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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

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

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

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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