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
The mathematics of novel magnetic memory materials. Magnetic memories are the world’s principal device for storing information. The next generation will have greatly increased access speed and data-storage capacity. This project will develop the mathematical theory of these new magnetic memory materials, a crucial first step in understanding and being able to fine-tune their properties.
A unifying framework for generalised distributed-order fractional models. This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous media. The project expects to generate a mathematical foundation for fractional modelling and clarity on the role of, and relationship between, the many variants of fracti ....A unifying framework for generalised distributed-order fractional models. This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous media. The project expects to generate a mathematical foundation for fractional modelling and clarity on the role of, and relationship between, the many variants of fractional operators used in modern practice and how to impose boundary conditions on finite domains. Expected outcomes of the project include an evaluation of dimensionality and/or complexity reduction of the governing equations in fractional transport models with a focus on groundwater applications.Read moreRead less
Mathematical and Numerical Models of Piezoelectric Wave Energy Converters. The project will investigate piezoelectric wave energy converters. We will derive the equations of motion in a form suitable for use in marine engineering paradigms using variational methods and then solve these analytically and with smoothed particle hydrodynamics. Using these innovative techniques, this project will generate new knowledge capable of elucidating the multifaceted physical phenomena that occur when comple .... Mathematical and Numerical Models of Piezoelectric Wave Energy Converters. The project will investigate piezoelectric wave energy converters. We will derive the equations of motion in a form suitable for use in marine engineering paradigms using variational methods and then solve these analytically and with smoothed particle hydrodynamics. Using these innovative techniques, this project will generate new knowledge capable of elucidating the multifaceted physical phenomena that occur when complex fluid motion and deformable structures interact. The project outcomes include the development of mathematical and computation methods to handle intricate behaviours of piezoelectric elastic-fluids systems. These groundbreaking methods will allow these wave energy systems to be analysed and their effectiveness assessed.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140101398
Funder
Australian Research Council
Funding Amount
$355,744.00
Summary
Quantifying the risk of groundwater contamination from hydraulic fracturing in coal seam gas operations in Australia. Concern for impacts to groundwater resources due to coal seam gas operations has led to heated debate in the community. This project will assess the risk to groundwater contamination from fracking in coal seam gas operations. It is critical that naturally occurring compounds in the coal seam and injected compounds are not mobilised to aquifers topped by water bores. This project ....Quantifying the risk of groundwater contamination from hydraulic fracturing in coal seam gas operations in Australia. Concern for impacts to groundwater resources due to coal seam gas operations has led to heated debate in the community. This project will assess the risk to groundwater contamination from fracking in coal seam gas operations. It is critical that naturally occurring compounds in the coal seam and injected compounds are not mobilised to aquifers topped by water bores. This project will build accurate, site-specific, dynamic numerical models of the hydraulic-fracturing process in coal seam gas operations. This will enable prediction of the maximum vertical extent of stimulated fractures in specific coal seams and will help establish criteria for when and where fracking in coal seam gas wells is safe in relation to groundwater contamination.Read moreRead less
Computational studies of melting and the solvation properties of ionic liquids. Ionic liquids are used in industry as green solvents and electrolytes, although there is not yet sufficient knowledge on the science of ionic liquids to enable optimal solvents to be readily designed. This project uses state of the art techniques in computational chemistry to solve practical problems related to the characteristics of ionic liquids.