Available Research Projects for PhD students and Post-docs

Multiscale modelling of systems with complex microscale detail (J.E. Bunder, A.J. Roberts)

In many science and engineering scenarios, the underlying microscopic model is known, but too complex for practical purposes. For such models, our computational and analytic methodologies are to extract the dynamics which emerge at large scales, leading to an improved prediction and understanding of the significant features of these complex systems. The methodology is designed for application in high performance computing.

This project develops systematic methods for the compact and accurate macroscale modelling of systems with microscopic irregular details. The methodology, both analytic and computational, is to apply to a large range of dynamical systems such as particle simulations, PDEs, difference equations, and discrete agents. These systems have complex microscopic features, e.g., lattice distortions, irregular time-dependent forcing, and variable loading. The computational modelling has a wide variety of engineering applications, from the synthesis of new `smart' materials to predicting crack development in composite materials. The results will empower us to effectively cross the scales from the detailed to the coarse scales of interest.

Complex Multiscale Systems: Modeling, Analysis and Scientific Computation (A.J. Roberts, J.E. Bunder)

In current modelling the underlying microscopic mechanisms are known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available. Our computational methodologies underpinned by mathematical analysis will circumvent this stumbling block to radically improve the modelling, exploration and understanding of complex systems in engineering and sciences.

This project develops and implements a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. Our wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or PDE or lattice equations). Comprehensively accounting for multiscale interactions between subgrid processes among macroscale variations ensures stability and accuracy. Based on dynamical systems theory and analysis, our approach will empower systematic analysis and understanding for optimal macroscopic simulation for forthcoming exascale computing.

Effective macroscopic modelling of stochastic systems and partial differential equations (A.J. Roberts)

This project develops a mathematical basis for effectively modelling highly complex, nonlinear, noisy systems in engineering and sciences. Potential application areas include climate modelling, nanotechnology, and modern micro-structured materials.

This project develops effective mathematical methodology to extract explicit and accurate macroscopic models from complex stochastic physical and engineering systems. The important class of systems we address are those microscopically described in space-time by stochastic partial differential equations. Due to micro-macro and nonlinear interaction, randomness on the microscopic scale feeds into macroscopic dynamics and needs to be accounted for as in our planned modelling. These results will provide effective theory and methodologies for the simulation and understanding of large, noisy complex systems.

Designing rubber-like metamaterials (Luke Bennetts)

`Metamaterials' is a catch-all term describing materials manufactured to have properties not found in nature. Rubber-like materials support longitudinal waves similar to fluids, which can be converted into lossy transverse waves by placing inclusions in the rubber. Coating a body with a thin rubber-like metamaterial, using suitably arranged inclusions and subwavelength resonances, can prevent sound loss from the body polluting the outside environment and/or the body being `seen', for example, by sonar. This project will develop semi-analytic methods, based on special functions and asymptotic theories, to advance the design of these rubber-like metamaterials.

Note that this project is available as part of the joint Adelaide-Nottingham PhD programme (further details).

Unsteady capillary stretching for microstructured tapers (Yvonne Stokes)

This project focuses on mathematical modelling of the fabrication of microstructured tapers used for whispering gallery resonator sensors, mass-spectrometry and medical devices. Their fabrication is by heating and pulling a suitable capillary/preform. Pressurisation of the air channel(s) may be required to achieve the desired geometry. Both flow and temperature sub-models will be required and asymptotic methods exploiting the slenderness of the taper will be used in their derivation. The model will be used to investigate the relationship between the length of the heated region and the temperature, the pulling tension and velocity, the surface tension and pressure, on the length of the taper and the cross-sectional geometry along its length. Experiments will be run, with assistance from skilled technicians, for comparison with the model. The project will be co-supervised by Prof. Heike Ebendorff-Heidepriem from the Institute for Photonics and Advanced Sensing at the University of Adelaide. (Further details)

Micro-bubble and micro-bottle blowing in a fibre for whispering gallery resonator sensors (Yvonne Stokes)

This PhD project focuses on mathematical modelling of the fabrication of whispering gallery resonator sensors by blowing a micro-bubble or micro-bottle in a heated microstrutured taper. Both flow and temperature sub-models will be required and asymptotic methods exploiting the slenderness and/or the small wall thickness of the taper will be used in their derivation. The model(s) developed will be used to investigate the relationship between surface tension, pressure, wall thickness of the fibre/taper and wall thickness and size of the bubble/bottle. The thinner the wall of the fibre/taper the more sensitive it will be to the applied pressure and the greater the chance of blow-out and, consequently, failure to achieve the desired sensor. Avoiding this, while still achieving thin-walled micro-bubbles/bottles, will be of key interest. The model(s) will be compared with experiments run with assistance from skilled technicians. The project will be co-supervised by Dr Yinlan Ruan from the Institute for Photonics and Advanced Sensing at the University of Adelaide. (Further details)

Calcium signalling and travelling wave response to oocyte fertilisation (Yvonne Stokes)

Recent experimental work by colleagues in the Robinson Institute, The University of Adelaide, showed a travelling-wave-like response of the cumulus cells surrounding a bovine oocyte, following fertilisation of the oocyte. Travelling waves have been observed on amphibian embryos and are known to be a result of calcium signalling. There is evidence that calcium signals, in the first instance triggered by oocyte fertilisation, are also the cause of the observed cumulus-cell response in bovine cumulus-oocyte complexes (COCs). Coupled models of calcium signalling at the cellular level (within oocyte and cumulus cells) and the response of the cells to the signal will be used to determine the biology behind the experimental observations.

Note that this project is available as part of the joint Adelaide-Nottingham PhD programme (further details).

Modelling growth and morphogenesis of colonic organoids (Edward Green)

Organoids are three-dimensional in vitro tissue cultures which mimic (to some degree) the distinctive in vivo structure of the organ from which they derive. In this project, we will focus on organoids grown from intestinal tissue, which are used for research into colorectal cancer, one of the most common cancer types. Although colonic organoids are being grown successfully by various research groups, at present their growth and development are not well understood. They can vary in morphology e.g. `budded' and `cystic' types are observed, but the reason for this, and its possible significance for the usefulness of the organoids in research is unknown. Furthermore, for potential applications in personalised medicine, there is a need to optimise the culture process to grow larger quantities of tissue more rapidly.

This project will develop new mathematical models for organoid growth and development, based on the principles of morphoelasticity. We will investigate the role of growth induced buckling in determining their form (cystic or budded), taking into account the potential roles of different cell populations, and chemical signals in this process. Our models will be validated against experiments being undertaken by Dr Daniel Worthley's group at the South Australian Health and Medical Research Institute (SAHMRI).

Note that this project is available as part of the joint Adelaide-Nottingham PhD programme (further details).


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