ANZIAM 2015

The 51st ANZIAM Conference was held on 1–5 February 2015 in the Outrigger Hotel, Surfers Paradise, Australia. A total of 229 people registered for the conference, with nine plenary presentations, 78 student presentations and 107 non-student presentations. Highlights of the conference included the plenary talks, presentations by the 2014 Michell and ANZIAM Medalists, the Women in Mathematics Lunch and the Conference Dinner and Awards Ceremony. The main conference was followed by a one-day workshop entitled ‘Discrete mathematical models in the life sciences’, held at Queensland University of Technology, Brisbane, on February 6, 2015.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

Reproducibility of scratch assays is affected by the initial degree of confluence: Experiments, modelling and model selection

Scratch assays are difficult to reproduce. Here we identify a previously overlooked source of variability which could partially explain this difficulty. We analyse a suite of scratch assays in which we vary the initial degree of confluence (initial cell density). Our results indicate that the rate of re-colonisation is very sensitive to the initial density. To quantify the relative roles of cell migration and proliferation, we calibrate the solution of the Fisher–Kolmogorov model to cell density profiles to provide estimates of the cell diffusivity, D, and the cell proliferation rate, λ. This procedure indicates that the estimates of D and λ are very sensitive to the initial density. This dependence suggests that the Fisher–Kolmogorov model does not accurately represent the details of the collective cell spreading process, since this model assumes that D and λ are constants that ought to be independent of the initial density. Since higher initial cell density leads to enhanced spreading, we also calibrate the solution of the Porous–Fisher model to the data as this model assumes that the cell flux is an increasing function of the cell density. Estimates of D and λ associated with the Porous–Fisher model are less sensitive to the initial density, suggesting that the Porous–Fisher model provides a better description of the experiments.

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Many biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

Improved cryptanalysis of the Common Scrambling Algorithm Stream Cipher

This paper provides a fresh analysis of the widely-used Common Scrambling Algorithm Stream Cipher (CSA-SC). Firstly, a new representation of CSA-SC with a state size of only 89 bits is given, a significant reduction from the 103 bit state of a previous CSA-SC representation. Analysis of this 89-bit representation demonstrates that the basis of a previous guess-and-determine attack is flawed. Correcting this flaw increases the complexity of that attack so that it is worse than exhaustive key search. Although that attack is not feasible, the reduced state size of our representation makes it obvious that CSA-SC is vulnerable to several generic attacks, for which feasible parameters are given.

The Dragon stream cipher: Design, analysis and implementation issues

Dragon is a word-based stream cipher. It was submitted to the eSTREAM project in 2005 and has advanced to Phase 3 of the software profile. This paper discusses the Dragon cipher from three perspectives: design, security analysis and implementation. The design of the cipher incorporates a single word-based non-linear feedback shift register and a non-linear filter function with memory. This state is initialized with 128- or 256-bit key-IV pairs. Each clock of the stream cipher produces 64 bits of keystream, using simple operations on 32-bit words. This provides the cipher with a high degree of efficiency in a wide variety of environments, making it highly competitive relative to other symmetric ciphers. The components of Dragon were designed to resist all known attacks. Although the design has been open to public scrutiny for several years, the only published attacks to date are distinguishing attacks which require keystream lengths greatly exceeding the stated 264 bit maximum permitted keystream length for a single key-IV pair.

Sir Neville Howse (VC), Private John Simpson Kirkpatrick and Private Martin O’Meara (VC) and their contributions to Australian military medicine

Medical personnel serving with the Defence Forces have contributed to the evolution of trauma treatment and the advancement of prehospital care within the military environment. This paper investigates the stories of an Australian Medical Officer, Sir Neville Howse, and two stretcher bearers, Private John Simpson (Kirkpatrick) and Private Martin O’Meara, In particular it describes the gruelling conditions under which they performed their roles, and reflects on the legacy that they have left behind in Australian society. While it is widely acknowledged that conflicts such as World War One should never have happened, as civilian and defence force paramedics, we should never forget the service and sacrifice of defence force medical personnel and their contribution to the body of knowledge on the treatment of trauma. These men and women bravely provided emergency care in the most harrowing conditions possible. However, men like Martin O’Meara may not have been given the same status in society today as Sir Neville Howse or Simpson and his donkey, due to the public’s lack of awareness and acceptance of war neurosis and conditions such as post traumatic stress disorder, reactive psychosis and somatoform disorders which were suffered by many soldiers during their wartime service and on their return home after fighting in war.

Scaling digital radiographs for templating in total hip arthroplasty using conventional acetate templates independent of calibration markers

We describe a scaling method for templating digital radiographs using conventional acetate templates independent of template magnification without the need for a calibration marker. The mean magnification factor for the radiology department was determined (119.8%, range117%-123.4%). This fixed magnification factor was used to scale the radiographs by the method described. 32 femoral heads on postoperative THR radiographs were then measured and compared to the actual size. The mean absolute accuracy was within 0.5% of actual head size (range 0 to 3%) with a mean absolute difference of 0.16mm (range 0-1mm, SD 0.26mm). Intraclass Correlation Coefficient (ICC) showed excellent reliability for both inter and intraobserver measurements with ICC scores of 0.993 (95% CI 0.988-0.996) for interobserver measurements and intraobserver measurements ranging between 0.990-0.993 (95% CI 0.980-0.997).

Vehicle energy throughput analysis as a drivetrain motor design aid

There are many variables to consider in the design of an electric motor. However, meeting the performance requirements for an electric vehicle drive may cause a designer to loose focus on its typical operation and hence fail to optimise the motor in the region where it processes the most power. This paper investigates operating requirements of electric vehicle motor drives using the University concept vehicle as an example. The paper outlines a methodology for determining primary operating region of a vehicle drive. The methodology is applied to standard driving cycles that are commonly used in the design and testing of vehicles.

Dynamic simulation of a light-weight, low-drag, hybrid-electric sports coupe

The University of Queensland UltraCommuter concept is an ultra- light, low-drag, hybrid-electric sports coupe designed to minimize energy consumption and environmental impact while enhancing the performance, styling, features and convenience that motorists enjoy. This paper presents a detailed simulation study of the vehicle's performance and fuel economy using ADVISOR, including a detailed description of the component models and parameters assumed. Results from the study include predictions of a 0-100 kph acceleration time of ≺9s, and top speed of 170 kph, an electrical energy consumption of ≺67 Wh/km in ZEV mode and a petrol-equivalent fuel consumption of ≺2.5 L/100 km in charge-sustaining HEV mode. Overall, the results of the ADVISOR modelling confirm the UltraCommuter's potential to achieve high performance with high efficiency, and the authors look forward to a confirmation of these estimates following completion of the vehicle.

Ironless wheel motor for a direct drive vehicle application

An ironless motor for use as direct wheel drive is presented. The motor is intended for use in a lightweight (600kg), low drag, series hybrid commuter vehicle under development at The University of Queensland. The vehicle will utilise these ironless motors in each of its rear wheels, with each motor producing a peak torque output of 500Nm and a maximum rotational speed of 1500rpm. The axial flux motor consists of twin Ironless litz wire stators with a central magnetic ring and simplified Halbach magnet arrays on either side. A small amount of iron is used to support the outer Halbach arrays and to improve the peak magnetic flux density. Ducted air cooling is used to remove heat from the motor and will allow for a continuous torque rating of 250Nm. Ironless machines have previously been shown to be effective in high speed, high frequency applications (+1000Hz). They are generally regarded as non-optimal for low speed applications as iron cores allow for better magnet utilisation and do not significantly increase the weight of a machine. However, ironless machines can also be seen to be effective in applications where the average torque requirement is much lower than the peak torque requirement such as in some vehicle drive applications. The low spinning losses in ironless machines are shown to result in very high energy throughput efficiency in a wide range of vehicle driving cycles.

Brake system performance requirements of a lightweight electric/hybrid rear wheel drive vehicle

Investigates the braking performance requirements of the UltraCommuter, a lightweight series hybrid electric vehicle currently under development at the University of Queensland. With a predicted vehicle mass of 600 kg and two in-wheel motors each capable of 500 Nm of peak torque, decelerations up to 0.46 g are theoretically possible using purely regenerative braking. With 99% of braking demands less than 0.35 g, essentially all braking can be regenerative. The wheel motors have sufficient peak torque capability to lock the rear wheels in combination with front axle braking, eliminating the need for friction braking at the rear. Emergency braking levels approaching 1 g are achieved by supplementation with front disk brakes. This paper presents equations describing the peak front and rear axle braking forces which occur under straight line braking, including gradients. Conventionally, to guarantee stability, mechanical front/rear proportioning of braking effort ensures that the front axle locks first. In this application, all braking is initially regenerative at the rear, and an adaptive ''by-wire'' proportioning system presented ensures this stability requirement is still satisfied. Front wheel drive and all wheel drive systems are also discussed. Finally, peak and continuous performance measures, not commonly provided for friction brakes, are derived for the UltraCommuter's motor capability and range of operation.