Advanced mathematical modelling and experimental investigation of new torque arms for shaft-mounted drives

Shaft-mounted gearboxes are widely used in industry. The torque arm that holds the reactive torque on the housing of the gearbox, if properly positioned creates the reactive force that lifts the gearbox and unloads the bearings of the output shaft. The shortcoming of these torque arms is that if the gearbox is reversed the direction of the reactive force on the torque arm changes to opposite and added to the weight of the gearbox overloads the bearings shortening their operating life. In this paper, a new patented design of torque arms that develop a controlled lifting force and counteract the weight of the gearbox regardless of the direction of the output shaft rotation is described. Several mathematical models of the conventional and new torque arms were developed and verified experimentally on a specially built test rig that enables modelling of the radial compliance of the gearbox bearings and elastic elements of the torque arms. Comparison showed a good agreement between theoretical and experimental results.

The application of a profluorescent nitroxide probe to detect reactive oxygen species derived from combustion-generated particulate matter

Particulate pollution has been widely recognised as an important risk factor to human health. In addition to increases in respiratory and cardiovascular morbidity associated with exposure to particulate matter (PM), WHO estimates that urban PM causes 0.8 million premature deaths globally and that 1.5 million people die prematurely from exposure to indoor smoke generated from the combustion of solid fuels. Despite the availability of a huge body of research, the underlying toxicological mechanisms by which particles induce adverse health effects are not yet entirely understood. Oxidative stress caused by generation of free radicals and related reactive oxygen species (ROS) at the sites of deposition has been proposed as a mechanism for many of the adverse health outcomes associated with exposure to PM. In addition to particle-induced generation of ROS in lung tissue cells, several recent studies have shown that particles may also contain ROS. As such, they present a direct cause of oxidative stress and related adverse health effects. Cellular responses to oxidative stress have been widely investigated using various cell exposure assays. However, for a rapid screening of the oxidative potential of PM, less time-consuming and less expensive, cell-free assays are needed. The main aim of this research project was to investigate the application of a novel profluorescent nitroxide probe, synthesised at QUT, as a rapid screening assay in assessing the oxidative potential of PM. Considering that this was the first time that a profluorescent nitroxide probe was applied in investigating the oxidative stress potential of PM, the proof of concept regarding the detection of PM–derived ROS by using such probes needed to be demonstrated and a sampling methodology needed to be developed. Sampling through an impinger containing profluorescent nitroxide solution was chosen as a means of particle collection as it allowed particles to react with the profluorescent nitroxide probe during sampling, avoiding in that way any possible chemical changes resulting from delays between the sampling and the analysis of the PM. Among several profluorescent nitroxide probes available at QUT, bis(phenylethynyl)anthracene-nitroxide (BPEAnit) was found to be the most suitable probe, mainly due to relatively long excitation and emission wavelengths (λex= 430 nm; λem= 485 and 513 nm). These wavelengths are long enough to avoid overlap with the background fluorescence coming from light absorbing compounds which may be present in PM (e.g. polycyclic aromatic hydrocarbons and their derivatives). Given that combustion, in general, is one of the major sources of ambient PM, this project aimed at getting an insight into the oxidative stress potential of combustion-generated PM, namely cigarette smoke, diesel exhaust and wood smoke PM. During the course of this research project, it was demonstrated that the BPEAnit probe based assay is sufficiently sensitive and robust enough to be applied as a rapid screening test for PM-derived ROS detection. Considering that for all three aerosol sources (i.e. cigarette smoke, diesel exhaust and wood smoke) the same assay was applied, the results presented in this thesis allow direct comparison of the oxidative potential measured for all three sources of PM. In summary, it was found that there was a substantial difference between the amounts of ROS per unit of PM mass (ROS concentration) for particles emitted by different combustion sources. For example, particles from cigarette smoke were found to have up to 80 times less ROS per unit of mass than particles produced during logwood combustion. For both diesel and wood combustion it has been demonstrated that the type of fuel significantly affects the oxidative potential of the particles emitted. Similarly, the operating conditions of the combustion source were also found to affect the oxidative potential of particulate emissions. Moreover, this project has demonstrated a strong link between semivolatile (i.e. organic) species and ROS and therefore, clearly highlights the importance of semivolatile species in particle-induced toxicity.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

The synthesis of novel nitroxides and their application as small-molecule antioxidants and profluorescent probes for oxidative stress

The detection and potential treatment of oxidative stress in biological systems has been explored using isoindoline-based nitroxide radicals. A novel tetraethyl-fluorescein nitroxide was synthesised for its use as a profluorescent probe for redox processes in biological systems. This tetraethyl system, as well as a tetramethyl-fluorescein nitroxide, were shown to be sensitive and selective probes for superoxide in vitro. The redox environment of cellular systems was also explored using the tetramethylfluorescein species based on its reduction to the hydroxylamine. Flow cytometry was employed to assess the extent of nitroxide reduction, reflecting the overall cellular redox environment. Treatment of normal fibroblasts with rotenone and 2-deoxyglucose resulted in an oxidising cellular environment as shown by the lack of reduction of the fluorescein-nitroxide system. Assessment of the tetraethyl-fluorescein nitroxide system in the same way demonstrated its enhanced resistance to reduction and offers the potential to detect and image biologically relevant reactive oxygen species directly. Importantly, these profluorescent nitroxide compounds were shown to be more effective than the more widely used and commercially available probes for reactive oxygen species such as 2’,7’-dichlorodihydrofluorescein diacetate. Fluorescence imaging of the tetramethyl-fluorescein nitroxide and a number of other rhodamine-nitroxide derivatives was undertaken, revealing the differential cellular localisation of these systems and thus their potential for the detection of redox changes in specific cellular compartments. As well as developing novel methods for the detection of oxidative stress, a number of novel isoindoline nitroxides were synthesised for their potential application as small-molecule antioxidants. These compounds incorporated known pharmacophores into the isoindoline-nitroxide structure in an attempt to increase their efficacy in biological systems. A primary and a secondary amine nitroxide were synthesised which incorporated the phenethylamine backbone of the sympathomimetic amine class of drugs. Initial assessment of the novel primary amine derivative indicated a protective effect comparable to that of 5-carboxy-1,1,3,3- tetramethylisoindolin-2-yloxyl. Methoxy-substituted nitroxides were also synthesised as potential antioxidants for their structural similarity to some amphetamine type stimulants. A copper-catalysed methodology provided access to both the mono- and di-substituted methoxy-nitroxides. Deprotection of the ethers in these compounds using boron tribromide successfully produced a phenolnitroxide, however the catechol moiety in the disubstituted derivative appeared to undergo reaction with the nitroxide to produce quinone-like degradation products. A novel fluoran-nitroxide was also synthesised from the methoxy-substituted nitroxide, providing a pH-sensitive spin probe. An amino-acid precursor containing a nitroxide moiety was also synthesised for its application as a dual-action antioxidant. N-Acetyl protection of the nitroxide radical was necessary prior to the Erlenmeyer reaction with N-acetyl glycine. Hydrolysis and reduction of the azlactone intermediate produced a novel amino acid precursor with significant potential as an effective antioxidant.

Application of infrared emission spectroscopy to the thermal transition of indium hydroxide to indium oxide nanocubes

Cubic indium hydroxide nanomaterials were obtained by a low temperature soft-chemical method without any surfactants. The transition of nano-cubic indium hydroxide to cubic indium oxide during dehydroxylation has been studied by infrared emission spectroscopy. The spectra are related to the structure of the materials and the changes in the structure upon thermal treatment. The infrared absorption spectrum of In(OH)3 is characterised by an intense OH deformation band at 1150 cm-1 and two O-H stretching bands at 3107 and 3221 cm-1. In the infrared emission spectra, the hydroxyl-stretching and hydroxyl-bending bands diminish dramatically upon heating, and no intensity remains after 200 °C. However, new low intensity bands are found in the OH deformation region at 915 cm-1 and in OH stretching region at 3437 cm-1. These bands are attributed to the vibrations of newly formed InOH bonds because of the release and transfer of protons during calcination of the nanomaterial. The use of infrared emission spectroscopy enables the low-temperature phase transition brought about through dehydration of In(OH)3 nanocubes to be studied.

An innovative robust reactive surgery assignment model

Online scheduling in the Operating Theatre Department is a dynamic process that deals with both elective and emergency patients. Each business day begins with an elective schedule determined in advance based on a mastery surgery schedule. Throughout the course of the day however, disruptions to this baseline schedule occur due to variations in treatment time, emergency arrivals, equipment failure and resource unavailability. An innovative robust reactive surgery assignment model is developed for the operating theatre department. Following the completion of each surgery, the schedule is re-solved taking into account any disruptions in order to minimise cancellations of pre-planned patients and maximise throughput of emergency cases. The single theatre case is solved and future work on the computationally more complex multiple theatre case under resource constraints is discussed.

Modelling of operating theatres using simulation

This paper describes the development of a simulation model for operating theatres. Elective patient scheduling is complicated by several factors; stochastic demand for resources due to variation in the nature and severity of a patient’s illness, unexpected complications in a patient’s course of treatment and the arrival of non-scheduled emergency patients which compete for resources. Extend simulation software was used for its ability to represent highly complex systems and analyse model outputs. Patient arrivals and lengths of surgery are determined by analysis of historical data. The model was used to explore the effects increasing patient arrivals and alternative elective patient admission disciplines would have on the performance measures. The model can be used as a decision support system for hospital planners.

Bow and stern flows with constant vorticity

Free surface flows of a rotational fluid past a two-dimensional semi-infinite body are considered. The fluid is assumed to be inviscid, incompressible, and of finite depth. A boundary integral method is used to solve the problem for the case where the free surface meets the body at a stagnation point. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterized by a train of waves upstream. It is shown numerically that the amplitude of these waves increases as each of the Froude number, vorticity and height of the body above the bottom increases.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Free surface problems for static Coulomb-Mohr granular solids

This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.

Performance analysis of hybrid liquid desiccant solar cooling system

This thesis investigates the coefficient of performance (COP) of a hybrid liquid desiccant solar cooling system. This hybrid cooling system includes three sections: 1) conventional air-conditioning section; 2) liquid desiccant dehumidification section and 3) air mixture section. The air handling unit (AHU) with mixture variable air volume design is included in the hybrid cooling system to control humidity. In the combined system, the air is first dehumidified in the dehumidifier and then mixed with ambient air by AHU before entering the evaporator. Experiments using lithium chloride as the liquid desiccant have been carried out for the performance evaluation of the dehumidifier and regenerator. Based on the air mixture (AHU) design, the electrical coefficient of performance (ECOP), thermal coefficient of performance (TCOP) and whole system coefficient of performance (COPsys) models used in the hybrid liquid desiccant solar cooing system were developed to evaluate this system performance. These mathematical models can be used to describe the coefficient of performance trend under different ambient conditions, while also providing a convenient comparison with conventional air conditioning systems. These models provide good explanations about the relationship between the performance predictions of models and ambient air parameters. The simulation results have revealed the coefficient of performance in hybrid liquid desiccant solar cooling systems substantially depends on ambient air and dehumidifier parameters. Also, the liquid desiccant experiments prove that the latent component of the total cooling load requirements can be easily fulfilled by using the liquid desiccant dehumidifier. While cooling requirements can be met, the liquid desiccant system is however still subject to the hysteresis problems.

Optimization problems for controlled mechanical systems : bridging the gap between theory and application

Mechanical control systems have become a part of our everyday life. Systems such as automobiles, robot manipulators, mobile robots, satellites, buildings with active vibration controllers and air conditioning systems, make life easier and safer, as well as help us explore the world we live in and exploit it’s available resources. In this chapter, we examine a specific example of a mechanical control system; the Autonomous Underwater Vehicle (AUV). Our contribution to the advancement of AUV research is in the area of guidance and control. We present innovative techniques to design and implement control strategies that consider the optimization of time and/or energy consumption. Recent advances in robotics, control theory, portable energy sources and automation increase our ability to create more intelligent robots, and allows us to conduct more explorations by use of autonomous vehicles. This facilitates access to higher risk areas, longer time underwater, and more efficient exploration as compared to human occupied vehicles. The use of underwater vehicles is expanding in every area of ocean science. Such vehicles are used by oceanographers, archaeologists, geologists, ocean engineers, and many others. These vehicles are designed to be agile, versatile and robust, and thus, their usage has gone from novelty to necessity for any ocean expedition.

A geometrical analysis of trajectory design for underwater vehicles

Designing trajectories for a submerged rigid body motivates this paper. Two approaches are addressed: the time optimal approach and the motion planning ap- proach using concatenation of kinematic motions. We focus on the structure of singular extremals and their relation to the existence of rank-one kinematic reduc- tions; thereby linking the optimization problem to the inherent geometric frame- work. Using these kinematic reductions, we provide a solution to the motion plan- ning problem in the under-actuated scenario, or equivalently, in the case of actuator failures. We finish the paper comparing a time optimal trajectory to one formed by concatenation of pure motions.