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New mathematical and computational techniques for partial differential equations in heterogeneous media

Mathematical models involving both partial differential equations (PDEs) and heterogeneous media are useful for simulating many important physical processes. This includes:groundwater flowpollutant transportheat transferdrug deliverytumour growth.This project focuses on developing new mathematical and computational techniques to solve, simulate and/or analyse PDEs in heterogeneous media.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
School
School of Mathematical Sciences
Research centre(s)

Optimal eradications

Eradication is the process of driving a population down to zero - to extinction. We eradicate:invasive species from islandsdiseases from human populationscancer cells from patients.Finding every last individual in a population is expensive and difficult. The rule of thumb is that you spend 95% of your resources removing the last 5% of the population. Many of the organisms we're trying to eradicate are also difficult to observe.In this project, we'll use experimental microcosms (i.e., populations of unicellular animals in test …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
School
School of Mathematical Sciences
Research centre(s)

How many species were saved by national parks?

National parks are the cornerstone of modern conservation efforts. They now cover more than 10% of the Earth’s land surface and are found on every continent and sea.We can prove that these national parks stop human destruction of habitat. We can prove that they benefit the lives and livelihoods of people who visit and surround them. However, we can't yet prove that they have stopped the extinction of a single species. This isn't because we don’t believe that they've helped. …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
School
School of Mathematical Sciences
Research centre(s)

Mathematical theory of human cognitive limits

The human brain has a proven ability to solve difficult problems. However, recent research in economics and psychology has revealed limits to human cognition. This includes situations where the assumption of an optimal Homo economicus has proven to be incorrect.Psychologists have called these issues 'cognitive biases' – situations where the human brain makes consistent and particular mistakes. They have spent a lot of time listing them, and testing them to make sure they are real. There are now dozens of …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
School
School of Mathematical Sciences
Research centre(s)

Optimising long-term management strategies for ecosystem conservation

Many ecosystems around the world can't withstand the stress of climate change with their decline being rapid and ongoing. New technologies must be developed to conserve these threatened ecosystems. This need poses a new mathematical challenge, as no methods exist to select and develop new conservation technologies that will secure ecosystems into the future.Technology development usually has two phases:choosing what technologies to developmaking a distinct choice years later about how the technologies will be deployed.Better and more cost-efficient choices now …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

Considering economics when prioritising species conservation

There are limited funds available for saving threatened species globally. Investing that money wisely can help ecologists and the government achieve more bang for their buck, and help more species and ecosystems.We can use many approaches  to help guide those investment decisions, including mathematical optimisation and operations research. However better considerations of economic factors are needed in order to reflect the complexity of real ecosystems and governments.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

Optimal monitoring of Antarctic ecosystems

The biodiversity of Antarctica is threatened by a changing climate, increase in tourist numbers and invasive species. Governments around the world want to conserve this continent's unique species and ecosystems, but careful planning is needed before undertaking expensive and difficult management actions.Data is only valuable when planning environmental management if it leads to improved outcomes. As new monitoring technologies and approaches are developed, it's critical that they're used to focus on the most important information gaps. Data should be rapidly …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

Developing optimal management approaches to sustain the Great Barrier Reef

The Great Barrier Reef is under significant threat from climate change.There are many options for management approaches to help sustain the reef, and many more are being developed. However, optimally planning these management actions is a difficult mathematical problem as they need to deploy over a large scale. This results in long timeframes for developing and executing these actions.This project will involve adapting the Modern Portfolio Theory to develop optimal management approaches to sustain the Great Barrier Reef.Modern Portfolio Theory …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

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