QUT offers a diverse range of student topics for Honours, Masters and PhD study. Search to find a topic that interests you or propose your own research topic to a prospective QUT supervisor. You may also ask a prospective supervisor to help you identify or refine a research topic.
Found 40 matching student topics
Displaying 13–24 of 40 results
Conservation is a noisy business: modelling the effects of stochasticity on wildlife management decisions
To conserve species in disturbed natural environments, we need to use mathematical models to predict the consequences of different interventions. Unfortunately, these models are based on partial information of complex systems, and the systems themselves are subject to substantial observational and process noise.We often use ordinary differential equations to describe ecosystems, like the classic logistic growth model:dn/dt = r n (1 - n / k)However, these models are deterministic, and they assume we know the values of the key parameters …
- Study level
- Master of Philosophy, Honours, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
Centre for the Environment
Exact and approximate solutions of diffusion on evolving domains
Classical applications of mathematical analysis involve solving partial differential equation models on fixed domains, e.g. 0 < x < L. Applications in biology, however, involve studying diffusive transport on rapidly evolving domains, e.g. 0 < x < L(t), where L(t) represents the length of the evolving tissue. While many problems have been addressed for the case where L(t) increases, less attention has been paid to cases where we consider diffusion on an oscillating domain.In this project we will construct exact …
- Study level
- Master of Philosophy, Honours, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
Understanding international governance in Antarctica through cooperative game theory
Antarctica is governed by a coalition of 29 countries ('consultative parties') who must agree unanimously before a law can be passed. This project will apply theories from social network analysis and cooperative game theory to map relationships between the different parties, and to predict their behaviour on a series of important environmental issues.
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
-
Centre for the Environment
Using catastrophe theory to prepare for global warming in Antarctica
According to dynamical systems theory, crises occur because couplings within a system (geophysical, ecological and social) create instabilities. Nonlinear feedbacks means that relatively small changes in circumstances can cause a rapid change to the system state. For example, a small increase in tourism visitors could lead to the invasion of a new species. Or, a gradual change in the average global temperature could lead to the collapse of Antarctic ice-shelves.In the coming decade, the Antarctic and sub-Antarctic are likely to …
- Study level
- PhD, Master of Philosophy, Honours, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
-
Centre for the Environment
Mathematical tools for stochastic and continuum transport models
Mathematical models of particle transport are fundamental to many applied disciplines including physics, biology, ecology and medicine. Particle transport is typically modelled using either a stochastic model, where probability rules govern the motion of individual particles, or a continuum model, where partial differential equations govern the concentration of particles in space and time. This project aims to use analytical and numerical techniques from applied and computational mathematics to address one or both of the following questions:what is the average time …
- Study level
- Master of Philosophy, Honours, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
Making predictions using simulation-based stochastic mathematical models
Stochastic simulation-based models are very attractive to study population-biology, disease transmission, development and disease. These models naturally incorporate randomness in a way that is consistent with experimental measurements that describe natural phenomena.Standard statistical techniques are not directly compatible with data produced by simulation-based stochastic models since the model likelihood function is unavailable. Progress can be made, however, by introducing an auxiliary likelihood function can be formulated, and this auxiliary likelihood function can be used for identifiability analysis, parameter estimation and …
- Study level
- PhD, Master of Philosophy, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
Hydrodynamic instabilities
This project will focus on the mathematical modelling of fluid flow, with a focus on how the application of linearisation and solution of linear partial differential equations can be used to predict the stability or instability of base flows. In order to explore this topic we will focus on one or more examples of hydrodynamic instabilities, for example, the Kelvin-Helmholtz instability, which can be observed on scales ranging from the every-day, to cloud formations, to atmospheric structures on gas giants …
- Study level
- Vacation research experience scheme
- School
- School of Mathematical Sciences
Mathematical modelling of cell-to-cell communication via extracellular vesicles (EVs)
Extracellular vesicles (EVs) are membrane bound packages of information constantly being released by all living cells, including bacteria. There are many types and sizes of EVs. Each EV type contains its own distinctive cargo consisting of characteristic DNA, RNA, and proteins. We are just beginning to understand the many roles of EVs to maintain the health of the cell producing the EVs, and to communicate with other cell types that take up the EVs produced by neighbouring cells. Since EVs …
- Study level
- Honours, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
Curvature dependence of reaction-diffusion wave front speed with nonlinear diffusion.
Reaction-diffusion waves describe the progression in space of wildfires, species invasions, epidemic spread, and biological tissue growth. When diffusion is linear, these waves are known to advance at a rate that strongly depends on the curvature of the wave fronts. How nonlinear diffusion affects the curvature dependence of the progression rate of these wavefronts remains unknown.
- Study level
- PhD, Master of Philosophy, Honours, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Biomedical Technologies
Optimising bone shape with memory networks
Bone is a dynamic tissue that optimises its shape to the mechanical loads that it carries. Bone mass is accrued where loads are high, and reduced where loads are low. This adaptation of bone tissue to mechanical loads is well-known and observed in many instances. However, what serves as a reference mechanical state in this shape optimisation remains largely unknown.
- Study level
- PhD, Master of Philosophy, Honours, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Biomedical Technologies
Efficient parameter estimation for agent-based models of tumour growth
Cancer is an extremely heterogeneous disease, particularly at the cellular level. Cells within a single cancerous tumour undergo vastly different rates of proliferation based on their location and specific genetic mutations. Capturing this stochasticity in cell behaviour and its effect on tumour growth is challenging with a deterministic system, e.g. ordinary differential equations, however, is possible with an agent-based model (ABM). In an ABM, cells are modelled as individual agents that have a probability of proliferation and movement in each …
- Study level
- Master of Philosophy, Honours, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
Surrogate models for accurate prediction and inference in mathematical biology
High fidelity mathematical models of biological phenomena are often complex and can require long computational runtimes which can make computational inference for parameter estimation intractable. In this project we will overcome this challenge by working with computationally simple low fidelity models and build a simple statistical model of the discrepancy between the high and low fidelity models. This approach provides the best of both worlds: we obtain high accuracy predictions using a computationally cheap model surrogate.
- Study level
- PhD, Master of Philosophy, Vacation research experience scheme
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
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