Microcantilevers for multifrequency atomic force microscopy. This project aims to design a microcantilever with high-performing sensors more sensitive and with better noise performance than the typical optical system used in commercial Atomic Force Microscopes (AFMs). The AFM, a nanotechnology instrument, uses a microcantilever (with an extremely shape probe) to interrogate a sample surface. It has made important discoveries in nanotechnology, life sciences, nanomachining, material science and d ....Microcantilevers for multifrequency atomic force microscopy. This project aims to design a microcantilever with high-performing sensors more sensitive and with better noise performance than the typical optical system used in commercial Atomic Force Microscopes (AFMs). The AFM, a nanotechnology instrument, uses a microcantilever (with an extremely shape probe) to interrogate a sample surface. It has made important discoveries in nanotechnology, life sciences, nanomachining, material science and data storage systems. Despite its success, the technique’s spatial resolution and quantitative measurements are limited. This project could lead to breakthrough technologies such as atomic force spectroscopy to study elastic modulus of nanostructures, and establish Australia's prominence in this emerging field.Read moreRead less
Complex dynamical systems: inferring form and function of interacting biological systems. Often in biology a large number of simple parts interacting according to simple rules can result in behaviour that is rich and varied. This project aims to develop the mathematics of complex systems theory to describe how such collections of simple interacting parts can form large complicated structures, and to deduce what dynamical behaviour can result.
Functional state observers for large-scale interconnected systems. This project will produce conceptual advances with new design rules to develop robust and efficient functional state observers for interconnected systems. The outcomes will advance the theory of functional observers and improve the operation, efficiency and performance of critical infrastructure such as power grids, water and traffic networks.
System identification of microstructure in the brain using magnetic resonance. Magnetic Resonance Imaging technologies will be exploited to probe the microstructure of the brain, using powerful Bayesian optimisation techniques and innovative uses of magnetic resonance. The project will in particular develop non-invasive imaging methods to quantify iron content in the brain, important for research on dementia and Alzheimer's disease.
Improving transient performance for systems with multiple inputs/outputs. This project aims to develop and test new mathematical techniques for the improvement of transient performance in tracking control systems. The fundamental problem to be addressed will be the design of controllers to rapidly track constant and time varying target reference signals without overshooting or undershooting for multiple-input multiple-output systems/plants. These new methods aim to offer improved accuracy and sp ....Improving transient performance for systems with multiple inputs/outputs. This project aims to develop and test new mathematical techniques for the improvement of transient performance in tracking control systems. The fundamental problem to be addressed will be the design of controllers to rapidly track constant and time varying target reference signals without overshooting or undershooting for multiple-input multiple-output systems/plants. These new methods aim to offer improved accuracy and speed in many engineering applications.Read moreRead less
What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms ....What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms underlying large-scale (in)stability for time-dependent dynamical systems, and reliable numerical methods for detecting instabilities. This research is expected to lead to improved characterisations of shocks or collapse in externally driven dynamical systems and assist scientists to gauge which predictions they can trust.Read moreRead less
Modern mathematics to unravel the birth of coherence in dynamical systems. This project aims to reveal the precise mathematical mechanisms underlying the emergence and disappearance of long-lived coherent features in dynamical systems. This project expects to generate new fundamental mathematics in the area of dynamical systems, using innovative operator-theoretic approaches to carefully tease apart the lifecycles of coherent structures. The expected outcomes of this project include new mathemat ....Modern mathematics to unravel the birth of coherence in dynamical systems. This project aims to reveal the precise mathematical mechanisms underlying the emergence and disappearance of long-lived coherent features in dynamical systems. This project expects to generate new fundamental mathematics in the area of dynamical systems, using innovative operator-theoretic approaches to carefully tease apart the lifecycles of coherent structures. The expected outcomes of this project include new mathematical theory and computational algorithms to anticipate the genesis and destruction of coherent objects, which are key organisers of complex geophysical flows. This breakthrough mathematics should provide significant benefits, such as improved prediction of eddy transport and persistence of weather and climate patterns.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE160100147
Funder
Australian Research Council
Funding Amount
$381,294.00
Summary
Coherent structures in chaotic dynamical systems. Using transfer operators and state-of-the-art multiplicative ergodic theory as a springboard, this project aims to develop innovative mathematics for bridging gaps between dynamical systems theory and applications. Coherent structures, such as oceanic eddies and atmospheric vortices, are prevalent in real-world dynamical systems and play a crucial role in both weather and climate systems. These structures arise in externally forced systems, and t ....Coherent structures in chaotic dynamical systems. Using transfer operators and state-of-the-art multiplicative ergodic theory as a springboard, this project aims to develop innovative mathematics for bridging gaps between dynamical systems theory and applications. Coherent structures, such as oceanic eddies and atmospheric vortices, are prevalent in real-world dynamical systems and play a crucial role in both weather and climate systems. These structures arise in externally forced systems, and the existing theory concerning their location, number and stability to model errors is much less understood than in the non-forced counterpart. The intended outcomes include new algorithms for the automatic detection of coherent structures and results about their stability under perturbations which are relevant to roles in both weather and climate systems.Read moreRead less
New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deter ....New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deterministic components. This project aims to develop mathematics and numerics to accurately quantify and assess these complicated variations. The project expects to provide powerful tools to predict harmful outcomes in biogeophysical systems, and assist with the development of mitigation strategies.Read moreRead less
TSuNAMi: Time Series Network Animal Modelling. Our proposal is motivated by and based upon the successful representation of time series as a network (or graph). We construct an abstract representation of a system from measurements of its changing behaviour over time. Properties of that structure (the network) then allow us to infer diagnostic information of the system. Specifically, we propose to apply this to livestock welfare during transport. By measuring the biological and environment condi ....TSuNAMi: Time Series Network Animal Modelling. Our proposal is motivated by and based upon the successful representation of time series as a network (or graph). We construct an abstract representation of a system from measurements of its changing behaviour over time. Properties of that structure (the network) then allow us to infer diagnostic information of the system. Specifically, we propose to apply this to livestock welfare during transport. By measuring the biological and environment condition of the animal we construct a network representation of that system. Geometric features of that network can then be used to infer health or duress of the subject. This proposal will develop the generic mathematical machinery to connect geometric features of the network with system behaviour. Read moreRead less