Multi-scale modelling of cell migration in developmental biology. Interpretative and predictive tools are needed for the comprehensive understanding of directed cell migration in the medical sciences. Mathematical models and modelling methodologies developed in this project will make a significant contribution to the investigation of cell migration and the testing and generation of hypotheses. Such models are needed to understand observed cellular patterns. This project will contribute to knowle ....Multi-scale modelling of cell migration in developmental biology. Interpretative and predictive tools are needed for the comprehensive understanding of directed cell migration in the medical sciences. Mathematical models and modelling methodologies developed in this project will make a significant contribution to the investigation of cell migration and the testing and generation of hypotheses. Such models are needed to understand observed cellular patterns. This project will contribute to knowledge of normal and abnormal developmental processes, especially in embryonic growth. Understanding these processes should lead to prediction and treatment of congenital disorders and contribute to a healthy start to life.Read moreRead less
Variational methods in partial differential equations. Research in partial differential equations is a very active area of modern mathematics linking nonlinear functional analysis, calculus of variations and differential geometry to applied sciences. This project will enable Australia-based researchers to participate in the forefront of mathematical research with leading international mathematicians by establishing new collaborations, strengthening on-going collaborations and providing internat ....Variational methods in partial differential equations. Research in partial differential equations is a very active area of modern mathematics linking nonlinear functional analysis, calculus of variations and differential geometry to applied sciences. This project will enable Australia-based researchers to participate in the forefront of mathematical research with leading international mathematicians by establishing new collaborations, strengthening on-going collaborations and providing international research experience for early career researchers. As a result, this proposal will enhance Australia's distinguished reputation in analysis and further link the UQ group with a number of mathematical institutes in USA and China.Read moreRead less
Geometric partial differential systems and their applications. This proposal addresses questions central to the understanding of nonlinear partial differential systems from classical, quantum field theory and liquid crystals. Applications to physical problems such as the Yang-Mills flow, Faddeev's model and liquid crystal systems are of great interest and importance in the broader scientific community. The project will yield internationally significant results in theoretical mathematics, with ....Geometric partial differential systems and their applications. This proposal addresses questions central to the understanding of nonlinear partial differential systems from classical, quantum field theory and liquid crystals. Applications to physical problems such as the Yang-Mills flow, Faddeev's model and liquid crystal systems are of great interest and importance in the broader scientific community. The project will yield internationally significant results in theoretical mathematics, with applications in physics and and other sciences. Specialist training will be provided for Australia's next generation of mathematicians. This project will enable Australian researchers to stay at the forefront of research in this area, strengthening links with a number of world-leading mathematicians.Read moreRead less
Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contri ....Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contributions to these topics: Regularity problem and energy minimality of weakly harmonic maps, Weak solutions of the liquid crystal equilibrium system, Yang-Mills heat flow and singular Yang-Mills connections.
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Determination of Conductivity Values for Anisotropic Tissue. Well established mathematical models governing the electrical potential in biological tissue can be combined with measurements of the electric potential on the surface of the tissue to provide insight into subsurface tissue damage. However, before such observations can be convincingly accepted, reliable values for the tissue conductivity must be obtained. The aim of this project is to develop mathematical techniques to calculate the co ....Determination of Conductivity Values for Anisotropic Tissue. Well established mathematical models governing the electrical potential in biological tissue can be combined with measurements of the electric potential on the surface of the tissue to provide insight into subsurface tissue damage. However, before such observations can be convincingly accepted, reliable values for the tissue conductivity must be obtained. The aim of this project is to develop mathematical techniques to calculate the conductivity values so that one can apply the equations to solve problems of potential distribution and proceed to accurately simulate electrical potential distributions in damaged tissue. More accurate and reliable conductivity values will allow a better understanding of the way electric current moves through the heart which, in turn, will result in more efficient defibrillators and better diagnosis of abnormal function.Read moreRead less
Statistical and mathematical modelling to improve health care outcomes in hospitals. The aim of this project is to develop new quantitative techniques based on mathematical and statistical modelling that improve the outcomes of health care in hospitals. Hospital outcomes for patients are sub-optimal due to adverse events such as hospital acquired infections and fully stretched facilities. Research from this project will lead to resource usage being optimised using operations research; the tra ....Statistical and mathematical modelling to improve health care outcomes in hospitals. The aim of this project is to develop new quantitative techniques based on mathematical and statistical modelling that improve the outcomes of health care in hospitals. Hospital outcomes for patients are sub-optimal due to adverse events such as hospital acquired infections and fully stretched facilities. Research from this project will lead to resource usage being optimised using operations research; the transmission of hospital acquired infections being better understood using mathematical models; and better monitoring of adverse events and analyses of studies using statistical tools. Opportunities will be provided for hospital staff to acquire knowledge of the significance of these outcomes .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
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
Computational modelling of nanofluids for industrial applications. The use of nanoparticles in heat transfer fluids, then known as nanofluids, increases their specific heat and thermal conductivity. Recent experimental works highlight that anomalous transport phenomena are evident in nanofluids that cannot be adequately described by classical conservation laws. We will extend these conservation laws to incorporate fractional operators to capture the fluid memory effects and the impact of particl ....Computational modelling of nanofluids for industrial applications. The use of nanoparticles in heat transfer fluids, then known as nanofluids, increases their specific heat and thermal conductivity. Recent experimental works highlight that anomalous transport phenomena are evident in nanofluids that cannot be adequately described by classical conservation laws. We will extend these conservation laws to incorporate fractional operators to capture the fluid memory effects and the impact of particle clustering. Computational modelling and experimental investigations will be undertaken to identify the heat transfer mechanisms of various nanofluids. The outcomes of the work will increase knowledge on nanofluids and offer a significant opportunity to improve the efficiency of many thermal engineering systems.Read moreRead less