Filter by faculty:

Found 5 matching student topics

Displaying 1–5 of 5 results

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

Equation learning for partial differential equation models of stochastic random walk models

Random walk models are often used to represent the motion of biological cells. These models are convenient because they allow us to capture randomness and variability. However, these approaches can be computationally demanding for large populations.One way to overcome the computational limitation of using random walk models is to take a continuum limit description, which can efficiently provide insight into the underlying transport phenomena.While many continuum limit descriptions for homogeneous random walk models are available, continuum limit descriptions for heterogeneous …

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 Data Science

Fairy circle landscapes formed in the Great Barrier Reef…but how?

Destabilising feedbacks between ecology and the local physical environment yield spatial pattern formation in various contexts throughout nature. For example, these feedbacks can lead to ring-shaped pattern formation in the spatial distribution of submerged aquatic plants. Recently, unusual crater-like structures have been identified in a large area of the Great Barrier Reef where the algae genus Halimeda constructs mounds called 'bioherms'.This project seeks to use partial differential equation models of the spatial growth of Halimeda to identify whether its long-term …

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 Data Science
Centre for the Environment

New mathematical and computational techniques for modelling with partial differential equations

Mathematical models involving partial differential equations (PDEs) are useful for simulating many important physical processes including heat and mass transfer, groundwater flow, pollutant transport and drug delivery. This project will focus on developing new mathematical and computational techniques to solve, approximate and/or analyse PDE models.Potential project topics include:developing new numerical and/or analytical methods for solving PDE modelsbuilding new reduced-order PDE models that are easier to solve, interpret or analyseextracting insight into time scales of PDE models, such as the amount …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences

The role of complex singularities in geometric flows

A popular topic in differential geometry involves studying the singularity structure of geometric flows. The most well-known example is mean curvature flow. In this example, surfaces evolve according to a flow rule that relates the speed of the surface to its curvature. Certain surfaces will evolve until singularities occur in finite time, and these singularities can be studied using similarity solutions and asymptotic analysis.In this project, a different perspective is applied to these problems, namely the use of complex variable …

Study level
Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences

Page 1 of 1