Communication and information storage mechanisms in complex dynamical brain networks. Recordings of electrical activity in the brain often cycle repetitively. The aim of this research is to explain how these brain rhythms assist the brain to coordinate simultaneous activity in several regions. Australian socioeconomic benefits include: (i) contributions to the knowledge base of theoretical neuroscience, enhancing Australia's reputation for cutting-edge research; (ii) strengthening of internation ....Communication and information storage mechanisms in complex dynamical brain networks. Recordings of electrical activity in the brain often cycle repetitively. The aim of this research is to explain how these brain rhythms assist the brain to coordinate simultaneous activity in several regions. Australian socioeconomic benefits include: (i) contributions to the knowledge base of theoretical neuroscience, enhancing Australia's reputation for cutting-edge research; (ii) strengthening of international collaborations with Europe and Japan; (iii) outcomes will ultimately impact on improved medical bionics and future interfaces between brain activity and machines or computers; and (iv) commercialization and technology transfer opportunities, via the transfer of results to biologically inspired engineering.Read moreRead less
Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscal ....Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscale segregation devices for separation of different cells in a blood sample, and of macroscale devices for separation of mineral particles from crushed ore). At present, the description of these processes is qualitative, with quantitative understanding seen as a challenge without intensive computation. The project plans to develop, solve and validate mathematical models to give a quantitative understanding of these processes.Read moreRead less
Shining the light on geometry of microstructured optical fibres. A fast, powerful computer code using new mathematical models and techniques will be produced and experimentally validated, for use in development of novel microstructured optical fibres for telecommunications and other applications. This code will reduce the time-consuming and expensive experimental iteration needed for development of these fibres.
Mathematics the key to modern glass and polymer fibre technology. This project aims to develop fully coupled flow and energy models to determine the preform structure and fibre-drawing parameters needed to fabricate a desired microstructured optical fibre by stretching of the preform to a fibre. It will focus on polymer to develop a non-Newtonian flow model, which can handle the subset of Newtonian glass fibre drawing. It will develop fast, powerful three-dimensional predictive tools to solve th ....Mathematics the key to modern glass and polymer fibre technology. This project aims to develop fully coupled flow and energy models to determine the preform structure and fibre-drawing parameters needed to fabricate a desired microstructured optical fibre by stretching of the preform to a fibre. It will focus on polymer to develop a non-Newtonian flow model, which can handle the subset of Newtonian glass fibre drawing. It will develop fast, powerful three-dimensional predictive tools to solve the models and experimentally validate solutions. This work will direct future design of microstructured optical fibres to empower next-generation optical-fibre technologies. Expected outcomes are fibre designs for telecommunications, medicine, biotechnology, sensing and imaging.Read moreRead less
Pattern formation of precursor films: a new mathematical model. This project aims to develop a new mathematical model to predict the pattern formation of a new class of permanent lubricants. Ionic liquids are conductive and do not evaporate, creating a unique opportunity to develop such coatings. These thin films form patterns where the pattern type (patches, stripes or holes) depends on the liquid/surface interaction. Only some patterns result in good lubrication; current limited understanding ....Pattern formation of precursor films: a new mathematical model. This project aims to develop a new mathematical model to predict the pattern formation of a new class of permanent lubricants. Ionic liquids are conductive and do not evaporate, creating a unique opportunity to develop such coatings. These thin films form patterns where the pattern type (patches, stripes or holes) depends on the liquid/surface interaction. Only some patterns result in good lubrication; current limited understanding of the pattern formation process hampers selection of a good lubricant for a chosen material. Current mathematical approaches are computationally expensive and time consuming. The new model expected from this project would provide a cheap, fast and reliable alternative for screening suitable liquid/surface pairs.Read moreRead less
Root-to-shoot: modeling the salt stress response of a plant vascular system. Salt and drought are the two major abiotic stresses affecting crop plant health, growth and development. We aim to understand salt and water transport in plants and the physiological effects of soil salinity. Using biophysical models, we will quantify the movement of salt through plant organs, tissues and cells, from root to leaf. We aim to answer the question of how salt moves across the different tissues and major org ....Root-to-shoot: modeling the salt stress response of a plant vascular system. Salt and drought are the two major abiotic stresses affecting crop plant health, growth and development. We aim to understand salt and water transport in plants and the physiological effects of soil salinity. Using biophysical models, we will quantify the movement of salt through plant organs, tissues and cells, from root to leaf. We aim to answer the question of how salt moves across the different tissues and major organs, how salt accumulates in root, leaf and shoot cells, and how movement and accumulation is controlled by the diversity of transport mechanisms operating in plants. We aim to quantify tissue tolerance, osmotic tolerance and ionic tolerance and discover new mechanisms by which plants can stave off the effect of salt stress.Read moreRead less
New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include po ....New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include powerful and reliable mathematical models ready for application, and national and international collaborations with scientists and mathematicians. This should provide significant benefits including increased capacity to use mathematical models in vascular biology and training young researchers in interdisciplinary methods.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE130100031
Funder
Australian Research Council
Funding Amount
$333,684.00
Summary
Mathematical modelling of the complex mechanics of biological materials and their role in tissue function and development. The mechanics of biological materials is complicated because they consist of many components such as fibres, proteins and polymers. We aim to use mathematical tools to understand how these components interact in tissues such as the spinal disc which will aid the development of new treatments to reverse the effects of injury, disease or aging.
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
Construction of near optimal oscillatory regimes in singularly perturbed control systems via solutions of Hamilton-Jacobi-Bellman inequalities. Problems of optimal control of systems evolving in multiple time scales arise in a great variety of applications (from diet to environmental modelling). This project addresses the challenge of analytically and numerically constructing rapidly oscillating controls that would 'near optimally coordinate' the slow and fast dynamics.