Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of di ....Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of disease.Read moreRead less
The stability and predictability of the Southern Hemisphere coupled ocean-atmosphere climate system. Our ability to adapt to and manage the effects of a changing climate is limited by our understanding of the ocean's response to changes in the atmospheric circulation. This project will establish the basis for the predictability of the climate system and provide state-of-the-art forecasts for climate adaptation.
Theory and applications of three dimensional fractal transformations. The purpose of this project is to develop the theory and algorithms for a new class of continuous mappings between fractals. Outcomes include a better understanding of fractals, substantially better algorithms for fractal compression and many new applications.
Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dis ....Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dissipative and higher order nonlinear terms. These are essential for a precise description of both giant waves in the ocean and strong pulses in optics. Read moreRead less
Efficient and convergent first-principles chemical dynamics. This project develops a new method for studying chemical systems using first principles quantum mechanics. The new method can solve a much larger range of chemical problems than its predecessors, allowing detailed and accurate descriptions of reactions and dynamics driven by thermal energy or activated by light.
Integrated Photonics for Secure Communication and Related Applications in Financial Transaction Data Analysis. The project includes excellent basic science, semiconductor device fabrication and applied mathematics with explicitly identified consequences for innovation. There is strong potential for national economic benefits through the manufacture of new integrated photonic devices, the application of these devices in secure communication systems, the research of advanced non-linear analysis pr ....Integrated Photonics for Secure Communication and Related Applications in Financial Transaction Data Analysis. The project includes excellent basic science, semiconductor device fabrication and applied mathematics with explicitly identified consequences for innovation. There is strong potential for national economic benefits through the manufacture of new integrated photonic devices, the application of these devices in secure communication systems, the research of advanced non-linear analysis protocols, and the implementation of these in financial transaction analysis. Professional development and research education of postgraduate students and early career researchers will be carried out in a multi-disciplinary research environment with ongoing uptake of the research in industry and commercial sectors.Read moreRead less
Exploding solitons. This project builds on previous work in which the existence of exploding solitons was confirmed. Explosions occur regularly in a variety of systems with continuous supply and dissipation of energy. Exploding solitons are more common than ordinary dissipative solitons and occupy large areas in the parameter space. They can be generated relatively easily, however the phenomenon is highly complex. This project aims to further understand exploding solitons so that the phenomeno ....Exploding solitons. This project builds on previous work in which the existence of exploding solitons was confirmed. Explosions occur regularly in a variety of systems with continuous supply and dissipation of energy. Exploding solitons are more common than ordinary dissipative solitons and occupy large areas in the parameter space. They can be generated relatively easily, however the phenomenon is highly complex. This project aims to further understand exploding solitons so that the phenomenon can be used for the generation of pulses with wide spectral output similar to `supercontinuum’ radiation. Research in this direction will provide the basis for building powerful laser sources with wide spectral output.Read moreRead less
Rogue waves in oceans and optical fibres. Rogue waves can sink large ships in the ocean. They appear more commonly than previously thought. Optical rogue waves, the laboratory counterparts of extreme ocean waves, will allow the project to study the main features of the phenomenon, provide the theoretical explanation for their existence and potentially help to eliminate these catastrophic events.