Discovery Early Career Researcher Award - Grant ID: DE240100674
Funder
Australian Research Council
Funding Amount
$370,237.00
Summary
New Frontiers in Large-Scale Polynomial Optimisation. Polynomial optimisation is ubiquitous in many areas of engineering and applied mathematics. The mathematical methods and algorithms used for polynomial problems of large size are not sufficiently developed, limiting their applicability for real-world problems. This project aims to develop a mathematical foundation and computational methods for large-scale polynomial optimisation. By using an innovative combination of a novel theory of algebra ....New Frontiers in Large-Scale Polynomial Optimisation. Polynomial optimisation is ubiquitous in many areas of engineering and applied mathematics. The mathematical methods and algorithms used for polynomial problems of large size are not sufficiently developed, limiting their applicability for real-world problems. This project aims to develop a mathematical foundation and computational methods for large-scale polynomial optimisation. By using an innovative combination of a novel theory of algebraic geometry and convex optimisation, this project expects to generate new knowledge and tools for solving these problems. Anticipated outcomes include a new generation of large-scale optimisation technologies, providing significant benefit to Australia's industries and international research standing.
Read moreRead less
How do vortices live in spatio-temporally complex flows? The project aims to understand the fundamental mechanism of vortices occurring in flows involving spatio-temporal complexity, by using the combination of dynamical systems theory and asymptotic analysis. This innovative combined mathematical analysis will be coupled with sophisticated computations to be enabled by the international interdisciplinary collaboration between the Mathematics and Engineering at Australia and Japan. The expected ....How do vortices live in spatio-temporally complex flows? The project aims to understand the fundamental mechanism of vortices occurring in flows involving spatio-temporal complexity, by using the combination of dynamical systems theory and asymptotic analysis. This innovative combined mathematical analysis will be coupled with sophisticated computations to be enabled by the international interdisciplinary collaboration between the Mathematics and Engineering at Australia and Japan. The expected outcomes are breakthroughs in the fundamental understanding of turbulence. This should lead to significant insight into better turbulent modellings used in, for example, wide range of engineering, physiological and geophysical flows.Read moreRead less
Next-generation methods for transport in poroelastic media with interfaces. Deformable porous structures are ubiquitous in the design of materials such as filters, sponges, and prosthetics. They often show complex mechano-chemical processes that occur across several spatio-temporal scales. To mathematically describe them requires coupled sets of nonlinear, multiphysical, and multiscale equations. This makes the design of accurate, efficient numerical methods challenging. The Fellowship aims to a ....Next-generation methods for transport in poroelastic media with interfaces. Deformable porous structures are ubiquitous in the design of materials such as filters, sponges, and prosthetics. They often show complex mechano-chemical processes that occur across several spatio-temporal scales. To mathematically describe them requires coupled sets of nonlinear, multiphysical, and multiscale equations. This makes the design of accurate, efficient numerical methods challenging. The Fellowship aims to address the mathematical characteristics encountered in poromechanics equations and their discretisation methods, and to devise novel mathematical and computational techniques for extending the analysis to cases where large deformations and the presence of interfaces and coupling with other neighbouring elements are relevant.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
Mathematics to underpin and drive novel inertial microfluidic technologies. Particles suspended in flow through microfluidic ducts migrate under inertial and drag forcing to different regions in the cross-section depending on particle size, duct geometry and control parameters, enabling isolation of, for example, cancer cells/microplastics from a blood/water sample. Device design needs mathematical models yielding understanding of the particle dynamics, and tools for determining geometry and con ....Mathematics to underpin and drive novel inertial microfluidic technologies. Particles suspended in flow through microfluidic ducts migrate under inertial and drag forcing to different regions in the cross-section depending on particle size, duct geometry and control parameters, enabling isolation of, for example, cancer cells/microplastics from a blood/water sample. Device design needs mathematical models yielding understanding of the particle dynamics, and tools for determining geometry and control parameters. Particle boundary conditions strongly influence the inertial lift and drag forces that drive particle motion. This project will develop these mathematical tools for boundary conditions applicable to both passive and active particles, so driving development of novel devices for existing and new applications.Read moreRead less
Comparative analysis of sensor noise for target detection in dragonfly eyes. Dragonflies hunt tiny prey in the low-light conditions of late dusk, a signal-to-noise problem that challenges any engineered system. Using a comparative approach across dragonfly species, we aim to use novel optical and physiological measures to determine how sensors with noise underlie target-detection, in varying scene brightness. The project outcomes will be a comparative characterisation of signal-to-noise measures ....Comparative analysis of sensor noise for target detection in dragonfly eyes. Dragonflies hunt tiny prey in the low-light conditions of late dusk, a signal-to-noise problem that challenges any engineered system. Using a comparative approach across dragonfly species, we aim to use novel optical and physiological measures to determine how sensors with noise underlie target-detection, in varying scene brightness. The project outcomes will be a comparative characterisation of signal-to-noise measures of dragonfly eye optics (including eye size) and early sensory neurons. We will match detection thresholds with downstream target-detecting neurons and dragonfly behaviour. This will provide insight into signal detection, which is a ubiquitous problem across information processing, computer vision and autonomous systems.Read moreRead less
Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods f ....Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods for solving a wide range of nonlinear problems with singularities and non-local properties. The expected outcomes of the project will significantly advance our methods for the modelling and control of many industrial systems and processes.
Read moreRead less
Robust Data-Driven Control for Safety-Critical Systems. This project aims to develop new approaches to controlling robotic and cyber-physical systems in safety-critical applications. This project expects to generate new knowledge in how to harness the power of machine learning for robot control, while guaranteeing safety and stability at all times. The outcomes of this project will be new algorithms and a deeper understanding of the interplay of data, learning, and models, as well as experimenta ....Robust Data-Driven Control for Safety-Critical Systems. This project aims to develop new approaches to controlling robotic and cyber-physical systems in safety-critical applications. This project expects to generate new knowledge in how to harness the power of machine learning for robot control, while guaranteeing safety and stability at all times. The outcomes of this project will be new algorithms and a deeper understanding of the interplay of data, learning, and models, as well as experimental validation on a surgical robot and a bipedal walking robot. This project will provide significant benefits by dramatically increasing the range of applications in which the power of machine learning can be safely applied to advance the capabilities and uptake of robotics.Read moreRead less
Control and learning for enhancing capabilities of quantum sensors. This project aims to develop new theories and algorithms to enhance capabilities in engineering quantum sensors from the perspective of systems and control. The project is significant because it is anticipated to advance key knowledge and provide systematic methods to enable achievement of high-precision sensing for wide applications, e.g., early disease detection, medical research, discovery of ore deposits and groundwater moni ....Control and learning for enhancing capabilities of quantum sensors. This project aims to develop new theories and algorithms to enhance capabilities in engineering quantum sensors from the perspective of systems and control. The project is significant because it is anticipated to advance key knowledge and provide systematic methods to enable achievement of high-precision sensing for wide applications, e.g., early disease detection, medical research, discovery of ore deposits and groundwater monitoring. The intended outcomes are fundamental theories, effective control and learning algorithms for achieving highly-sensitive sensors. These outcomes should make important contributions to and deliver new knowledge and skills for Australia's sensing industries, which could benefit Australia's economic growth.Read moreRead less
Physico-chemical effects on long-time fluid transport for CO2 geostorage. This project aims to develop an efficient multi-scale laboratory-based modelling framework for the analysis of nonequilibrium transport and reaction processes occurring in CO2 storage scenarios. In a significant technological advance two non-destructive analysis techniques, Xray computed tomography and nuclear magnetic resonance, are combined with pore-scale simulations to address uncertainties in dynamic wettability alter ....Physico-chemical effects on long-time fluid transport for CO2 geostorage. This project aims to develop an efficient multi-scale laboratory-based modelling framework for the analysis of nonequilibrium transport and reaction processes occurring in CO2 storage scenarios. In a significant technological advance two non-destructive analysis techniques, Xray computed tomography and nuclear magnetic resonance, are combined with pore-scale simulations to address uncertainties in dynamic wettability alteration occurring during gravity driven convection. Expected outcomes are the in-situ characterisation of solid-surface interactions and predictions of multi-phase fluid flow. The project benefits the Australian resources sector by improving injectivity, storage efficiency and security of supercritical CO2 storage projects.Read moreRead less