Experimental and Numerical Modelling of Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, energy, food and pharmaceutical, which are fundamental to the Australian economy. Commercially available computer codes for simulating such systems are currently widely used in many Australian industrial sectors. This research project will address the prevalent deficiency in many of these computer codes and develop new models capable of ....Experimental and Numerical Modelling of Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, energy, food and pharmaceutical, which are fundamental to the Australian economy. Commercially available computer codes for simulating such systems are currently widely used in many Australian industrial sectors. This research project will address the prevalent deficiency in many of these computer codes and develop new models capable of predicting a wide range of industrial bubbly flow problems. The resultant improved computer codes will provide industries with significant benefits - especially reduced times and costs in their design and production.Read moreRead less
Ergodic theory and number theory. Recent advances in the theory of measured dynamical systems investigated by the proponents include new versions of entropy, and the study of spectral theory for non-singular systems. These will be further developed in this joint project with the French CNRS. The results are expected to have interesting applications in physics and number theory.
Entropy and maximal entropy in Markov systems. Entropy is a measure of how well-ordered a system is: chaotic systems have high entropy. Two approaches to entropy are available, via the limiting behaviour of the orbits of points, which yields topological entropy, and via the behaviour of the distributions of measures of partitions, yielding measure-theoretic entropy. The topological entropy is the least upper bound of entropies of all possible measures. We study when there is a measure which real ....Entropy and maximal entropy in Markov systems. Entropy is a measure of how well-ordered a system is: chaotic systems have high entropy. Two approaches to entropy are available, via the limiting behaviour of the orbits of points, which yields topological entropy, and via the behaviour of the distributions of measures of partitions, yielding measure-theoretic entropy. The topological entropy is the least upper bound of entropies of all possible measures. We study when there is a measure which realises this bound, describing the structure of such systems via Markov and Bratteli diagrams. Our methods will be applied to new versions of entropy for non-singular systems. This will assist in the description of chaotic behaviour.Read moreRead less
Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in ....Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in mathematical language, when the dynamical system is amenable. The proposed strategy involves extending Rieffel's notion of proper actions; the construction should be of wide applicability apart from the intended applications to amenability.Read moreRead less
The structure of quantum groups. We propose to study the structure of mathematical objects used in describing symmetries of micro-scale phenomena. The project will significantly develop already well established Australian-Korean cooperation in this exciting and rapidly growing area of research. The results will be immediately applicable to related fields of mathematics, most notably to noncommutative geometry. In the long run, the outcomes will help in better understanding of fundamental problem ....The structure of quantum groups. We propose to study the structure of mathematical objects used in describing symmetries of micro-scale phenomena. The project will significantly develop already well established Australian-Korean cooperation in this exciting and rapidly growing area of research. The results will be immediately applicable to related fields of mathematics, most notably to noncommutative geometry. In the long run, the outcomes will help in better understanding of fundamental problems of modern quantum physics.Read moreRead less
Interactive video on-demand for e-learning. Life long learning has become an integral part of many people's career development. Interactive video on-demand (VoD) can be used to deliver video learning materials to students when they choose to study. The aim of this project is to investigate the research issues on designing scalable interactive VoD for e-learning. Comparing with previous work in the area, this project takes a holistic approach, which includes multicast, distributed smart caches an ....Interactive video on-demand for e-learning. Life long learning has become an integral part of many people's career development. Interactive video on-demand (VoD) can be used to deliver video learning materials to students when they choose to study. The aim of this project is to investigate the research issues on designing scalable interactive VoD for e-learning. Comparing with previous work in the area, this project takes a holistic approach, which includes multicast, distributed smart caches and video coding as its building blocks. Huazhong University, who is active in e-learning research, provides an ideal location to trial interactive VoD techniques, due to their large student population. Read moreRead less
Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also ....Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also help to maintain Australia's strong position in international research in the mathematical sciences.Read moreRead less
Cooperative Management of Virtual Teams and Enterprises. Thanks to the proliferation of the Internet and web technologies, it is now possible to exploit the power of these technologies to facilitate the cooperation of teams of workers across distances. Such virtual teams and virtual enterprises are expected to overcome many problems associated in the modern service industry spanning continents. Countries (such as Australia) that are located far from the main markets (e,g, Europe and North Americ ....Cooperative Management of Virtual Teams and Enterprises. Thanks to the proliferation of the Internet and web technologies, it is now possible to exploit the power of these technologies to facilitate the cooperation of teams of workers across distances. Such virtual teams and virtual enterprises are expected to overcome many problems associated in the modern service industry spanning continents. Countries (such as Australia) that are located far from the main markets (e,g, Europe and North America) stand to gain substantially from successful deployment of such virtual organisations. Researchers from UNSW and LORIA France have been working together on the development of cooperative management models for virtual enterprises. This application seeks funding for the travel of researchers across these countries to facilitate this research.Read moreRead less
An interactive drama engine in virtual reality. In computer games, the narrative is generally limited to a graph of possibilities predetermined by an author. In this project, our aim is to go beyond predetermined graphs and build an Interactive Drama Engine to provide the users of the system a fully immersive interactive dramatic experience in a virtual world. Integration of interactive narrative and virtual reality hardware and software is a novel approach to the current problems in digital med ....An interactive drama engine in virtual reality. In computer games, the narrative is generally limited to a graph of possibilities predetermined by an author. In this project, our aim is to go beyond predetermined graphs and build an Interactive Drama Engine to provide the users of the system a fully immersive interactive dramatic experience in a virtual world. Integration of interactive narrative and virtual reality hardware and software is a novel approach to the current problems in digital media. It is expected to lead to the development of new generation interactive films and computer games that benefit from the Interactive Drama engine in the context of narrative.Read moreRead less
Computational Schemes for Initial-Boundary Value Problems. Many physical phenomena can be modelled as initial-boundary value problems described by partial differential equations. Simulations of such models require efficient and robust computational algorithms. The main aim of this project is to propose numerical algorithms for two dimensional spatial problems and three dimensional time-space models. A major focus of the project is to investigate methods that require about half the computation ....Computational Schemes for Initial-Boundary Value Problems. Many physical phenomena can be modelled as initial-boundary value problems described by partial differential equations. Simulations of such models require efficient and robust computational algorithms. The main aim of this project is to propose numerical algorithms for two dimensional spatial problems and three dimensional time-space models. A major focus of the project is to investigate methods that require about half the computational resources over celebrated schemes for solving boundary value problems.Read moreRead less