Large Time Behavior of Solutions to Stochastic Partial Differential Equations. We will study equilibria of complex systems described by stochastic partial differential equations. The rates of convergence to equilibrium will be obtained for the equations driven by Gaussian and general Levy noises under physically relevant assumptions. The benefits of this project to the nation include enhancing its scientific standing in the international community, the training of Australian researchers in foref ....Large Time Behavior of Solutions to Stochastic Partial Differential Equations. We will study equilibria of complex systems described by stochastic partial differential equations. The rates of convergence to equilibrium will be obtained for the equations driven by Gaussian and general Levy noises under physically relevant assumptions. The benefits of this project to the nation include enhancing its scientific standing in the international community, the training of Australian researchers in forefront methods of mathematical analysis of complex systems and development of close ties with the world leaders in this area of research. The project will advance our understanding of complex systems arising in Phyiscs, Engineering, Social and Life Sciences, hence fits into the Priority Goal: Breakthrough Science. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101352
Funder
Australian Research Council
Funding Amount
$330,000.00
Summary
Inverting the Signature Transform for Rough Paths and Random Processes. The signature transform provides an effective summary of the essential information encoded in multidimensional paths that are highly oscillatory and involve complicated randomness. The main goal of this project is to develop new algorithmic methods to reconstruct rough paths and random processes from the signature transform at various quantitative levels. This project expects to make theoretical breakthrough on the significa ....Inverting the Signature Transform for Rough Paths and Random Processes. The signature transform provides an effective summary of the essential information encoded in multidimensional paths that are highly oscillatory and involve complicated randomness. The main goal of this project is to develop new algorithmic methods to reconstruct rough paths and random processes from the signature transform at various quantitative levels. This project expects to make theoretical breakthrough on the significant open problem of signature inversion, thereby advancing knowledge in the areas of rough path theory and stochastic analysis. The newly developed methods will be utilised in combination with the emerging signature-based approach to study important problems in financial data analysis and visual speech recognition.
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Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial the ....Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial theory to name a few. These structures will be further developed, leading to the analytic form of distribution functions quantifying classes of complex systems. Analogous statistical quantification is the essence of recently proposed methods to analyze artificial complex systems such as the stock market.Read moreRead less
Models for Australian Electricity Derivatives. Electricity derivatives, such as electricity futures and options are used to manage the risk associated with volatility in prices of electricity. This project aims to develop models for pricing electricity derivatives specifically suited for Australia. Because of the non-storable nature of electricity the standard option pricing principle of "no-arbitrage" does not apply to electricity options, such as caps and floors, but applies to options on elec ....Models for Australian Electricity Derivatives. Electricity derivatives, such as electricity futures and options are used to manage the risk associated with volatility in prices of electricity. This project aims to develop models for pricing electricity derivatives specifically suited for Australia. Because of the non-storable nature of electricity the standard option pricing principle of "no-arbitrage" does not apply to electricity options, such as caps and floors, but applies to options on electricity futures. Therefore a specific model is needed that takes into account the pricing principle of "no-arbitrage" and combines it with other factors that drive electricity prices. The novel element in this proposal is incorporation of the weather forecasts into the models for electricity options. As a result of this study appropriate models for electricity derivatives for various geographical regions in Australia will be developed.Read moreRead less
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.
Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics. This research is relevant to solute transport and plume evolution in heterogeneous media. Detailed modelling of these processes is computer-intensive, while the diffusion models of this project offer a more economical alternative. Our study will also benefit the research on the salinity problem. Excessive demand for irrigation water to support agricultural production has stretched freshwater a ....Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics. This research is relevant to solute transport and plume evolution in heterogeneous media. Detailed modelling of these processes is computer-intensive, while the diffusion models of this project offer a more economical alternative. Our study will also benefit the research on the salinity problem. Excessive demand for irrigation water to support agricultural production has stretched freshwater aquifers beyond their long-term yield. Large areas of land have been lost to saltwater intrusion. This proposal will provide suitable tools to predict the level and movement of saltwater in the aquifers. Application to the development of management strategies would bring direct benefit to coastal areas where salinity is a sustainability issue.Read moreRead less
Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized ran ....Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized random fields allow us to formulate a comprehensive program to tackle some key problems including modeling, processing and statistical estimation of fractional diffusion. Advances made in this program will in turn benefit the developments in related scientific fields.Read moreRead less
Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms tha ....Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms that will make possible practical analysis of operator-analytic models.Read moreRead less
Mechanism design for next generation random access wireless protocols. Australia is well placed to take the lead in replacing carbon-intensive travel by teleconferencing, because of its isolation and geographic dispersion. Because these large distances introduce inevitable delays, it is important that the network itself add as little delay as possible for such real-time services. Our novel and practical resource allocation scheme will enable Australians (including Australian industries and rural ....Mechanism design for next generation random access wireless protocols. Australia is well placed to take the lead in replacing carbon-intensive travel by teleconferencing, because of its isolation and geographic dispersion. Because these large distances introduce inevitable delays, it is important that the network itself add as little delay as possible for such real-time services. Our novel and practical resource allocation scheme will enable Australians (including Australian industries and rural communities) to receive better service at lower cost. This project will put Australia on the international stage as a leading contributor to wireless Internet technology. We will provide training for PhD students and postdoctoral fellows in this important area.Read moreRead less
Multi-Group Stochastic Modelling of Population Balance for Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, nuclear, energy, food and pharmaceutical, which are fundamental to the Australian economy. Commercially available computer codes for simulating such systems are currently widely used in many Australian industrial sectors. This research project will address the prevalent deficiency in many of these computer codes and ....Multi-Group Stochastic Modelling of Population Balance for Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, nuclear, energy, food and pharmaceutical, which are fundamental to the Australian economy. Commercially available computer codes for simulating such systems are currently widely used in many Australian industrial sectors. This research project will address the prevalent deficiency in many of these computer codes and develop new models capable of predicting a wide range of industrial bubbly flow problems. The resultant improved computer codes will provide industries with significant benefits and, in particular, reduce times and costs in their design and production. Read moreRead less