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
Geometric methods in mathematical physiology. This project will develop new geometric methods for the analysis of multiple-scales models of physiological rhythms and patterns, and will design diagnostic tools to identify key parameters that cause and control these signals. Thus, this project will deliver powerful mathematics for detecting and understanding fundamental issues of physiological systems.
Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory ....Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory will result in innovative platform and springboard diving techniques and improved performance. The reach of new insights generated by this work extends to many other fields, including robotics, spacecraft dynamics and nano technology.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE120101113
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Mathematical modelling of breast cancer immunity: guiding the development of preventative breast cancer vaccines. The project will apply various methods from mathematical modelling to simulate anti-breast cancer immune responses to incipient tumours. Results from simulation and analysis will help develop, assess, and optimise preventative breast cancer vaccines for further testing in future experimental studies.
A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of ....A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of these shock waves, while simultaneously unifying existing regularisation techniques under a single, geometric banner. It will devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.Read moreRead less
Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory ....Bodies in space. By investigating how a change in shape of the human body can produce a change in spatial orientation, the project will bring a fundamental advance of knowledge in the intersection of applied mathematics, sports science and mechanical engineering. These knowledge advances will lead to a novel theory regarding the control of the aerial dynamics of athletes, specifically springboard and platform divers. When applied in collaboration with world class Australian athletes, this theory will result in innovative platform and springboard diving techniques and improved performance. The reach of new insights generated by this work extends to many other fields, including robotics, spacecraft dynamics and nano technology.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
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.
Dynamics of atherosclerotic plaque formation, growth and regression. This project aims to provide a mathematical framework to interpret plaque growth. Many biological processes contribute to the growth of atherosclerotic plaques inside arteries. Lipoproteins enter the artery walls and stimulate tissues to signal to cells which duly respond so that fatty streaks form and grow into dangerous plaques that cause heart attacks or stroke. These processes are often nonlinear and operate on widely varyi ....Dynamics of atherosclerotic plaque formation, growth and regression. This project aims to provide a mathematical framework to interpret plaque growth. Many biological processes contribute to the growth of atherosclerotic plaques inside arteries. Lipoproteins enter the artery walls and stimulate tissues to signal to cells which duly respond so that fatty streaks form and grow into dangerous plaques that cause heart attacks or stroke. These processes are often nonlinear and operate on widely varying time scales. The project plans to use systems of ordinary differential equations, partial differential equations with non-standard boundary conditions, and bifurcation theory to find how nonlinear processes shape plaque growth. The expected results may demonstrate the importance of bifurcations, dynamics and nonlinear systems in plaque growth and provide new models to interpret biological data.Read moreRead less
A probabilistic and geometric understanding of transport and metastability in mathematical geophysical flows. Complicated fluid flow is at the heart of physical oceanography and atmospheric science. This project will develop new mathematical technologies to reveal hidden transport barriers around which complicated fluid flow is organised. This project will lead to more accurate circulation predictions from ocean and atmosphere models.