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
Unifying discrete and continuous methods in quantum information theory. This project aims to address a critical gap in quantum information theory by unifying the way that both discrete and continuous quantum systems are represented in mathematical models. This project expects to generate new knowledge in quantum information science by using cutting-edge mathematical tools and insights from signal processing theory. Expected outcomes of this project include a new mathematical framework for use in ....Unifying discrete and continuous methods in quantum information theory. This project aims to address a critical gap in quantum information theory by unifying the way that both discrete and continuous quantum systems are represented in mathematical models. This project expects to generate new knowledge in quantum information science by using cutting-edge mathematical tools and insights from signal processing theory. Expected outcomes of this project include a new mathematical framework for use in quantum science and technology development. This should provide significant benefits, such as new ways to efficiently simulate certain quantum processes on ordinary computers and novel approaches to handling noise in quantum computers.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230100054
Funder
Australian Research Council
Funding Amount
$432,000.00
Summary
Spectral estimates in the presence of a magnetic field. Estimates on eigenvalues of integral operators are at the core of numerous results in the study of quantum phenomena and in associated mathematical fields. This project aims to establish detailed spectral properties of the integral operators arising in quantum models incorporating magnetic fields. An anticipated goal is the generation of new and significant theoretical results in analysis that will open novel approaches to the use of magnet ....Spectral estimates in the presence of a magnetic field. Estimates on eigenvalues of integral operators are at the core of numerous results in the study of quantum phenomena and in associated mathematical fields. This project aims to establish detailed spectral properties of the integral operators arising in quantum models incorporating magnetic fields. An anticipated goal is the generation of new and significant theoretical results in analysis that will open novel approaches to the use of magnetic differential operators. This is expected to benefit Australian science by invigorating collaboration between mathematics and theoretical physics, by providing research training relevant to emerging quantum science based technology and strengthening research collaborations with world leading scientists.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230100829
Funder
Australian Research Council
Funding Amount
$425,100.00
Summary
Geometric approaches to quantum many body problems. The project aims to utilise results from differential geometry and related areas to investigate the physics of interacting many-body quantum systems. This project expects to generate new knowledge in the area of mathematical physics with broad applications in quantum information, condensed matter physics and statistical mechanics. The key focus will lie on the development of variational methods for the efficient simulation of quantum evolution ....Geometric approaches to quantum many body problems. The project aims to utilise results from differential geometry and related areas to investigate the physics of interacting many-body quantum systems. This project expects to generate new knowledge in the area of mathematical physics with broad applications in quantum information, condensed matter physics and statistical mechanics. The key focus will lie on the development of variational methods for the efficient simulation of quantum evolution and the characterisation of suitable quantum state families by their correlation structures.Read moreRead less
Creating Hybrid Exponential Asymptotics for use with Computational Data. Asymptotic analysis is a vital tool for studying small influences with critical effects. This project aims to create an innovative fully-automated asymptotic framework for studying phenomena which are invisible to classical approximation methods, using new ideas from asymptotics and numerical complex analysis. The outcome will be the first framework that can be used on data from numerical simulations or real-life measuremen ....Creating Hybrid Exponential Asymptotics for use with Computational Data. Asymptotic analysis is a vital tool for studying small influences with critical effects. This project aims to create an innovative fully-automated asymptotic framework for studying phenomena which are invisible to classical approximation methods, using new ideas from asymptotics and numerical complex analysis. The outcome will be the first framework that can be used on data from numerical simulations or real-life measurements, and which can be applied automatically without hands-on expert input. It will be used to design submerged structures and efficient vessels with minimal energy loss from surface waves. Expected benefits include making powerful methods accessible to scientists, and new paths for energy-efficient industrial design.Read moreRead less
Transformative simulation techniques for complex polymer networks. The study of long chain polymers like DNA using computer simulations has uncovered exciting insights over many years. Generally these have been limited to simple topologies, interactions, and environments. This project aims to develop the next generation of simulation techniques to tackle a new frontier of polymer models, including those with complex topologies like stars, knots, and links, which have hitherto been inaccessible. ....Transformative simulation techniques for complex polymer networks. The study of long chain polymers like DNA using computer simulations has uncovered exciting insights over many years. Generally these have been limited to simple topologies, interactions, and environments. This project aims to develop the next generation of simulation techniques to tackle a new frontier of polymer models, including those with complex topologies like stars, knots, and links, which have hitherto been inaccessible. Expected outcomes include new simulation methods which harness modern computational clusters, leading to greater understanding of polymers with complex topologies and in complicated environments. Important elements of biological processes may be discovered, such as how polymer structure affects DNA transcription.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE240100097
Funder
Australian Research Council
Funding Amount
$389,670.00
Summary
Mathematical models for actin scavenging and biofilm removal. The project aims to develop mathematical models for actin scavenging and biofilm removal, processes that combine to alleviate tissue damage and inflammation. Actin scavenging eliminates the protein F-actin which is released during cell death, but this process is not fully-understood. Biofilms are colonies of micro-organisms, for example bacteria, that are highly resistant to antimicrobial treatment. This project expects to generate ne ....Mathematical models for actin scavenging and biofilm removal. The project aims to develop mathematical models for actin scavenging and biofilm removal, processes that combine to alleviate tissue damage and inflammation. Actin scavenging eliminates the protein F-actin which is released during cell death, but this process is not fully-understood. Biofilms are colonies of micro-organisms, for example bacteria, that are highly resistant to antimicrobial treatment. This project expects to generate new knowledge, using an innovative combination of mathematical modelling and cell biology experiments. Expected outcomes include new theory and software, yielding the benefits of increased understanding of cell biology, and potential to enhance development of smart materials that eliminate biofilms.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
Understanding the mechanisms that inhibit and promote biofilm expansion. Yeasts have been used for biotechnology throughout recorded history. They are important human pathogens, and major experimental models of eukaryotic cells. Although yeasts are some of the most studied organisms in biology, their modes of colony biofilm formation are not fully understood. Methods to investigate the environmental and genetic processes that drive colony biofilm formation will be developed in this proposed pro .... Understanding the mechanisms that inhibit and promote biofilm expansion. Yeasts have been used for biotechnology throughout recorded history. They are important human pathogens, and major experimental models of eukaryotic cells. Although yeasts are some of the most studied organisms in biology, their modes of colony biofilm formation are not fully understood. Methods to investigate the environmental and genetic processes that drive colony biofilm formation will be developed in this proposed project. They will provide a deeper understanding of the mechanisms that inhibit and promote biofilm formation, and colonial morphology in the different modes of growth of Saccharomyces cerevisiae, with implications for this and other biofilm-forming yeasts of biotechnological or medical importance.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE240100755
Funder
Australian Research Council
Funding Amount
$430,788.00
Summary
Fluid dynamics of underground hydrogen storage. The project seeks to understand the flow of hydrogen in underground porous layers. This will be achieved through mathematical models of the continuum mechanics governing the injection and withdrawal of hydrogen. The framework will account for a variety of physical and biological mechanisms. Underground storage of zero-carbon hydrogen provides an ideal route to overcome the intermittency of renewable energy. The project outcomes include a mathematic ....Fluid dynamics of underground hydrogen storage. The project seeks to understand the flow of hydrogen in underground porous layers. This will be achieved through mathematical models of the continuum mechanics governing the injection and withdrawal of hydrogen. The framework will account for a variety of physical and biological mechanisms. Underground storage of zero-carbon hydrogen provides an ideal route to overcome the intermittency of renewable energy. The project outcomes include a mathematical description of the response of two-phase flow instabilities to injection and withdrawal, and dynamical insights into the role of microbial growth on flow in porous media. Expected benefits are increased efficiency of hydrogen recovery and the reduced cost of site selection.
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