Joel is a third-year Bachelor of Mathematics student studying at the Queensland University of Technology, majoring in Applied and Computational Mathematics, as well as Statistical Science. A Vice-Chancellor’s Scholar, Joel has a keen interest in sports and how Mathematics can be applied to the field, as well as a growing interest in Mathematical Biology and Mathematics in Agriculture.
Patterns in Turing patterns: sequential growth and the inhibitory cascade
Certain repeating elements of the body, such as teeth, fingers, limbs and vertebrae, are shown to 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 structures 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. This project will develop mathematical and computational models to investigate possible biological mechanisms of sequentially patterned growth. These models will be based on reaction–diffusion problems on growing domains [2, 3] and generalisations of Turing-like patterning mechanisms.
 Kavanagh KD, Evans AR, Jernvall J (2007) Predicting evolutionary patterns of mammalian teeth from development, Nature 449:427–433
 Simpson MJ, Landman KA, Newgreen DF (2006) Chemotactic and diffusive migration on a nonuniformly growing domain: numerical algorithm development and applications, J Comp App Math 192:282–300
 Buenzli PR (2016) Governing equations of tissue modelling and remodelling: A unified generalised description of surface and bulk balance, PLoS ONE 11:e0152582