Complex Multiscale Systems: Modeling, Analysis and Scientific Computation. This project aims to develop and implement a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. The wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or partial differential equations or la ....Complex Multiscale Systems: Modeling, Analysis and Scientific Computation. This project aims to develop and implement a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. The wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or partial differential equations or lattice equations). Comprehensively accounting for multiscale interactions between subgrid processes among macroscale variations ensures stability and accuracy. Based on dynamical systems theory and analysis, this approach is expected to empower systematic analysis and understanding for optimal macroscopic simulation for forthcoming exascale computing.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140101268
Funder
Australian Research Council
Funding Amount
$386,820.00
Summary
Stochastic mathematical modelling of the Wnt signalling pathway. The Wnt signalling pathway is pivotal in multicellular organisms, regulating cellular processes such as proliferation, apoptosis and migration. Faulty Wnt signalling is associated with degenerative diseases, developmental disorders and cancers and is therefore a potential target for therapeutic drugs. This project will perform a stochastic spatial simulation of the Wnt signalling pathway which will be matched to experimental data. ....Stochastic mathematical modelling of the Wnt signalling pathway. The Wnt signalling pathway is pivotal in multicellular organisms, regulating cellular processes such as proliferation, apoptosis and migration. Faulty Wnt signalling is associated with degenerative diseases, developmental disorders and cancers and is therefore a potential target for therapeutic drugs. This project will perform a stochastic spatial simulation of the Wnt signalling pathway which will be matched to experimental data. The model will be extended to integrate with the cell cycle. Increased proliferation in tumours has been linked to mutations in Wnt components. Using the extended model, the effect of Wnt-targeting therapeutic cancer drugs on cancer cell proliferation rates will be predicted and compared to experiments.Read moreRead less
Flow structures and transport: predictability and control. Moving flow structures (the boundary of an eddy, the flow interface between two fluids) are crucial in fluid mixing and in the transport of heat, pollutants and nutrients. This project will analyse their roles in improving predictions of spreading extents and rates for geophysical-scale problems, and in controlling transport at the micro-scale. Inaccuracies in currently available numerical diagnostics for transport prediction will be com ....Flow structures and transport: predictability and control. Moving flow structures (the boundary of an eddy, the flow interface between two fluids) are crucial in fluid mixing and in the transport of heat, pollutants and nutrients. This project will analyse their roles in improving predictions of spreading extents and rates for geophysical-scale problems, and in controlling transport at the micro-scale. Inaccuracies in currently available numerical diagnostics for transport prediction will be comprehensively evaluated via comparison with recent exact models. Analytical methods for quantifying transport under unsteady flow protocols will be developed, and used to answer questions on controlling transport in microfluidic applications in conjunction with experimentalists.Read moreRead less
Uncertainties in coherent transport of particles and intrinsic properties. This Project aims to quantify the uncertainty of a model output in terms of uncertainties in modelling assumptions, by developing new mathematical techniques and applying them to real-world data. This will be in the context of assessing the accuracy of tracking coherently moving structures (e.g., hurricanes, oceanic biodiversity hotspots, pollutant patches, insect swarms) from experimental/observational data sets. Novel, ....Uncertainties in coherent transport of particles and intrinsic properties. This Project aims to quantify the uncertainty of a model output in terms of uncertainties in modelling assumptions, by developing new mathematical techniques and applying them to real-world data. This will be in the context of assessing the accuracy of tracking coherently moving structures (e.g., hurricanes, oceanic biodiversity hotspots, pollutant patches, insect swarms) from experimental/observational data sets. Novel, data-tested, mathematical methods for uncertainty quantification of coherent structures will be developed as Project outcomes. Project benefits include new insights into protecting the environment, improved uncertainty quantification in climate modelling, and the generation of interdisciplinary knowledge and training.Read moreRead less
A coordinate-independent theory for multi-time-scale dynamical systems. Biochemical reaction networks operate inherently on many disparate timescales, and identifying this temporal hierarchy is key to understanding biological behaviour. Currently, the existing dynamical systems theory is not able to rigorously analyse many important biological systems and networks due to this inherent non-standard multi-time-scale splitting. This project aims to remove these stumbling blocks and develop a coordi ....A coordinate-independent theory for multi-time-scale dynamical systems. Biochemical reaction networks operate inherently on many disparate timescales, and identifying this temporal hierarchy is key to understanding biological behaviour. Currently, the existing dynamical systems theory is not able to rigorously analyse many important biological systems and networks due to this inherent non-standard multi-time-scale splitting. This project aims to remove these stumbling blocks and develop a coordinate-independent mathematical theory that weaves together results from geometric singular perturbation theory, differential and algebraic geometry and reaction network theory to decompose and explain the structure in the dynamic hierarchy of events in non-standard multi-time-scale systems and networks.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.
Discovery and tracking of coherent structures in geophysical flows. Coherent structures in geophysical flows play fundamental roles by organising fluid flow and obstructing transport. For example, ocean eddies strongly influence the transportation of heat, nutrients, phytoplankton, and fish larvae, in both the horizontal and vertical direction. Many coherent structures are very difficult to detect and track by direct measurement (for example satellite observations), and current mathematical tech ....Discovery and tracking of coherent structures in geophysical flows. Coherent structures in geophysical flows play fundamental roles by organising fluid flow and obstructing transport. For example, ocean eddies strongly influence the transportation of heat, nutrients, phytoplankton, and fish larvae, in both the horizontal and vertical direction. Many coherent structures are very difficult to detect and track by direct measurement (for example satellite observations), and current mathematical techniques cannot provide an adequate global description. This project aims to create innovative new mathematical theory and numerical methods to discover and track coherent structures over time frames of physical importance, contributing significantly to our understanding of their role in the oceans' biosphere and climate.Read moreRead less
Innovative mathematics using transfer operators to reveal hidden ordered structures in geophysical flows. Complicated fluid flow is at the heart of physical oceanography and atmospheric science. This research will develop new mathematical technologies to reveal hidden ordered structures around which complicated fluid flow is organised. This new analytical approach will lead to more accurate circulation predictions from ocean and atmosphere models.