Viscous Effects in Free-Surface Flows. Australia has a proud record of achievement in the field of free-surface fluid mechanics. This project will build and extend these research achievements. It will provide new information about how fluid layers overturn and mix, which is an important process in oceanography. It will examine the sloshing behaviour of fluid in moving storage tanks, which is important in fuel transport and building design. The project will develop new mathematical methods fo ....Viscous Effects in Free-Surface Flows. Australia has a proud record of achievement in the field of free-surface fluid mechanics. This project will build and extend these research achievements. It will provide new information about how fluid layers overturn and mix, which is an important process in oceanography. It will examine the sloshing behaviour of fluid in moving storage tanks, which is important in fuel transport and building design. The project will develop new mathematical methods for solving these problems accurately, and will contribute to the next generation of research mathematicians in Australia. Read moreRead less
Structure and informatics of the genetic code. Recent advances in biotechnology have seen its emergence as a highly
quantitative, numerically-based discipline. To exploit the available
data to the full will require, alongside computing power, new
analytical techniques. This project aims to develop such techniques,
by handling the systematics of the genetic code with methods derived
from theoretical physics and chemistry. Expected outcomes include a
dynamical (quantum field theory) model ....Structure and informatics of the genetic code. Recent advances in biotechnology have seen its emergence as a highly
quantitative, numerically-based discipline. To exploit the available
data to the full will require, alongside computing power, new
analytical techniques. This project aims to develop such techniques,
by handling the systematics of the genetic code with methods derived
from theoretical physics and chemistry. Expected outcomes include a
dynamical (quantum field theory) model of phylogenetic branching,
analyses of nucleic acid structure and content (spin chain models of
RNA binding and of DNA open reading frames), and insights into the
origin of the code itself (via numerical codon similarity measures).
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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.
Markov invariants and phylogenetic tree reconstruction. The project will assist Australia to progress as an innovator in the production phylogenetic tree reconstruction techniques.
Identifying species is a difficult task with environmental, social and economic benefits to Australia. DNA evidence and phylogenetic methods clearly achieve this task. Conservation of rare species depends upon identification and hence robust phylogenetic analysis. Phylogenetically identifying fish species has econom ....Markov invariants and phylogenetic tree reconstruction. The project will assist Australia to progress as an innovator in the production phylogenetic tree reconstruction techniques.
Identifying species is a difficult task with environmental, social and economic benefits to Australia. DNA evidence and phylogenetic methods clearly achieve this task. Conservation of rare species depends upon identification and hence robust phylogenetic analysis. Phylogenetically identifying fish species has economic importance as different fish species are all managed separately, having different catch limits, catch areas and market values. Using effective phylogenetic methods, epidemiologists can track the spread of a disease through a population. Read moreRead less
Creating new stochastic models to understand the evolution of gene families. This project aims to extend stochastic modelling techniques in order to develop mathematically rigorous and biologically relevant models for the evolution of gene families. The project expects to model evolutionary processes such as gene retention, duplication and loss, and the generation of new gene functions. The duplication and subsequent re-purposing of genes is thought to be a key mechanism for generating evolution ....Creating new stochastic models to understand the evolution of gene families. This project aims to extend stochastic modelling techniques in order to develop mathematically rigorous and biologically relevant models for the evolution of gene families. The project expects to model evolutionary processes such as gene retention, duplication and loss, and the generation of new gene functions. The duplication and subsequent re-purposing of genes is thought to be a key mechanism for generating evolutionary novelty. By applying these models to genome data, the project expects to be able to quantify the importance of these different evolutionary mechanisms. The project will strengthen collaborative links between researchers in stochastic modelling and molecular evolutionary biology.Read moreRead less
Algebraically informed models of biological sequence evolution. To make sense of the patterns they see in the natural world, biologists across fields as diverse as genetics, epidemiology and biogeography need an accurate picture of evolutionary history. DNA sequences provide an exciting means to establish this picture of the past, but to decode it successfully requires mathematical models of how DNA evolves. Mathematical inconsistencies have been identified with current approaches. In particular ....Algebraically informed models of biological sequence evolution. To make sense of the patterns they see in the natural world, biologists across fields as diverse as genetics, epidemiology and biogeography need an accurate picture of evolutionary history. DNA sequences provide an exciting means to establish this picture of the past, but to decode it successfully requires mathematical models of how DNA evolves. Mathematical inconsistencies have been identified with current approaches. In particular, understanding the effect of natural selection in different parts of the tree of life requires models that behave robustly in the face of shifting evolutionary processes. This project aims to use insights from algebraic methods to construct mathematically consistent models of wide biological utility.Read moreRead less
An efficient approach to the computation of bacterial evolutionary distance. This project aims to apply advanced mathematical tools to improve our understanding of bacterial evolution. Bacteria account for as much total Earth biomass as all plant species put together, and have an unparalleled ability to evolve quickly and adapt to changing environments. Unfortunately, the existing mathematical models used to model bacterial evolution are generally computationally intractable. This project will r ....An efficient approach to the computation of bacterial evolutionary distance. This project aims to apply advanced mathematical tools to improve our understanding of bacterial evolution. Bacteria account for as much total Earth biomass as all plant species put together, and have an unparalleled ability to evolve quickly and adapt to changing environments. Unfortunately, the existing mathematical models used to model bacterial evolution are generally computationally intractable. This project will rectify this situation by using representation theory to transform combinatorial group theory into linear algebra, allowing for the application of advanced methods of numeric approximation. This will provide a better understanding of how bacteria evolve and improve our ability to manage their impact.Read moreRead less
Outflows, Jets and Plumes. This project studies how fluid flows out from a small concentrated object into a second surrounding fluid. New solution methods will be provided, and new results about how these fluid flows evolve will be obtained. These are important problems with significance in modelling underwater explosions. They are also important in astrophysics, and will help explain the shapes of outflows from some stars or galaxies. The outcomes of the project will be a deeper mathematical un ....Outflows, Jets and Plumes. This project studies how fluid flows out from a small concentrated object into a second surrounding fluid. New solution methods will be provided, and new results about how these fluid flows evolve will be obtained. These are important problems with significance in modelling underwater explosions. They are also important in astrophysics, and will help explain the shapes of outflows from some stars or galaxies. The outcomes of the project will be a deeper mathematical understanding of which outflow shapes are stable, and under what circumstances they might become unstable. This will provide valuable information about galaxy shapes, and a new suite of computational methods for solving such problems.Read moreRead less
Mathematical and computational analysis of ship wakes. This project aims to develop mathematical and computational tools to compute the energy in a given ship wake and to determine a range of properties of a ship by taking simple measurements of the water height as the ship travels past. The expected outcomes of this project include a suite of algorithms that back-calculate the hull shape and operating conditions of a moving ship given only the surface height data measured at a single point. The ....Mathematical and computational analysis of ship wakes. This project aims to develop mathematical and computational tools to compute the energy in a given ship wake and to determine a range of properties of a ship by taking simple measurements of the water height as the ship travels past. The expected outcomes of this project include a suite of algorithms that back-calculate the hull shape and operating conditions of a moving ship given only the surface height data measured at a single point. These results should have direct implications for measuring damage to coastal zones by ship wakes and for surveillance of shipping channels.Read moreRead less
Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent ....Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent research breakthroughs, including novel datasets derived from satellite and field observations. The outcomes are expected to quantify sea ice retreat due to ocean waves for the first time, with potentially major implications for coupled wave–sea ice modelling in climate studies.Read moreRead less