**Acting Head of School, School of Mathematical Sciences**

*
PhD (University of Queensland), Bachelor of Science (University of Queensland)*

Professor Scott McCue is Academic Lead for Development and Diversity in the School of Mathematical Sciences.

**Background:** Scott McCue was award a PhD in Applied Mathematics from the University of Queensland in May 2000. His PhD supervisor was Professor Lawrence Forbes, who is now at the University of Tasmania. Scott was a Postdoctoral Research Fellow at the University of Nottingham from 1999-2001, under the supervision of Professors David Riley and John King. He was then a Postdoctoral Research Fellow at the University of Wollongong from 2002-2004 under the supervision of Professor James Hill, who is now at the University of South Australia. In 2004 Scott took up a position as Lecturer in Applied Mathematics at Griffith University. He moved to QUT in 2007 as Lecturer in Mathematics, was promoted to Senior Lecturer in 2009, Associate Professor in 2012, and Professor in 2016.

In 2009 Scott was awarded the JH Michell Medal. In 2019 he was awarded the EO Tuck Medal. In 2019 he was a Simons Visiting Fellow at the Isaac Newton Institute of Mathematical Sciences at the University of Cambridge.

**Research discipline:** Applied and Computational Mathematics

**Areas of expertise**

- Fluid mechanics
- Heat and mass transfer
- Interfacial dynamics
- Asymptotic analysis
- Mathematical biology

**Topics of research** (click for examples)

Stefan problems (mathematics of melting, freezing and crystal formation)

- Asymptotic analysis for melting/freezing a ball
- Singularity formation for ill-posed Stefan problems
- Melting crystals in microgravity
- Effect of surface tension and kinetic undercooling on radially-symmetric melting
- Extinction analysis for inward solidification
- Numerical methods for pattern formation due to crystal growth from undercooled melt
- Related mathematical models for the penetration of solvent through glassy polymers and drug diffusion

Free surface flows (mathematics of water wave problems)

- Properties of ship wakes
- Exponential asymptotics for low Froude number flows
- Flow due to source or sink
- 2D flows past surface piercing objects
- Stokes waves
- Computing ship wave patterns in 3D
- Time-frequency analysis of ship wakes

Hele-Shaw flows (viscous flow between two closely held flat plates)

- Bubble contraction in Hele-Shaw flows
- Doubly connected Hele-Shaw flows
- Pattern formation due to viscous fingering
- Saffman-Taylor instability with kinetic undercooling
- Selection problems for steadily propagating bubbles

Thin film flows (viscous flow with small aspect ratio)

- Fingering patterns due to flow of thin viscous film down a smooth surface
- Flow of a single drop: rivulets, corner singularities and pearling
- Spreading of thin films of leaf surfaces with industrial applications
- Extensional flow of viscous drop due to gravity

Droplet impaction

- Impaction of surfactant-laden droplets on leaf surfaces
- Simulation of agrichemical spraying of plants
- Experimental validation

Mathematical biology

- Models for wound healing
- Multiscale-modelling of cell biology
- Modelling cell invasion with nonlinear diffusion
- Cell proliferation and migration assays
- Tumour-growth models
- Collective cell motion of melanoma cells
- Biological tissue deformation
- Random walk models for cell motion
- Transport through crowded media
- Parameter estimation using experimental data

Other odds and ends

- Non-local geometric flows, mean curvature flows, curve-lengthening flow
- Linear and nonlinear diffusion

### Additional information

- McCue S, (2018) Short, flat-tipped, viscous fingers: novel interfacial patterns in a Hele-Shaw channel with an elastic boundary, Journal of Fluid Mechanics p1-4
- Buttle N, Pethiyagoda R, Moroney T, McCue S, (2018) Three-dimensional free-surface flow over arbitrary bottom topography, Journal of Fluid Mechanics p166-189
- Simpson M, Jin W, Vittadello S, Tambyah T, Ryan J, Gunasingh G, Haass N, McCue S, (2018) Stochastic models of cell invasion with fluorescent cell cycle indicators, Physica A: Statistical Mechanics and its Applications p375-386
- Browning A, McCue S, Binny R, Plank M, Shah E, Simpson M, (2018) Inferring parameters for a lattice-free model of cell migration and proliferation using experimental data, Journal of Theoretical Biology p251-260
- Pethiyagoda R, Moroney T, McCue S, (2018) Efficient computation of two-dimensional steady free-surface flows, International Journal for Numerical Methods in Fluids p607-624
- Pethiyagoda R, Moroney T, Macfarlane G, Binns J, McCue S, (2018) Time-frequency analysis of ship wave patterns in shallow water: modelling and experiments, Ocean Engineering p123-131
- Pethiyagoda R, McCue S, Moroney T, (2017) Spectrograms of ship wakes: identifying linear and nonlinear wave signals, Journal of Fluid Mechanics p189-209
- Massinon M, De Cock N, Forster W, Nairn J, McCue S, Zabkiewicz J, Lebeau F, (2017) Spray droplet impaction outcomes for different plant species and spray formulations, Crop Protection p65-75
- Green C, Lustri C, McCue S, (2017) The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences p1-20
- Dallaston M, McCue S, (2016) A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences p1-15

- Title
- Mathematical and Computational Analysis of Ship Wakes
- Primary fund type
- CAT 1 - Australian Competitive Grant
- Project ID
- DP180103260
- Start year
- 2018
- Keywords

- Title
- Mathematical and computational models for agrichemical retention on plants
- Primary fund type
- CAT 1 - Australian Competitive Grant
- Project ID
- LP160100707
- Start year
- 2017
- Keywords
- Fluid mechanics; Droplet impaction; Evaporation; Leaf surface models; Mathematical software

- Title
- Asymptotics of the exponentially small
- Primary fund type
- CAT 1 - Australian Competitive Grant
- Project ID
- DP140100933
- Start year
- 2014
- Keywords
- Asymptotic methods; Fluid mechanics; Applied differential equations

- Title
- A new hierarchy of mathematical models to quantify the role of ghrelin during cell invasion
- Primary fund type
- CAT 1 - Australian Competitive Grant
- Project ID
- DP140100249
- Start year
- 2014
- Keywords
- Mathematical modelling; Mathematical biology; Multiscale modelling

- Title
- Modelling Interactions of Spray Droplets with Plants
- Primary fund type
- CAT 1 - Australian Competitive Grant
- Project ID
- LP100200476
- Start year
- 2011
- Keywords
- Mathematical Modelling; Leaf Surface Models; Plant Architectural Models; Spray Droplet Interception; Droplet Spreading; Agrichemical Spray Retention

- Title
- A Mathematical Model of the Roles of Contraction and Oxygen in Human Wound Healing
- Primary fund type
- CAT 1 - Australian Competitive Grant
- Project ID
- DP0878011
- Start year
- 2008
- Keywords
- Biomathematics; Mathematical Modelling; Wound Healing

- Investigating the Reproducibility of In Vitro Cell Biology Assays Using Mathematical Models (2017)
- Modelling transport through biological environments that contain obstacles (2017)
- Mathematical and Computational Analysis of Kelvin Ship Wave Patterns (2016)
- Mathematical Modelling of the Impaction and Spreading of Spray Droplets on Leaves (2015)
- Stefan Problems for Melting Nanoscaled Particles (2015)
- Mathematical Models of Bubble Evolution in a Hele-Shaw Cell (2013)
- Mathematical modelling of controlled drug release from polymer micro-spheres: incorporating the effects of swelling, diffusion and dissolution via moving boundary problems (2013)