A Grid based platform for multi-scaled biological simulation. Heart disease currently affects over 3.5 million Australians. In 2006 it claimed the lives of almost 46,000 Australians (34% of all deaths). We will develop enabling technology that underpins cardiac disease research, offering potential for new treatments and pharmaceutical therapies. Even a small improvement in this area can translate into significant national benefit. Further, the mathematical techniques and software tools we will d ....A Grid based platform for multi-scaled biological simulation. Heart disease currently affects over 3.5 million Australians. In 2006 it claimed the lives of almost 46,000 Australians (34% of all deaths). We will develop enabling technology that underpins cardiac disease research, offering potential for new treatments and pharmaceutical therapies. Even a small improvement in this area can translate into significant national benefit. Further, the mathematical techniques and software tools we will develop, whilst focused on heart tissue, will have broader applicability, and may underpin advancements in other disciplines. Finally, we expect that the software solutions and infrastructure will have both commercial and strategic value in their own right.Read moreRead less
THE DEVELOPMENT OF MECHANISTIC MODELS FOR BUBBLY FLOWS WITH HEAT AND MASS TRANSFER. Commercially available CFD computer codes are currently widely used in many Australian industrial sectors. It is clearly recognised that the state-of-the-art models for dealing with complex bubbly flows with/without heat and mass transfer in these computer codes require further developments and improvements. This research project will address the prevalent deficiency in many of these computer codes. It is antici ....THE DEVELOPMENT OF MECHANISTIC MODELS FOR BUBBLY FLOWS WITH HEAT AND MASS TRANSFER. Commercially available CFD computer codes are currently widely used in many Australian industrial sectors. It is clearly recognised that the state-of-the-art models for dealing with complex bubbly flows with/without heat and mass transfer in these computer codes require further developments and improvements. This research project will address the prevalent deficiency in many of these computer codes. It is anticipated that through this major development of new models capable of predicting a wide range of industrial bubbly flow problems and implementation thereafter in these computer codes, industries will experience significant benefits especially reduce time and costs in their design and production.Read moreRead less
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
The Time-Varying Eigenvalue Problem with Application to Signal Processing and Control. Linear models are ubiquitous in representing physical processes. Decomposing a linear model into its fundamental components is known as the eigenvalue problem. In applications as wide ranging as astronomy, aircraft control systems, Internet search engines and communication systems, it is necessary to perform this decomposition of a pertinent time varying linear model on the fly. This project aims to develop si ....The Time-Varying Eigenvalue Problem with Application to Signal Processing and Control. Linear models are ubiquitous in representing physical processes. Decomposing a linear model into its fundamental components is known as the eigenvalue problem. In applications as wide ranging as astronomy, aircraft control systems, Internet search engines and communication systems, it is necessary to perform this decomposition of a pertinent time varying linear model on the fly. This project aims to develop significantly faster and more accurate algorithms for this time varying eigenvalue problem than currently exist. Very modern techniques will be employed to achieve this aim, and the potential benefits to Australian hi-tech industries are great.
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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
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
Interface-aware numerical methods for stochastic inverse problems. This project aims to design novel high-performance numerical tools for solving large-scale forward and inverse problems dominated by stochastic interfaces and quantifying associated uncertainties. In real-world applications such as groundwater, these tools are instrumental for assimilating big datasets into mathematical models for providing reliable predictions. By advancing and integrating high-order polytopal schemes, multileve ....Interface-aware numerical methods for stochastic inverse problems. This project aims to design novel high-performance numerical tools for solving large-scale forward and inverse problems dominated by stochastic interfaces and quantifying associated uncertainties. In real-world applications such as groundwater, these tools are instrumental for assimilating big datasets into mathematical models for providing reliable predictions. By advancing and integrating high-order polytopal schemes, multilevel methods, transport maps, and dimension reduction, this project's anticipated outcomes are highly accurate and cost-efficient numerical schemes, certified by rigorous mathematical analysis. This should provide data-centric simulation tools with enhanced reliability, for engineering and scientific applications.Read moreRead less
Towards predictive 4D computational models for the heart. This project aims to develop novel high-performance numerical algorithms for multiscale and multiphysics PDEs with dynamic interfaces, the development and analysis of a novel PDE system modelling the electromechanics of heart and torso, and the combination of these numerical techniques and models to deliver predictive tools for patient-specific simulations of the cardiac function. It involves the design and mathematical analysis of space- ....Towards predictive 4D computational models for the heart. This project aims to develop novel high-performance numerical algorithms for multiscale and multiphysics PDEs with dynamic interfaces, the development and analysis of a novel PDE system modelling the electromechanics of heart and torso, and the combination of these numerical techniques and models to deliver predictive tools for patient-specific simulations of the cardiac function. It involves the design and mathematical analysis of space-time variational discretisations on embedded meshes, 4D computational geometry algorithms for numerical integration and multilevel solvers. By combining scientific computing and machine learning, one anticipated outcome of this research is a new generation of nonlinear PDE approximations and solvers.Read moreRead less
A new numerical analysis for partial differential equations with noise. This project aims to design novel numerical methods, grounded in rigorous mathematical foundations, for partial differential equations with stochastic source terms, such as for instance those modelling fluid flows with random perturbations. To ensure the accuracy of numerical simulations, preserving certain quantities of importance (mass, flux) is critical. The project's goal is to develop finite volume and high-order numeri ....A new numerical analysis for partial differential equations with noise. This project aims to design novel numerical methods, grounded in rigorous mathematical foundations, for partial differential equations with stochastic source terms, such as for instance those modelling fluid flows with random perturbations. To ensure the accuracy of numerical simulations, preserving certain quantities of importance (mass, flux) is critical. The project's goal is to develop finite volume and high-order numerical methods that are applicable in real-world settings, designed to achieve this preservation of essential quantities, and mathematically proven to be robust. The expected benefits are cost-efficient and reliable numerical tools for the scientific simulation of phenomena subjected to uncontrolled influence.Read moreRead less
Discrete functional analysis: Bridging pure and numerical mathematics. This project aims to create the first numerical analysis tools to design robust, mathematically proven algorithms for engineering problems in underground flows. These equations are essential to accurately model and understand phenomena such as oil extraction, carbon sequestration and groundwater contamination. The project will provide powerful mathematical tools to improve the reliability of numerical simulations for such cha ....Discrete functional analysis: Bridging pure and numerical mathematics. This project aims to create the first numerical analysis tools to design robust, mathematically proven algorithms for engineering problems in underground flows. These equations are essential to accurately model and understand phenomena such as oil extraction, carbon sequestration and groundwater contamination. The project will provide powerful mathematical tools to improve the reliability of numerical simulations for such challenges and significantly improve the reliability of the predictions under assumptions that are compatible with field applications.Read moreRead less