Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with inter ....Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with international researchers and engineering scientists. This is important for the advance of science and technology in
Australia.Read moreRead less
Developing a robust model for pricing inter-related volatility-based financial derivative contracts. Volatility-based financial contracts were developed in the late 1990s to provide an easy way for investors to gain exposure to the future level of volatility and thus provide a means by which they could speculate on its future levels and also hedge unpredictable volatility risk. This would potentially save them from losing vast quantities of money. However these products can only be efficient pr ....Developing a robust model for pricing inter-related volatility-based financial derivative contracts. Volatility-based financial contracts were developed in the late 1990s to provide an easy way for investors to gain exposure to the future level of volatility and thus provide a means by which they could speculate on its future levels and also hedge unpredictable volatility risk. This would potentially save them from losing vast quantities of money. However these products can only be efficient products for trading and risk management if they are priced correctly. This project will benefit investors by providing empirically viable models that will be able to be easily implemented to provide accurate and fast pricing solutions.Read moreRead less
High dimensional problems of integration and approximation. In many applications, notably financial mathematics, problems of
integration and approximation of functions in very high dimensions
are of great interest. By finding modern mathematical solutions to
these problems, we will therefore contribute to Australia's future
success in developing innovative technologies for industrial and
economic applications. By researching at an internationally
competitive level and by cooperating with i ....High dimensional problems of integration and approximation. In many applications, notably financial mathematics, problems of
integration and approximation of functions in very high dimensions
are of great interest. By finding modern mathematical solutions to
these problems, we will therefore contribute to Australia's future
success in developing innovative technologies for industrial and
economic applications. By researching at an internationally
competitive level and by cooperating with international experts, we
will have a share in further strengthening the excellent role of
Australian research institutions within the international scientific
community in mathematics and scientific computing.Read moreRead less
Innovative Methods for Very High Dimensional Problems. Real world problems tend to involve an enormous number of variables. This "curse of dimensionality" poses great difficulty in application areas such as statistics, finance, economics, and physics. These high dimensional problems are not confined to Australia, and there is great demand worldwide for effective and efficient methods to tackle these problems. The novel methods developed here will lead to improvements in prevailing computational ....Innovative Methods for Very High Dimensional Problems. Real world problems tend to involve an enormous number of variables. This "curse of dimensionality" poses great difficulty in application areas such as statistics, finance, economics, and physics. These high dimensional problems are not confined to Australia, and there is great demand worldwide for effective and efficient methods to tackle these problems. The novel methods developed here will lead to improvements in prevailing computational technologies, which will help to enhance Australia's reputation as a leading scientific innovator. The international collaborations will increase the research output of the country, build up the knowledge base in the discipline, draw international interest, and initiate linkages.Read moreRead less
Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journa ....Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journals and international conferences, and from direct collaboration with internationally leading scientists from USA, UK and Germany. The project will also increase the pool of trained mathematicians with expertise in areas important for applications.
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Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science ....Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science; ocean engineering; medical research; meteorology and global environmental sciences.Read moreRead less
Multi-Group Stochastic Modelling of Population Balance for Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, nuclear, 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 ....Multi-Group Stochastic Modelling of Population Balance for Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, nuclear, 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 and, in particular, reduce times and costs in their design and production. Read moreRead less
Fuzzy finite element analysis of smart structures using concepts of optimization. The major aim of this research is to develop an innovative approach using fuzzy finite element method for the analysis and design of smart control systems for civil engineering structures subjected to vibrations due to earthquakes. The significance of this project is the proposal to combine, for the first time, techniques such as finite element, fuzzy logic and optimization in a unified manner. The final result wil ....Fuzzy finite element analysis of smart structures using concepts of optimization. The major aim of this research is to develop an innovative approach using fuzzy finite element method for the analysis and design of smart control systems for civil engineering structures subjected to vibrations due to earthquakes. The significance of this project is the proposal to combine, for the first time, techniques such as finite element, fuzzy logic and optimization in a unified manner. The final result will produce an efficient design tool for a structural system integrated with smart sensors/actuators for vibration control.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
A unified framework for analyzing the timescale of interest for traffic measurements, modelling and performance analysis. The revenue generated from traditional telecommunication services is continuing to drop. New value-added services such as multimedia services become the fastest growing revenue-generating sector in Australia's telecommunications industry. The ubiquitous presence of scaling behaviour in network traffic presents a big challenge for delivering better Quality-of-Service (QoS) whi ....A unified framework for analyzing the timescale of interest for traffic measurements, modelling and performance analysis. The revenue generated from traditional telecommunication services is continuing to drop. New value-added services such as multimedia services become the fastest growing revenue-generating sector in Australia's telecommunications industry. The ubiquitous presence of scaling behaviour in network traffic presents a big challenge for delivering better Quality-of-Service (QoS) which is demanded by the new services. A complete understanding of the scaling behaviour and its impact is very important. This research addresses a key problem of defining the timescale range of interest for the scaling behaviour. The research outcome benefits a number of areas, which are all critical for developing enhanced QoS support and better network management.Read moreRead less