Harmonic analysis of differential operators in Banach spaces. This proposal aims to develop harmonic analysis (the mathematical tools used in digital music and photography) in new contexts. It focuses on boundary value problems (the theory behind medical or geological imaging) and stochastic equations (which describe phenomena with random components such as the behaviour of financial markets).
Fundamental investigation of heat and mass transfer in nanofluids: a mechanistic approach. This project aims to develop a mathematical model in order to predict complex boiling in using nanofluids as new coolant for heat removal. Implementation and resultant computer codes thereafter will provide industries with significant benefits and reduce times and costs in their future design of ultra-high efficient heat removal systems.
Discovery Early Career Researcher Award - Grant ID: DE120100163
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Modelling and simulation of instabilities in unsaturated soils due to wetting. Ground instabilities due to wetting are a critical issue that will be investigated through this project via the development of risk assessment tools. A rational engineering approach and calculation framework will be developed in order to predict failures and facilitate the design of new safer structures.
Fitting non-Gaussian diffusion models to evolutionary data: towards a generalized framework for phylogenetic comparative analyses. This project aims to develop cutting-edge statistical methods for evolutionary biology in order to answer big questions using data derived from multiple species. Such methods are needed because of the variety of multi-species data that are becoming available, which cannot be dealt with correctly using current methods. The research is significant because it will provi ....Fitting non-Gaussian diffusion models to evolutionary data: towards a generalized framework for phylogenetic comparative analyses. This project aims to develop cutting-edge statistical methods for evolutionary biology in order to answer big questions using data derived from multiple species. Such methods are needed because of the variety of multi-species data that are becoming available, which cannot be dealt with correctly using current methods. The research is significant because it will provide a new way of fitting a wide class of statistical models to evolutionary data, in a very general setting. Further, this project will unite current methodology in a broader framework so that the proposed new methods are a generalisation of currently accepted theory. The outcomes will include a freely-available software package that implements the methods in a user-friendly form.Read moreRead less
Congestion control of networks: a unified stochastic framework. Systems such as the internet, wireless networks and the power grid require efficient allocation of shared resources. This research will develop ways to reduce delays in the internet and allow for growth in the power grid, without requiring additional infrastructure.
Advanced matrix-analytic methods with applications. Over the last twenty-five years, matrix-analytic methods have proved to be very successful in formulating and analysing certain classes of stochastic models. Motivated by applications, this project will investigate more advanced matrix-analytic methods than have hitherto been studied.
Random walks with long memory. This project aims to study novel random walk models with long memory, including systems of multiple random walkers that interact through their environment. This would provide a mathematical understanding of phenomena such as aggregation in colonies of bacteria, and ant colony optimisation algorithms. The project aims to produce highly cited publications, and to train future researchers.
Overseeing the internet: new paradigms of network measurement. Like the electricity network, the internet is a core infrastructure, and so must be reliable and efficient. A gap in bandwidth supply is like a blackout in terms of lost business and productivity. This project will provide the measurement breakthroughs to ensure that network behaviour can be accurately and comprehensively monitored.
Discovery Early Career Researcher Award - Grant ID: DE140100993
Funder
Australian Research Council
Funding Amount
$293,520.00
Summary
Mathematics of importance: The optimal importance sampling algorithm for estimating the probability of a black swan event. Rare event simulation and modelling is critical to our understanding of high-cost hard-to-predict events such as nuclear accidents, natural disasters, and financial crises. Quantitative analysis of such high-impact events demands the accurate estimation of the probability of occurrence of such rare events. In realistic models this probability is very difficult to estimate, ....Mathematics of importance: The optimal importance sampling algorithm for estimating the probability of a black swan event. Rare event simulation and modelling is critical to our understanding of high-cost hard-to-predict events such as nuclear accidents, natural disasters, and financial crises. Quantitative analysis of such high-impact events demands the accurate estimation of the probability of occurrence of such rare events. In realistic models this probability is very difficult to estimate, because exact simple analytical formulas are not available and the existing estimation methods fail spectacularly. There is an urgent need for new efficient methodology. This project develops a new Monte Carlo method that will be able to estimate reliably and accurately rare-event probabilities. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE160101147
Funder
Australian Research Council
Funding Amount
$294,336.00
Summary
Predicting extremes when events occur in bursts. This project seeks to advance knowledge in extreme value theory. Extreme value theory is essential to quantify risks in complex systems, such as the risk of network failures. Current statistical models for the occurrence of extremes assume that events happen regularly. This assumption, however, is at odds with human actions and many biological and physical events, which occur in bursts. There is a strong need to understand the effect of such ‘burs ....Predicting extremes when events occur in bursts. This project seeks to advance knowledge in extreme value theory. Extreme value theory is essential to quantify risks in complex systems, such as the risk of network failures. Current statistical models for the occurrence of extremes assume that events happen regularly. This assumption, however, is at odds with human actions and many biological and physical events, which occur in bursts. There is a strong need to understand the effect of such ‘bursty dynamics’ on the frequency and magnitude of extreme events. This project aims to develop extreme value theory for bursty events and thus lay the mathematical groundwork for the estimation and prediction of extremes in a variety of scientific contexts.Read moreRead less