Complex Multiscale Systems: Modeling, Analysis and Scientific Computation. This project aims to develop and implement a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. The wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or partial differential equations or la ....Complex Multiscale Systems: Modeling, Analysis and Scientific Computation. This project aims to develop and implement a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. The wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or partial differential equations or lattice equations). Comprehensively accounting for multiscale interactions between subgrid processes among macroscale variations ensures stability and accuracy. Based on dynamical systems theory and analysis, this approach is expected to empower systematic analysis and understanding for optimal macroscopic simulation for forthcoming exascale computing.Read moreRead less
Uncertainties in coherent transport of particles and intrinsic properties. This Project aims to quantify the uncertainty of a model output in terms of uncertainties in modelling assumptions, by developing new mathematical techniques and applying them to real-world data. This will be in the context of assessing the accuracy of tracking coherently moving structures (e.g., hurricanes, oceanic biodiversity hotspots, pollutant patches, insect swarms) from experimental/observational data sets. Novel, ....Uncertainties in coherent transport of particles and intrinsic properties. This Project aims to quantify the uncertainty of a model output in terms of uncertainties in modelling assumptions, by developing new mathematical techniques and applying them to real-world data. This will be in the context of assessing the accuracy of tracking coherently moving structures (e.g., hurricanes, oceanic biodiversity hotspots, pollutant patches, insect swarms) from experimental/observational data sets. Novel, data-tested, mathematical methods for uncertainty quantification of coherent structures will be developed as Project outcomes. Project benefits include new insights into protecting the environment, improved uncertainty quantification in climate modelling, and the generation of interdisciplinary knowledge and training.Read moreRead less
Viscous extensional flow and drop breakoff. Honey falling from a spoon is an everyday example of a viscous fluid in a free extensional flow which may eventually break up into drops. Such flows are important in modern technologies including ink-jet printing, welding, soldering and molten metal processing, polymer and glass fibre spinning, and for rheological measurement. We seek to increase understanding of the mechanisms governing such flows, particularly the role of initial conditions and the ....Viscous extensional flow and drop breakoff. Honey falling from a spoon is an everyday example of a viscous fluid in a free extensional flow which may eventually break up into drops. Such flows are important in modern technologies including ink-jet printing, welding, soldering and molten metal processing, polymer and glass fibre spinning, and for rheological measurement. We seek to increase understanding of the mechanisms governing such flows, particularly the role of initial conditions and the geometry of the original containing vessel, together with balances between forces such as inertia, gravity, viscosity, viscoelasticity, and surface tension, through a theoretical, computational and experimental study of the fluid mechanics.Read moreRead less
New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software ....New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software implementations. Both nonsmooth and integer optimisation problems have a good mathematical basis, but there are "gaps"; existing methods cannot always solve real industrial problems. This project will deliver better methods, built on better theory, and so will yield better solutions for important applications.Read moreRead less
A novel approach to controlling boundary-layer separation. This project will involve fundamental research into the control of the fluid dynamical phenomena of boundary-layer separation and transition to turbulence. The project will be built upon a firm foundation of mathematical modelling of the complex behaviour of fluid flows that are near the onset of flow separation or turbulence. The project will produce results that will permit the development of control strategies that can be implemented ....A novel approach to controlling boundary-layer separation. This project will involve fundamental research into the control of the fluid dynamical phenomena of boundary-layer separation and transition to turbulence. The project will be built upon a firm foundation of mathematical modelling of the complex behaviour of fluid flows that are near the onset of flow separation or turbulence. The project will produce results that will permit the development of control strategies that can be implemented in a wide variety of important technological applications, such as drag reduction in the aerospace and ship industries as well as the control of stall (or loss of lift) in modern aircraft.Read moreRead less
Robust fluid mixing through topological chaos. The Australian chemicals and plastics industry has an annual turnover of over $20 billion and employs over 77,000 people; fluid mixing is fundamental to this industry, yet the industry is recognised as underinvesting in research and development in this essential area. Furthermore, frontier technologies such as biotechnology and the next generation of smart materials also crucially rely on fluid mixing. This project aims to evaluate a new paradigm ( ....Robust fluid mixing through topological chaos. The Australian chemicals and plastics industry has an annual turnover of over $20 billion and employs over 77,000 people; fluid mixing is fundamental to this industry, yet the industry is recognised as underinvesting in research and development in this essential area. Furthermore, frontier technologies such as biotechnology and the next generation of smart materials also crucially rely on fluid mixing. This project aims to evaluate a new paradigm (topological chaos) for the design of mixers, to provide better and more robust mixers that work from microscopic to industrial scales.Read moreRead less
Systematically model the large-scale complexity of turbulent floods and thin film flows. This project continues development of new models, and computer
simulation, of turbulent flood, river and estuarine flow. The models
will be based systematically upon established turbulence models to
resolve accurately the complex physical processes. The development of
new and robust computer models for thin layers of coating fluid will
aid many industrial processes. We also aim to provide correct ini ....Systematically model the large-scale complexity of turbulent floods and thin film flows. This project continues development of new models, and computer
simulation, of turbulent flood, river and estuarine flow. The models
will be based systematically upon established turbulence models to
resolve accurately the complex physical processes. The development of
new and robust computer models for thin layers of coating fluid will
aid many industrial processes. We also aim to provide correct initial
conditions and boundary conditions for simpler cases of the above
flows. The approach leads to a greater understanding of the range of
applicability of the models through better estimating the errors in the
modelling process. The project develops a fundamental enabling
methodology for engineering and the sciences.
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A theoretical investigation into the effect of nonlinear wave interactions in promoting transition-to-turbulence. The problem of transition-to-turbulence remains one of the fundamental unanswered questions in fluid dynamics. An understanding of the processes leading to transition is necessary if the active control of turbulence is to be achieved. This project will focus attention on a new class of waves, which have only recently been described the CI, in order to determine how they are triggered ....A theoretical investigation into the effect of nonlinear wave interactions in promoting transition-to-turbulence. The problem of transition-to-turbulence remains one of the fundamental unanswered questions in fluid dynamics. An understanding of the processes leading to transition is necessary if the active control of turbulence is to be achieved. This project will focus attention on a new class of waves, which have only recently been described the CI, in order to determine how they are triggered and how they may serve to actively promote the early development of turbulence in a broad class of fluid flows.Read moreRead less
Optimal Transforms of Random Vectors. This proposal focusses on development of optimal transforms to describe and model nonlinear phenomena when only statistical information is known. An optimal transform is a mathematical procedure that enables us to process information in a way that is most suited to the task in hand. These transforms have been successfully used in approximation, information theory, communications, control theory and signal and image processing. Applications include modelli ....Optimal Transforms of Random Vectors. This proposal focusses on development of optimal transforms to describe and model nonlinear phenomena when only statistical information is known. An optimal transform is a mathematical procedure that enables us to process information in a way that is most suited to the task in hand. These transforms have been successfully used in approximation, information theory, communications, control theory and signal and image processing. Applications include modelling of physical, chemical and biological systems, filtering and compression of signals and data classification and clustering. We propose two new hybrid models for realistic transforms in a general structural framework.
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Optimal nose shaping for delayed boundary-layer separation and transition in axisymmetric flow. The aim of this project is to design a smooth nose for a body of revolution placed in axisymmetric flow of a viscous fluid at high Reynolds number, such that the boundary layer on the body remains unseparated. This can always be done with a sufficiently long nose, but our objective here is to minimise the necessary nose length. Outer potential flows will be provided via ring sources. The potential flo ....Optimal nose shaping for delayed boundary-layer separation and transition in axisymmetric flow. The aim of this project is to design a smooth nose for a body of revolution placed in axisymmetric flow of a viscous fluid at high Reynolds number, such that the boundary layer on the body remains unseparated. This can always be done with a sufficiently long nose, but our objective here is to minimise the necessary nose length. Outer potential flows will be provided via ring sources. The potential flows will be used to determine inner boundary layer solutions. Transition-to-turbulence will be considered by undertaking 2D and 3D stability computations.Read moreRead less