Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journa ....Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journals and international conferences, and from direct collaboration with internationally leading scientists from USA, UK and Germany. The project will also increase the pool of trained mathematicians with expertise in areas important for applications.
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New Directions in Non-linear Mathematical Asymptotics. Major challenges such as predicting epidemics or modelling cancer rely on our understanding of simple mathematical models with extremely complicated solutions. The first and only model in the literature to reproduce the three-phase cycle of immune response in HIV/AIDS was based on cellular automata. Its results are extremely sensitive to infinitesimally small changes in parameters. Yet, no technique exists to study such variation in cellular ....New Directions in Non-linear Mathematical Asymptotics. Major challenges such as predicting epidemics or modelling cancer rely on our understanding of simple mathematical models with extremely complicated solutions. The first and only model in the literature to reproduce the three-phase cycle of immune response in HIV/AIDS was based on cellular automata. Its results are extremely sensitive to infinitesimally small changes in parameters. Yet, no technique exists to study such variation in cellular automata. This research will provide new methods for prediction and analysis of such models. Read moreRead less
A new asymptotic toolbox for nonlinear discrete systems and particle chains. This project aims to pioneer a mathematical toolbox of new asymptotic techniques for discrete systems driven by vanishingly small influences. The purpose of these techniques is to permit the asymptotic study of discrete problems in which significant effects originate due to subtle causes that are invisible to existing asymptotic methods. Discrete systems play a significant role in modern applied mathematics, and it is v ....A new asymptotic toolbox for nonlinear discrete systems and particle chains. This project aims to pioneer a mathematical toolbox of new asymptotic techniques for discrete systems driven by vanishingly small influences. The purpose of these techniques is to permit the asymptotic study of discrete problems in which significant effects originate due to subtle causes that are invisible to existing asymptotic methods. Discrete systems play a significant role in modern applied mathematics, and it is vital that mathematical tools be designed in order to explore their behaviour. The aim of this project is to open new pathways for resolving open scientific problems, providing benefits such as understanding the energy dissipation of particle chains and granular lattices contained in small-scale technological components.Read moreRead less
Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice. Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advan ....Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice. Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advanced computation of special functions driven by pursuit of challenging research problems. The focus is on tractable components that arose in prior research on effective high-precision algorithms for multiple integrals, such as arise throughout mathematical physics, number theory and elsewhere.Read moreRead less
Fundamental Studies in System Identification. To operate a dynamic system such as a chemical process plant or an economy one needs two things; the equations describing the system; a way of regulating the system to provide desired outcomes. System identification provides the first; control engineering design provides the second. This proposal addresses three important problems in system identification and control. Firstly since the equations can never be known precisely we aim to determine what i ....Fundamental Studies in System Identification. To operate a dynamic system such as a chemical process plant or an economy one needs two things; the equations describing the system; a way of regulating the system to provide desired outcomes. System identification provides the first; control engineering design provides the second. This proposal addresses three important problems in system identification and control. Firstly since the equations can never be known precisely we aim to determine what is the best one can do? Secondly to provide then tight error bounds for the control design;
thirdly to develop new methods for some hitherto unresolved problems in system identification.Read moreRead less
Model reduction of open markov quantum systems: theory and algorithms. This project will advance international efforts in quantum technology research by developing methods and tools to find simpler lower complexity models for certain photonic (light based) devices for information processing. Such simplification methods can critically reduce the complexity of designing complex technologies based on these devices.
Stabilisation of nonlinear quantum feedback control systems. One of the most exciting technological developments of this century promises to be the development of quantum technology. Quantum feedback systems will play a key part of this technology and this project will develop the underlying fundamental theory which will be crucial to the systematic design of quantum feedback control systems.
Consensus-based theory of robust and resilient distributed estimation. The invention of cheap sensors, programmable microcontrollers and fast wireless communication protocols has created new opportunities for distributed monitoring and control of resources in many technological areas vital for Australia. The project will develop the fundamental theory which will underpin cutting edge technologies in those areas.
Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their ....Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their operation. Standard control system methods do not take into account the special features of quantum systems and there is a need for new control theories that deal with stabilisation and synchronisation as quantum technologies become more advanced. Read moreRead less
A New Approach to Sampled-Data Control Design for Nonlinear Systems. This project aims to exploit new sampling and sampled-data modelling insights to bridge the continuous/sampled-data gap in the control of nonlinear systems. The goal is to investigate the impact of these insights on the control design problem and provide a new class of digital control laws for continuous time non-linear systems.