The Australian National University
Department of Applied Mathematics
Research School of Physical Sciences and Engineering
document location: http://wwwrsphysse.anu.edu.au/~web110/education.php

Information for prospective students

Students can pursue research projects at many levels in the Department including

  • Advanced studies courses as part of the ANU PhB program.
  • Summer vacation scholarships.
  • Honours projects in conjunction with the many of the Science or Engineering departments at ANU.
  • Masters degree by research.
  • Doctoral research within the PhD program.

Prospective students are encouraged to visit the department. If you live outside Canberra we may be able to cover some of your travel and accommodation costs. Please contact the Head of Department if you are interested in this offer.


Honours Projects

Below are some potential honours projects in experimental, theoretical, and computational areas. More topics may be available - see the Department's research page for more information. Many of these projects can be expanded into Master's or even Doctoral thesis topics. Please contact the relevant staff members if you are interested.

Tomaso Aste

DNA intrinsic curvature from atomic force measurements: This project concerns the development of a statistical theory to interpret high-resolution atomic force measurements of DNA molecules adsorbed on surfaces.  The aim is to predict the angles that a given sequence of DNA will produce once adsorbed on the surface starting from the physical properties of adsorption of DNA molecules.

The Pursuit of Loose Packing: Which is the lowest limit at which a disordered packing of equal spheres can be mechanically stable? The project aims to seek an answer to this question by starting from experimental samples measured by X-ray Computed Tomography and performing ‘virtual experiments’ by using Discrete Elements simulation techniques. The discrete elements code has been already implemented, it must be modified and optimised for the project aims. See Granular Matter web page for further information and references.

Complex Networks: This project aims to use Homology Theory to characterize complex networks and, by means of embeddings onto surfaces, extract hierarchies and clustering. This approach will be applied to the study of correlations in financial markets, to the extraction of information from DNA microarray and biological systems. The project will be co-supervised by A/Prof Tiziana Di Matteo.

Econophysics: This project concerns “econophysics” the application of tools from statistical physics to the study of economics systems and financial markets in particular. The project will be co-supervised by A/Prof Tiziana Di Matteo.

Please see this page for additional information on the projects listed above.

 

Christoph Arns

Structure - physical property relationships

Given the 3D structure of a porous or composite material, direct calculation of many interesting physical properties, e.g. fluid permeability, electrical conductivity, diffusivity, elastic moduli, NMR relaxation response to name a few, are possible and can be correlated to structural understanding in a way often not accessible to conventional experiment. Below projects center around the quickly advancing world of computational physics in some major application areas utilizing supercomputing resources.
Advanced materials
Many natural materials show spatial varying physical properties due to the way they were formed, e.g. deposition of sand grains at a beach. This project focusses on the understanding of physical properties of heterogeneous materials generated by statistical processes showing a spatial gradient. Given the spatial trend of the morphology generating process, resulting spatial trends in physical properties like fluid permeability and electrial conductivity are calculated and characterised in terms of general regional morphological measures.
Reactive flow
Chemically active compounds are abundant in porous materials and lead to a change of surface properties and/or structure over time. This are important processes in many areas of science and engineering, e.g. bridge construction, underground storage of CO2, or nuclear waste storage. In this project effects of surface property changes under the conditions of fluid-saturated porous media with respect to macroscopic flow and self-diffusion are analysed.
Nuclear magnetic resonance
The estimation of flow properties from information about diffusional processes has a long history in the oil and gas industry. Standard methods correlate the NMR relaxation response to permeability, because a direct continuous measurement of permeability is not feasible downhole. In this study information additional structural information e.g. from 3D imaging at the pore scale is used to improve such correlations.

Vince Craig

Fire fighting foam
Develop a home based kit for producing foam for firefighting from a garden hose. Initially using Molasses as a foaming agent, develop a venture system that incorporates first molasses and then air into the water flow. The nozzle at the end of the hose should also be engineered to maximize foam performance.
Phase Change Emulsions
To experimentally follow the evolution of volatile emulsion droplets as they undergo a phase change from liquid to gas. Following have developed a theory to describe the behavior of PCEÕs. Predictions are made as to the temperature at which the phase change will occur and the total volume change of the emulsion as a function of droplet size. Using light scattering this evolution can be followed experimentally.
Nanorheology
The direct measurement of minute surface forces with nanometer separation control using Atomic Force Microscopy is now routine. An extension of this technique allows the flow properties of highly confined materials from Newtonian liquids to single molecules to be investigated by oscillating the substrate and carefully monitoring the response of the substrate. This world leading research is challenging, but the rewards are significant.
Interparticle forces in concentrated salt solutions
To understand the interaction forces in concentrated electrolyte solutions. This industry supported project aims to directly measure the surface forces between a range of mineral surfaces in concentrated electrolyte solutions. Surfaces suitable for experimental studies using the Atomic Force Microscope will be prepared by Atomic Layer by Layer deposition and Chemical Vapor Deposition. The adhesion and friction between a range of surfaces will be studied as a function of the type and concentration of electrolyte.
Film Stress Measurements
Films ranging from single molecular layers to everyday coatings exhibit film stress. Film stress arises from the change in the intermolecular or interparticle forces during film curing and therefore measurements of film stress are both industrially important and of fundamental interest. We are able to measure film stress using micro-cantilevers and also using macroscopic cantilevers on a custom built instrument.
Bubble Coalescence in electrolyte solutions
Pure liquids do not foam. But if a small quantity of surfactant is added they foam considerably. This effect is understood. The addition of electrolytes to water in some cases enhances foaming Ð and this simple observation is not at all understood Ð but we are able to predict what will happen. We wish to extend this study to include both non Ðelectrolytes such as sugars and electrolytes in solvents other than water. This novel investigation is aimed at probing very fundamental properties of interfaces relevant to a great variety of systems from biology to minerals processing.

Mark Knackstedt

Seeing in 3D: Imaging and analysis of complex materials

These projects involve imaging the structure of complex materials in 3D at the micron scale. This allows a student to work with a world class facility including an x-ray microtomographic experimental facility along with a number of mature programs for image interpretation, property analysis and 3D interactive visualization. The facility has demonstrated that the physical properties of real-world materials can be predicted from numerical simulation on microtomographic images. This development has enabled a new numerical laboratory approach to the study of complex materials. Studies span from basic to applied. On the fundamental side we study morphological descriptors of complex materials, map the topology of porous solids, and describe the interaction between local structure and fluid distributions (see additional projects with Adrian Sheppard and Vanessa Robins).
Transport of contaminants and solutes in aquifers
This study is focused on analysing the transport of fluids, colloids and solutes through aquifers. A detailed 3D study of pore structure and fluid transport at the laboratory scale can be undertaken using the Applied Maths micro-CT facility. This work will provide detailed information on pore structure in aquifer sands and transport and dispersive properties of aquifer samples at the pore scale. Results of this detailed laboratory scale study and its impact on field scale flow properties of an aquifer will be undertaken.
Restoration of Sandstone Monuments
Many castles, monuments and churches in the UK are primarily built of sandstone. Recently a significant body of research has recently been undertaken into the cleaning and conservation of stone buildings, particularly those constructed of sandstone, and the debate concerning the best methods to conserve stone buildings remains controversial. To date standard laboratory tests have been used to measure relative changes in pore structure and mechanical properties. The ability to undertake 3D imaging studies of the properties of sandstone samples will give added insight into the degradation and potential restoration processes.
Medical Diagnosis of bone disease
Age-related bone fractures due to osteoporosis and other conditions impose a significant social and economic problem on our increasingly aging population. In Australia alone, the cost of treating age-related hip, spine and wrist fractures is more than $1 Billion p.a. The assessment of bone quality is important in the diagnosis of age related bone fragility and for studying the efficacy of bone therapeutic interventions. The development of effective strategies for both prevention and treatment requires an understanding of the role of bone microarchitecture and mineralisation.
Advanced Composites, Biomaterials and Controlled Release Systems
Optimising the properties of new materials demands control over internal microstructure. While the engineering potential of advanced materials is considerable, our ability to design and optimise structures is ad hoc since local structure in these materials is rarely understood. With an understanding of the microstructure, the design of advanced foamed materials, tissue engineered constructs, controlled release substances and biocomposites tailored to specific end-use demands will be accelerated.
Oil and Gas production
In Australia the petroleum industry spends billions of dollars annually on exploration for oil and gas. A considerable amount is spent on obtaining core material, performing tests on the core material and interpreting test measurements. Billion dollar field development decisions are made on the basis of these interpretations. A major uncertainty in the interpretations is how pore scale structure relates to the hydrocarbon recovery. An increased understanding of rock microstructure and scaling behaviour is a key element in reducing this uncertainty.

Vanessa Robins

3D Crystalline structures from 2D hyperbolic tilings
Joint projects with Stephen Hyde.

Crystalline frameworks (nets) are a standard way to describe three-dimensional structure in solid-state science. To achieve directed logical design of new materials, we need to know what framework structures are possible and which are most likely to form from a given set of building blocks.

Our understanding of the variety of 3D networks that can be realised in euclidean space is far from complete. We have developed a new route to the formation of nets by mapping tilings of the 2D hyperbolic plane onto periodic minimal surfaces in 3D space. The techniques involve discrete symmetry groups, computational geometry and topology, and advanced computer visualisation.

Open problems include:

  • Systematic enumeration of multi-component interpenetrating nets.
  • Characterisation of self-interpenetrating nets (periodic knotting).
  • Online interactive generation and caching of network structures.
  • Data-mining physical properties (such as percolation or elasticity) of previously enumerated nets.
EPINET, our online database has a comprehensive overview of the wider project.

Topological Persistence in 3D image analysis
Joint projects with Adrian Sheppard.

Tomographic facilities such as the one in Applied Maths are enabling us to peer inside an enormous range of complex materials with unprecedented clarity and resolution. The need to study these data in a quantitative manner has resulted in a new computational discipline dedicated to the processing of large 3D images and to the characterisation of the complex structures that are now being unveiled.

One of the most fundamental descriptions of an object is in terms of its topology - how many connected components, handles, and enclosed voids it has. Topological persistence is a method for distinguishing between features that are significant and those that are introduced by noise. This project involves adapting existing algorithms for analysing unstructured meshes to the context of 3D voxel data.


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