Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress ....Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress in a feasible time frame. In three dimensions this project will strengthen the distinguished computational topology community in Melbourne, led by pioneers such as Rubinstein, Goodman, Hodgson as well as the applicant himself.Read moreRead less
Tractable topological computing: Escaping the hardness trap. Computational topology is a young and energetic field that uses computers to solve complex geometric problems driven by pure mathematics, and with diverse applications in biology, signal processing and data mining. A major barrier is that many of these problems are thought to be fundamentally and intractably hard. This project aims to defy such barriers for typical real-world inputs by fusing geometric techniques with technologies from ....Tractable topological computing: Escaping the hardness trap. Computational topology is a young and energetic field that uses computers to solve complex geometric problems driven by pure mathematics, and with diverse applications in biology, signal processing and data mining. A major barrier is that many of these problems are thought to be fundamentally and intractably hard. This project aims to defy such barriers for typical real-world inputs by fusing geometric techniques with technologies from the field of parameterised complexity, creating powerful, practical solutions for these problems. It is expected to shed much-needed light on the vast and puzzling gap between theory and practice, and give researchers fast new software tools for large-scale experimentation and cutting-edge computer proofs.Read moreRead less
Modelling interactions of spray droplets with plants. This project addresses the National Research Priority of an environmentally sustainable Australia by developing sophisticated mathematical models and interactive software that will identify environmentally friendlier technologies to efficiently deliver agrichemicals while minimising large scale water usage. National benefits will accrue from the provision for postdoctoral, PhD and IT staff training, while direct links with industry will provi ....Modelling interactions of spray droplets with plants. This project addresses the National Research Priority of an environmentally sustainable Australia by developing sophisticated mathematical models and interactive software that will identify environmentally friendlier technologies to efficiently deliver agrichemicals while minimising large scale water usage. National benefits will accrue from the provision for postdoctoral, PhD and IT staff training, while direct links with industry will provide technology transfer to end-users to ensure community uptake. The project will benefit rural and regional communities by providing long-term solutions in the areas of water use and quality, pesticide pollution reduction, and improved environment and human health care.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE150101137
Funder
Australian Research Council
Funding Amount
$312,000.00
Summary
Two-scale numerical modelling of coupled transport in heterogeneous media. Groundwater constitutes a vital part of water resources in Australia, however, the quality of this water is susceptible to contamination. This project aims to develop an innovative two-scale mathematical model for contaminant transport that accounts for small-scale heterogeneities found in the unsaturated zone of an aquifer located between the ground surface and the underlying groundwater. The project aims to develop valu ....Two-scale numerical modelling of coupled transport in heterogeneous media. Groundwater constitutes a vital part of water resources in Australia, however, the quality of this water is susceptible to contamination. This project aims to develop an innovative two-scale mathematical model for contaminant transport that accounts for small-scale heterogeneities found in the unsaturated zone of an aquifer located between the ground surface and the underlying groundwater. The project aims to develop valuable environmental insights, a simulation tool that will help in making decisions regarding the future management of Australian groundwater resources, and a general two-scale modelling and simulation framework for other important environmental and industrial problems involving coupled transport in heterogeneous media.Read moreRead less
Generic complexity in computational topology: breaking through the bottlenecks. The project will focus on key computational problems in three-dimensional topology, with the aims of illuminating the theoretical limitations of such problems, developing new computational tools for solving them, and applying these tools to a variety of applications. The project will generate theoretical research, practical software, and rich experimental data.
Mathematical and computational models for agrichemical retention on plants. Mathematical and computational models for agrichemical retention on plants. This project aims to build interactive software that simulates agrichemical spraying for multiple virtual plants reconstructed from scanned data. Mathematical modelling and computer simulation could offer an alternative to expensive experimental programs for agrichemical spraying of plants. This project will use contemporary fluid mechanics to bu ....Mathematical and computational models for agrichemical retention on plants. Mathematical and computational models for agrichemical retention on plants. This project aims to build interactive software that simulates agrichemical spraying for multiple virtual plants reconstructed from scanned data. Mathematical modelling and computer simulation could offer an alternative to expensive experimental programs for agrichemical spraying of plants. This project will use contemporary fluid mechanics to build practical mathematical models for droplet impaction, spreading and evaporation on leaf surfaces, and experimentally calibrate and validate the models. The software is expected to drive the development of agrichemical products that increase retention, minimise environmental impacts, and reduce costs for end-users.Read moreRead less