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How do collisions control tissue growth?

Biological tissue growth occurs mostly at or near the tissue's surface, where spatial interactions between the tissue and its surroundings can have strong influences onto the local rate of growth.This project will investigate how collisions between molecules or cells with an evolving tissue are dependent on the tissue shape and how these collisions may control tissue growth rate and tissue composition.

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

Novel techniques for modelling with partial differential equations in heterogeneous media

Mathematical models involving heterogenous media comprising two or more constituent materials with different physical properties are widespread across scientific and engineering disciplines.For example, modelling the flow of pollutants or water below the earth’s surface involves dealing with a highly heterogeneous geological structure.Solving such mathematical models is particularly challenging when the heterogeneity is explicitly accounted for in the model.As a result this project aims to answer natural questions such as:Can we develop accurate and efficient numerical or semi-analytical methods to solve …

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

Mathematical models for MRI to probe tissue microstructure

Magnetic resonance imaging (MRI) can reveal exquisite details about the complex structure and function of human and animal brain tissue. However, magnetic resonance imaging signal behaviour at high or ultra-high field strengths has shown increased deviation from the classically expected mono-exponential relaxation. Characterising the underlying mechanism of anomalous relaxation and diffusion can contribute to a better understanding of the interaction of proton spins with their surroundings.In recent years, mathematical models based on fractional calculus have been developed and have shown …

Study level
PhD, Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Improving quality of diffusion MRI: detection of motion artefacts

Diffusion Magnetic Resonance Imaging (MRI) can provide valuable insight into microstructural properties of the brain white matter in health and disease. However, obtaining high-quality diffusion MRI data is challenging because of relatively long acquisition times and the patients’ inability to remain still for this length of time. Diffusion MRI data is particularly prone to artefacts caused by motion due to head movement and cardiac pulsation. These artefacts need to be detected and corrected to provide accurate measures of microstructure.In this …

Study level
Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Chemistry, Physics and Mechanical Engineering

Size patterns in Turing patterns: how to grow body segments

Certain repeating elements of the body, such as teeth, fingers, limbs and vertebrae, follow the rule that the size of the middle element of a group of three is the average size of the three elements. This simple rule constrains how the relative sizes of segments develop in the embryo and evolve over long periods of time. The precise mechanisms that determine the number and size of repeating structures, such as fingers and teeth, remain largely unknown.

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

Collisions with evolving surfaces

The density of impacts of particles colliding with an evolving surface is of particular interest for several industrial and biological applications. These include etching and deposition processes [1], the incorporation of molecules in a tissue during its growth, budding cell membranes, and biological tissue growth [2]. Impacts on an evolving surface are generated unevenly depending on the relative velocity between the particles and the surface. The distribution of impacts further evolves in a curvature-dependent manner due to the local distortions …

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

Adoption of retro technologies

There's a vibrant computing community dedicated to embracing long-ago obsolete computer systems. Within it, there's a growing sub-community playing equally obsolete computer and arcade games. And not only are LPs still available, despite their supposed replacement by cassetes, then CDs, then digital music, but they have been the fastest-growing music format in the US in recent years.This research project investigates the characteristics of the adopters of such retro-technologies.Some of the central questions include:Why do these individuals retro-use and what do …

Study level
Master of Philosophy, Honours
Faculty
QUT Business School
Lead unit
School of Management

Computational mathematics

We are offering opportunities to conduct research in various aspects of:computational mathematicsincluding numerical solution of PDEslevel set methodspreconditioningparallel and GPU computing.Applications include:modelling interfacial dynamics and moving boundary problemsheat and mass transport and anomalous diffusion.

Study level
Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

The mathematics of robustness in molecular communication networks

Robustness, and the ability to function and thrive amid changing and unfavourable environments, is a fundamental requirement for living systems. In the past, it has been a mystery how large and complex biological networks can exhibit robust performance since complexity is generally associated with fragility.Exciting recent research here at QUT has suggested a resolution to this paradox through the discovery that robust adaptive signalling networks must be constructed from a small number of well-defined universal modules ("motifs"). The existence of …

Study level
PhD, Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

The dynamics of planar localised structures

While patterns observed in the natural sciences are in general (at least) two-dimensional, our mathematical understanding of the interaction of two-dimensional, or planar, localised structures is still in its infancy. In this project, we aim to further this understanding and examine the interaction of fundamental two-dimensional, or planar, patterns such as spots and stripes in reaction-diffusion equations, by developing and extending state-of-the-art mathematical techniques. These fundamental planar structures form the backbone of more complex patterns and are, for example, observed …

Study level
PhD
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Active-transport mechanisms for robust biological patterning

The underlying mechanisms that generate shapes and patterns in biology are characterized by a remarkable robustness, despite the uncontrollable parameter variability. More than half a century ago, Alan Turing published a landmark mathematical study entitled “The Chemical Basis of Morphogenesis” to explain how patterns in biology could be produced via certain classes of reaction-diffusion systems.This mathematical theory proposed the novel idea that two homogeneously dispersed “morphogens” - chemicals that determine a cell’s fate or characteristics - can autonomously generate spatial …

Study level
PhD, Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Fractional differential equations and anomalous diffusion

Applications include modelling electrical signal propagation in the heart, improved magnetic resonance imaging techniques for identifying the microstructure of the brain, and tumour growth models that account for nonlocal effects and heterogeneities in biological tissue.These projects involve computational mathematics, fractional calculus and numerical solutions of partial differential equations using MATLAB.

Study level
Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

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