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
Discovery Early Career Researcher Award - Grant ID: DE180101098
Funder
Australian Research Council
Funding Amount
$374,200.00
Summary
New mathematical theory for fluid motion on surfaces with holes. This project aims to develop new explicit mathematical results to enhance the understanding of potential theory – a fundamental area of mathematics - on surfaces with complicating geometrical properties. There are very few such fundamental results on complicated curved surfaces, such as those with holes. This project should provide a toolbox for solving many different mathematical problems on curved surfaces. The new results should ....New mathematical theory for fluid motion on surfaces with holes. This project aims to develop new explicit mathematical results to enhance the understanding of potential theory – a fundamental area of mathematics - on surfaces with complicating geometrical properties. There are very few such fundamental results on complicated curved surfaces, such as those with holes. This project should provide a toolbox for solving many different mathematical problems on curved surfaces. The new results should also have application to the analysis of fluid flows over porous media and practical engineering structures.Read moreRead less
Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelec ....Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelectric sensor technology. Expected outcomes include manufactured proof-of-concept sensors that enable measurement of local stress fields. This should provide significant benefits, such as improved future robot capability and reliability, and research training for next-generation Australian computational mathematicians. Read moreRead less
Asymptotics of the exponentially small. Asymptotic analysis plays a vital role in studying the complex interfacial dynamics that are fundamental for practical problems in fluid mechanics such as the withdrawal of oil and gas from underground reservoirs and the optimal design of ship hulls to minimise wave drag. These applications exhibit extremely small physical effects that may be crucially important but cannot be described using classical asymptotic analysis. This project will develop state of ....Asymptotics of the exponentially small. Asymptotic analysis plays a vital role in studying the complex interfacial dynamics that are fundamental for practical problems in fluid mechanics such as the withdrawal of oil and gas from underground reservoirs and the optimal design of ship hulls to minimise wave drag. These applications exhibit extremely small physical effects that may be crucially important but cannot be described using classical asymptotic analysis. This project will develop state of the art mathematical techniques in exponential asymptotics to address this deficiency in the classical theory, and provide a deeper understanding of pattern formation, instabilities and wave propagation on the interface between two fluids.Read moreRead less
Mathematical and computational analysis of ship wakes. This project aims to develop mathematical and computational tools to compute the energy in a given ship wake and to determine a range of properties of a ship by taking simple measurements of the water height as the ship travels past. The expected outcomes of this project include a suite of algorithms that back-calculate the hull shape and operating conditions of a moving ship given only the surface height data measured at a single point. The ....Mathematical and computational analysis of ship wakes. This project aims to develop mathematical and computational tools to compute the energy in a given ship wake and to determine a range of properties of a ship by taking simple measurements of the water height as the ship travels past. The expected outcomes of this project include a suite of algorithms that back-calculate the hull shape and operating conditions of a moving ship given only the surface height data measured at a single point. These results should have direct implications for measuring damage to coastal zones by ship wakes and for surveillance of shipping channels.Read moreRead less
Mathematical modelling of the dynamics of multi-layered biological tissues. The project intends to develop a mathematical model of the basic mechanisms that determine the self-organisation of cells into complex tissues during the development of the embryo. Tissue function requires a non-trivial tissue architecture often composed of multiple cell layers which exhibit a remarkable capacity for renewal and defect correction. A cardinal part of embryonic development involves robust shaping of multi- ....Mathematical modelling of the dynamics of multi-layered biological tissues. The project intends to develop a mathematical model of the basic mechanisms that determine the self-organisation of cells into complex tissues during the development of the embryo. Tissue function requires a non-trivial tissue architecture often composed of multiple cell layers which exhibit a remarkable capacity for renewal and defect correction. A cardinal part of embryonic development involves robust shaping of multi-layered tissue morphologies. The project plans to use mathematical models to determine how complex, three-dimensional structures arise from adaptive multicellular biomechanical interactions. It plans to develop a novel computational modelling framework to represent and analyse such systems, which may be applicable to a wide range of problems where tissue mechanics is a key factor such as bone remodelling and wound healing.Read moreRead less
How motor proteins contract the cell cortex and form a cell division ring. This project aims to develop a detailed physical model for motor proteins and filaments and, based on it, derive a fluid-type mean-field mathematical model, which will facilitate numerical simulations and lead to testable predictions. This study will also provide detailed quantitative information on how these processes can be controlled by modifying concentration and properties of structural and motor proteins. This has p ....How motor proteins contract the cell cortex and form a cell division ring. This project aims to develop a detailed physical model for motor proteins and filaments and, based on it, derive a fluid-type mean-field mathematical model, which will facilitate numerical simulations and lead to testable predictions. This study will also provide detailed quantitative information on how these processes can be controlled by modifying concentration and properties of structural and motor proteins. This has potential applications in tumour therapy, developmental biology and in the bioengineering of nanomaterials.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