Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using pow ....Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using powerful geometric tools from conformal geometry, the project will extend this to less symmetric spaces. The knowledge generated from this project will extend to more general geometric contexts providing a concrete setting for the study of the associated natural equations in curved spaces.Read moreRead less
Switching Dynamics Approach for Distributed Global Optimisation . This project aims to create a breakthrough switching dynamics approach and new technology to speed up finding optimal solutions. It will develop a distributed switching dynamics based optimisation scheme for global optimisation problems in industrial big-data environments where timely decision making is required. It will result in a practical technology for industry optimisation problems such as economic energy dispatch in smart g ....Switching Dynamics Approach for Distributed Global Optimisation . This project aims to create a breakthrough switching dynamics approach and new technology to speed up finding optimal solutions. It will develop a distributed switching dynamics based optimisation scheme for global optimisation problems in industrial big-data environments where timely decision making is required. It will result in a practical technology for industry optimisation problems such as economic energy dispatch in smart grids and optimal charging and discharging tasks in a large network of electric vehicles, helping Australian power industry improve efficiency and security, as well as training the next generation scientists and engineers for Australia in this emerging field.Read moreRead less
Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, i ....Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, integer models usually assume the data is known with certainty, which is often not the case in the real world. This project will develop new theory and algorithms to enhance the analysis of integer models, including those that incorporating uncertainty, while also enabling the use of parallel computing paradigms. Read moreRead less
Multiobjective Memetic Algorithms for Multi-task Symbolic Regression. This project aims at developing the new generation of symbolic regression methods using a yet unexplored way to represent mathematical functions. We will use memetic algorithms to create mathematical models for symbolic regression. Our memetic computing approach will be data-driven and will use multi-objective optimization and multi-task evolutionary computation for symbolic regression, addressing a core need of many areas of ....Multiobjective Memetic Algorithms for Multi-task Symbolic Regression. This project aims at developing the new generation of symbolic regression methods using a yet unexplored way to represent mathematical functions. We will use memetic algorithms to create mathematical models for symbolic regression. Our memetic computing approach will be data-driven and will use multi-objective optimization and multi-task evolutionary computation for symbolic regression, addressing a core need of many areas of science and technology. A large number of datasets will be investigated to benchmark the new methods. The expected outcomes will help support our national priorities with new data analytic capabilities. With a strong and interdisciplinary team in three continents, the project will attract international collaboration. Read moreRead less
Unravelling the dominant drivers of ion specificity. This project aims to understand what governs the sensitivity of many technological and biological processes to the precise nature of the salt present in solution. The term ‘ion-specific’ encompasses all the circumstances in which the influence of a salt in solution depends on the precise chemical nature of the salt, not just the electrical charge on the ions that form the salt. As such, ion-specific effects abound and have important consequenc ....Unravelling the dominant drivers of ion specificity. This project aims to understand what governs the sensitivity of many technological and biological processes to the precise nature of the salt present in solution. The term ‘ion-specific’ encompasses all the circumstances in which the influence of a salt in solution depends on the precise chemical nature of the salt, not just the electrical charge on the ions that form the salt. As such, ion-specific effects abound and have important consequences in most situations involving solutions, including cellular functions and battery technology. This project will enable us to understand and control the influence of specific ions, building on our recently described fundamental ion-specific series with colloid science experiments and quantum simulations. This project should overcome current challenges in predicting ion-specific effects leading to progress in a wide variety of applications of colloid and interface science, from sensor interfaces to self-assembly.Read moreRead less
Laser emission at the limit of glass transparency using nanocrystal doping . We will create a new composite glass providing strong fluorescence which fully exploits the high transmission of glass in the mid-infrared. When combined with emerging rare earth ion transitions and precise excitation processes, this project will help solve an important problem in optics; that the overall efficiency and power produced from deep mid-infrared light sources is not sufficient for all industries. The primary ....Laser emission at the limit of glass transparency using nanocrystal doping . We will create a new composite glass providing strong fluorescence which fully exploits the high transmission of glass in the mid-infrared. When combined with emerging rare earth ion transitions and precise excitation processes, this project will help solve an important problem in optics; that the overall efficiency and power produced from deep mid-infrared light sources is not sufficient for all industries. The primary outcome will be a series of robust fibre-based gain modules suitable for high power and very short optical pulses in the mid-infrared. These light sources will beneficially impact medicine, defence, sensing and manufacturing providing excellent opportunities for increasing Australian productivity and global competitiveness. Read moreRead less