PhD Top-Up Scholarship and Honours Cadetship in 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. 

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. Pre-processing 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.

 

For further details contact:

Dr Gary Froyland, (02) 9385 7050, G.Froyland@unsw.edu.au

Applications close 31 October, 2005.

**Mention you saw it on the AustMS website**