series models are most commonly used to examine the effects of ambient temperature on mortality. However, some key methodological issues remain to be addressed. For example, few studies have used spatiotemporal models to assess the effects of spatial temperatures on mortality. Few studies have used a case-crossover design to examine the delayed (distributed lag) and non-linear relationship between temperature and mortality. Also, little evidence is available on the effects of temperature changes on mortality, and on differences in heat-related mortality over time. This thesis aimed to address the following research questions: 1. How to combine case-crossover design and distributed lag non-linear models? 2. Is there any significant difference in effect estimates between time series and spatiotemporal models? 3. How to assess the effects of temperature changes between neighbouring days on mortality? 4. Is there any change in temperature effects on mortality over time? To combine the case-crossover design and distributed lag non-linear model, datasets including deaths, and weather conditions (minimum temperature, mean temperature, maximum temperature, and relative humidity), and air pollution were acquired from Tianjin China, for the years 2005 to 2007. I demonstrated how to combine the case-crossover design with a distributed lag non-linear model. This allows the case-crossover design to estimate the non-linear and delayed effects of temperature whilst controlling for seasonality. There was consistent U-shaped relationship between temperature and mortality. Cold effects were delayed by 3 days, and persisted for 10 days. Hot effects were acute and lasted for three days, and were followed by mortality displacement for non-accidental, cardiopulmonary, and cardiovascular deaths. Mean temperature was a better predictor of mortality (based on model fit) than maximum or minimum temperature. It is still unclear whether spatiotemporal models using spatial temperature exposure produce better estimates of mortality risk compared with time series models that use a single site’s temperature or averaged temperature from a network of sites. Daily mortality data were obtained from 163 locations across Brisbane city, Australia from 2000 to 2004. Ordinary kriging was used to interpolate spatial temperatures across the city based on 19 monitoring sites. A spatiotemporal model was used to examine the impact of spatial temperature on mortality. A time series model was used to assess the effects of single site’s temperature, and averaged temperature from 3 monitoring sites on mortality. Squared Pearson scaled residuals were used to check the model fit. The results of this study show that even though spatiotemporal models gave a better model fit than time series models, spatiotemporal and time series models gave similar effect estimates. Time series analyses using temperature recorded from a single monitoring site or average temperature of multiple sites were equally good at estimating the association between temperature and mortality as compared with a spatiotemporal model. A time series Poisson regression model was used to estimate the association between temperature change and mortality in summer in Brisbane, Australia during 1996–2004 and Los Angeles, United States during 1987–2000. Temperature change was calculated by the current day's mean temperature minus the previous day's mean. In Brisbane, a drop of more than 3 �C in temperature between days was associated with relative risks (RRs) of 1.16 (95% confidence interval (CI): 1.02, 1.31) for non-external mortality (NEM), 1.19 (95% CI: 1.00, 1.41) for NEM in females, and 1.44 (95% CI: 1.10, 1.89) for NEM aged 65.74 years. An increase of more than 3 �C was associated with RRs of 1.35 (95% CI: 1.03, 1.77) for cardiovascular mortality and 1.67 (95% CI: 1.15, 2.43) for people aged < 65 years. In Los Angeles, only a drop of more than 3 �C was significantly associated with RRs of 1.13 (95% CI: 1.05, 1.22) for total NEM, 1.25 (95% CI: 1.13, 1.39) for cardiovascular mortality, and 1.25 (95% CI: 1.14, 1.39) for people aged . 75 years. In both cities, there were joint effects of temperature change and mean temperature on NEM. A change in temperature of more than 3 �C, whether positive or negative, has an adverse impact on mortality even after controlling for mean temperature. I examined the variation in the effects of high temperatures on elderly mortality (age . 75 years) by year, city and region for 83 large US cities between 1987 and 2000. High temperature days were defined as two or more consecutive days with temperatures above the 90th percentile for each city during each warm season (May 1 to September 30). The mortality risk for high temperatures was decomposed into: a "main effect" due to high temperatures using a distributed lag non-linear function, and an "added effect" due to consecutive high temperature days. I pooled yearly effects across regions and overall effects at both regional and national levels. The effects of high temperature (both main and added effects) on elderly mortality varied greatly by year, city and region. The years with higher heat-related mortality were often followed by those with relatively lower mortality. Understanding this variability in the effects of high temperatures is important for the development of heat-warning systems. In conclusion, this thesis makes contribution in several aspects. Case-crossover design was combined with distribute lag non-linear model to assess the effects of temperature on mortality in Tianjin. This makes the case-crossover design flexibly estimate the non-linear and delayed effects of temperature. Both extreme cold and high temperatures increased the risk of mortality in Tianjin. Time series model using single site’s temperature or averaged temperature from some sites can be used to examine the effects of temperature on mortality. Temperature change (no matter significant temperature drop or great temperature increase) increases the risk of mortality. The high temperature effect on mortality is highly variable from year to year.

Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock

We present a rigorous validation of the analytical Amadei solution for the stress concentration around an arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients b11 and b55 are not equal. It is shown from theoretical considerations and published experimental data that the b11 and b55 are not equal for realistic rocks. Second, we develop a 3D finite element elastic model within a hybrid analytical–numerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic, transverse isotropic and orthorhombic symmetries. It is concluded that the analytical Amadei solution is valid with no restriction on the borehole orientation or the symmetry of the elastic anisotropy.

Multicomponent charge transport in electrolyte solutions

The work presented in this thesis investigates the mathematical modelling of charge transport in electrolyte solutions, within the nanoporous structures of electrochemical devices. We compare two approaches found in the literature, by developing onedimensional transport models based on the Nernst-Planck and Maxwell-Stefan equations. The development of the Nernst-Planck equations relies on the assumption that the solution is infinitely dilute. However, this is typically not the case for the electrolyte solutions found within electrochemical devices. Furthermore, ionic concentrations much higher than those of the bulk concentrations can be obtained near the electrode/electrolyte interfaces due to the development of an electric double layer. Hence, multicomponent interactions which are neglected by the Nernst-Planck equations may become important. The Maxwell-Stefan equations account for these multicomponent interactions, and thus they should provide a more accurate representation of transport in electrolyte solutions. To allow for the effects of the electric double layer in both the Nernst-Planck and Maxwell-Stefan equations, we do not assume local electroneutrality in the solution. Instead, we model the electrostatic potential as a continuously varying function, by way of Poisson’s equation. Importantly, we show that for a ternary electrolyte solution at high interfacial concentrations, the Maxwell-Stefan equations predict behaviour that is not recovered from the Nernst-Planck equations. The main difficulty in the application of the Maxwell-Stefan equations to charge transport in electrolyte solutions is knowledge of the transport parameters. In this work, we apply molecular dynamics simulations to obtain the required diffusivities, and thus we are able to incorporate microscopic behaviour into a continuum scale model. This is important due to the small size scales we are concerned with, as we are still able to retain the computational efficiency of continuum modelling. This approach provides an avenue by which the microscopic behaviour may ultimately be incorporated into a full device-scale model. The one-dimensional Maxwell-Stefan model is extended to two dimensions, representing an important first step for developing a fully-coupled interfacial charge transport model for electrochemical devices. It allows us to begin investigation into ambipolar diffusion effects, where the motion of the ions in the electrolyte is affected by the transport of electrons in the electrode. As we do not consider modelling in the solid phase in this work, this is simulated by applying a time-varying potential to one interface of our two-dimensional computational domain, thus allowing a flow field to develop in the electrolyte. Our model facilitates the observation of the transport of ions near the electrode/electrolyte interface. For the simulations considered in this work, we show that while there is some motion in the direction parallel to the interface, the interfacial coupling is not sufficient for the ions in solution to be "dragged" along the interface for long distances.

From solving puzzles to designing solutions : integrating design thinking into evidence based practice

Evidence based practice (EBP) focuses on solving ‘tame’ problems, where literature supports question construction toward determining a solution. What happens when there is no existing evidence, or when the need for agility precludes a full EBP implementation? How might we build a more agile and innovative practice that facilitates the design of solutions to complex and wicked problems, particularly in cases where there is no existing literature? As problem solving and innovation methods, EBP and design thinking overlap considerably. The literature indicates the potential benefits to be gained for evidence based practice from adopting a human-centred rather than literature-focused foundation. The design thinking process is social and collaborative by nature, which enables it to be more agile and produce more innovative results than evidence based practice. This paper recommends a hybrid approach to maximise the strengths and benefits of the two methods for designing solutions to wicked problems. Incorporating design thinking principles and tools into EBP has the potential to move its applicability beyond tame problems and continuous improvement, and toward wicked problem solving and innovation. The potential of this hybrid approach in practice is yet to be explored.

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.

Analytical benchmark solutions for steel frame structures subject to local buckling effects

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. This paper contains a comprehensive set of analytical benchmark solutions for steel frames comprising non-compact sections, which can be used to verify the accuracy of simplified concentrated plasticity methods of advanced analysis. The analytical benchmark solutions were obtained using a distributed plasticity shell finite element model that explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. A brief description and verification of the shell finite element model is provided in this paper.