Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in mi ....Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in microscale tissue properties are lacking. The tools developed by this project will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain. Additionally, the mathematical tools developed will be transferable to other applications where diffusion and transport in heterogeneous porous media play a role.Read moreRead less
Extracting macroscopic variables and their dynamics in multiscale systems with metastable states. There are practical barriers to the simulation of complex systems such as molecular systems and the climate system because of the high-dimensionality of the models and the presence of multiscale dynamics. This project will lift these barriers by uncovering the most relevant variables and by creating innovative multiscale simulation algorithms.
Quantifying complexity and measuring structure within complex systems. Most interesting systems are complex. The complex systems of interest in this project are characterised by a simple dynamical behaviour on each individual part; and a complicated web of interaction between the many distinct parts. The project will focus on the massive system of interacting neurones in the brain, and transmission of influenza via interpersonal contacts. This project will provide a better model of that web of i ....Quantifying complexity and measuring structure within complex systems. Most interesting systems are complex. The complex systems of interest in this project are characterised by a simple dynamical behaviour on each individual part; and a complicated web of interaction between the many distinct parts. The project will focus on the massive system of interacting neurones in the brain, and transmission of influenza via interpersonal contacts. This project will provide a better model of that web of interactions; and new methods for statistically validating this model against data. Existing models of complex networks are statistically biased so, by employing robust statistical methodologies, this problem will be rectified and provide a method for randomly choosing representative complex systems. Read moreRead less
Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dis ....Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dissipative and higher order nonlinear terms. These are essential for a precise description of both giant waves in the ocean and strong pulses in optics. Read moreRead less
Rogue waves in oceans and optical fibres. Rogue waves can sink large ships in the ocean. They appear more commonly than previously thought. Optical rogue waves, the laboratory counterparts of extreme ocean waves, will allow the project to study the main features of the phenomenon, provide the theoretical explanation for their existence and potentially help to eliminate these catastrophic events.
New mathematics to improve understanding of anomalously diffusing reactions. Standard mathematical models for particles that diffuse and react are based on assumptions that improving technologies have revealed do not always hold. This project aims to create a mathematical framework that generalises existing approaches, taking into account observations of complicated transport behaviour at many scales, and including the impact of this anomalous transport on reactions. The development of the fram ....New mathematics to improve understanding of anomalously diffusing reactions. Standard mathematical models for particles that diffuse and react are based on assumptions that improving technologies have revealed do not always hold. This project aims to create a mathematical framework that generalises existing approaches, taking into account observations of complicated transport behaviour at many scales, and including the impact of this anomalous transport on reactions. The development of the framework will involve innovative approaches utilising mathematical techniques, including dynamical systems, fractional calculus, and stochastic processes. This project aims to deliver new mathematical models that can be adopted in applications across different discipline areas, and especially in biological systems. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101581
Funder
Australian Research Council
Funding Amount
$411,000.00
Summary
Stability and Complexity: New insights from Random Matrix Theory. Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project includ ....Stability and Complexity: New insights from Random Matrix Theory. Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project include development and expansion of an innovative mathematical framework and techniques which allow a unified and universal approach to the question of stability in large complex systems. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140100620
Funder
Australian Research Council
Funding Amount
$395,220.00
Summary
Inference, control and protection of interdependent spatial networked structures. Networked structures are everywhere and modern societies largely depend on their proper functioning. Some of these networks are spatial with each node having a geographical tag. Examples include power grids, the internet and transportation networks. These networks are often interdependent where their functioning depends on each other. This project will establish a mathematical framework to efficiently observe and c ....Inference, control and protection of interdependent spatial networked structures. Networked structures are everywhere and modern societies largely depend on their proper functioning. Some of these networks are spatial with each node having a geographical tag. Examples include power grids, the internet and transportation networks. These networks are often interdependent where their functioning depends on each other. This project will establish a mathematical framework to efficiently observe and control interdependent spatial networks and develop design strategies in order to maximise residency of spatial networks against catastrophic failures in their components. The outcomes of the project will protect the Australian power grid and transportation networks against random and intentional failures. Read moreRead less
Efficient and convergent first-principles chemical dynamics. This project develops a new method for studying chemical systems using first principles quantum mechanics. The new method can solve a much larger range of chemical problems than its predecessors, allowing detailed and accurate descriptions of reactions and dynamics driven by thermal energy or activated by light.
A study of ultracold atom interferometry and interactions through high-performance computing. This project involves a design and study of hyper-sensitive machines to detect changes in motion based on using clouds of atoms near absolute zero temperature. Matter at these ultracold temperatures can be harnessed to detect variations of both space and time, enabling novel quantum measurement devices to be built.