PhD Top-Up Scholarships and Honours Cadetship in Dynamical Systems and Mine Optimisation, $26-27000

Dynamical Systems, Transfer Operators and Ergodic Theory

APA PhD Top-Up Scholarship of $6000 p.a. (plus $1000 travel allowance p.a.) for 3 years. Total value with APA of around $26000 p.a. tax free: Successful applicants should hold an APA, have excellent honours year results and a strong background in pure and/or applied mathematics. Applications close 31 October, 2005.

Honours Cadetship of $2000 are available for 2006: Successful applicants should have a strong background in pure and/or applied mathematics. Applications close 30 November, 2005.

Your PhD or Honours project work will be motivated by mathematically challenging unsolved problems in the areas of: Ergodic Theory, Nonlinear Time Series Analysis, Mathematical Modelling, Nonlinear and Random Dynamical Systems, Markov chains, Graph Theory, Spectral Theory, Functional Analysis, and Coding and Information Theory.

The mathematical content of the projects can vary from highly theoretical to more computational or applications oriented, depending upon interests and skills. Detailed below are two available projects from an applications perspective.

Detecting Eddies and Transport Barriers in the Global Ocean: Eddies play a key role in global ocean circulation, affecting transport of heat, freshwater, carbon, nutrients, and marine biota. In order to understand oceanic dynamical transport, one must understand barriers to transport such as eddies and other persistent structures. Eddy activity can be routinely detected from space by satellite altimetry, but at present there is no dynamical understanding of the formation and persistence of eddies. Spectral techniques from Dynamical Systems have been shown to be particularly effective for identifying persistent behaviour, however their application in ocean dynamics is in its infancy. This project will focus on developing and applying powerful spectral techniques to low-dimensional models of the global ocean.

Constructing Compact Global Ocean Models with High Spatial Resolution: Ocean models constructed directly from satellite data are very high dimensional and prohibit the use of sophisticated tools of analysis. Preprocessing the raw satellite data to draw out the dominant dynamical modes can substantially lower the dimension of the data without any loss in spatial resolution. The goal of this project is to develop new (or extend existing) model reduction techniques that will create a reduced data set with a judicious focus on the dynamical scales and modes that carry the behaviour we wish to capture. The ability to cleverly reduce the system dimension will dramatically impact on the computational burden of simulating ocean models and lead to substantial improvements in the predictability of the global ocean.

There is also a PhD Top-Up Scholarship in Mine Optimisation and Valuation available.

For further details contact:
Dr Gary Froyland, (02) 9385 7050, G.Froyland@unsw.edu.au

Mine Optimisation and Valuation

A PhD APA Top-Up Scholarship of $7000 p.a. (plus $2000 travel allowance p.a.) is available for 3 years in the area of Mine Optimisation and Valuation. Total value with APA of around $28000 p.a. tax free. This is a joint UNSW/BHP Billiton endeavour, and represents an excellent opportunity to participate in mathematics research on projects with input from industry. Your PhD work will be motivated by the following two mathematically challenging unsolved problems. Successful applicants should have excellent honours year results and a background in optimisation or operations research. Applications close 31 October, 2005. The projects involve mathematics in the areas of Operations Research, Optimisation, Integer Programming, Probability/Stochastics, Numerical Analysis, Financial Mathematics, and Mathematical Modelling.

Compression of Optimisation Models: The optimization problems that arise from mining project valuations are huge. Some form of model compression is required if the problem is to become computationally tractable. This compression commonly takes the form of grouping areas of different mineralisation into larger units. The state-of-the-art in grouping technology is at present little better than an educated guess. Poor grouping will lead to poor mining plans that undervalue the mining project. In order to build mine plans of maximum value, efficient optimization model compression methods are required, so that the optimization is tractable, but the model loses a minimum amount of accuracy through this compression. This project will focus on developing structured methods of grouping with good model compression properties.

Uncertainty in Mine Planning: Mine plans are subject to uncertainties on several fronts: the selling price of the commodity, the market volume of the commodity, and the inaccuracy of grade and quality estimates for the minerals underground. Stochastic price and volume models can provide raw data to quantify price and market volume uncertainty. Stochastic grade simulations provide raw data with which to quantify the problem of mineral grade and quality inaccuracy. Mathematical techniques to build optimal mine plans based on stochastic price and grade models are in their infancy. The goal of this project is to develop rigorous optimization and valuation methods that take into account uncertainties in metal price and/or mineral grade. Of particular interest are techniques that build mine plans that can respond rapidly to changing circumstances to maximise the mine's value.

For further details contact: Dr Gary Froyland, (02) 9385 7050, G.Froyland@unsw.edu.au