Front stability of infinitely steep travelling waves in population biology
Uploaded to arXiv. (2023).
Publications
Preprints
Analytic shock-fronted solutions to a reaction-diffusion equation with negative diffusivity
Submitted to Stud. Appl. Math. (2023).
Peer-Reviewed Journal Articles
Survival, extinction, and interface stability in a two-phase moving boundary model of biological invasion
Extends previous results for reaction—diffusion moving-boundary problems to a model for two populations. Published in Physica D (2023).
Pattern formation and front stability for a moving-boundary model of biological invasion and recession
Advancing planar travelling waves of the Fisher-Stefan model are linearly stable. Receding waves are unstable, but short-wavelength perturbations are stabilised by surface tension. Published in Physica D (2023).
F-actin bending facilitates net actomyosin contraction by inhibiting expansion with plus-end-located myosin motors
We derive, analyse, and solve a PDE model for two actin filaments, and show that filament bending enables net contraction. Published in J. Math. Biol. (2022).
The effect of geometry on survival and extinction in a moving-boundary problem motivated by the Fisher-KPP equation
We explore a moving-boundary problem where population survival and extinction are both possible, and find the conditions for survival in 2D geometry. Published in Physica D (2022).
Thin-film lubrication model for biofilm expansion under strong adhesion
We derive and solve a mathematical model for biofilm growth in the lubrication regime, and compare results with extensional flow solutions. Published in Phys. Rev. E (2022).
Protein friction and filament bending facilitate contraction of disordered actomyosin networks
A computational study using Julia code, showing how F-actin bending and protein friction give rise to actomyosin contraction. Published in Biophys. J. (2021).
A thin-film extensional flow model for biofilm expansion by sliding motility
We derive and solve a multi-phase, thin-film fluid model for a yeast biofilm, and show that it can explain experimental expansion speed and biofilm shape. Published in Proc. Royal Soc. A (2019).
Diffusion-limited growth of microbial colonies
We use agent-based and reaction—diffusion models to investigate the conditions in which cells undergo directed growth towards a nutrient source. This is an indicator of diffusion-limited growth. Published in Sci. Rep. (2018).
Nutrient-limited growth with non-linear cell diffusion as a mechanism for floral pattern formation in yeast biofilms
We propose a reaction--diffusion model for yeast biofilm growth, and show the model can explain a characteristic flower-like pattern. Published in J. Theor. Biol. (2018).
Predicting channel bed topography in hydraulic falls
This paper uses experimental surface wave profiles to predict topographic disturbances, using a potential flow model and the KdV equation. Published in Phys. Fluids (2015).
Theses
Mathematical modelling of pattern formation in yeast biofilms
My PhD thesis that combines experiments, image processing, reaction--diffusion modelling, and thin-film fluid mechanics to understand growth and pattern formation in yeast biofilms.