My research interests are in the mathematical modelling of real-world systems, generally focussing on those that include the dynamics of non-Newtonian fluids. I am particularly interested in anisotropic fluids such as liquid crystals, where viscoelasticity is an important consideration, as is their behaviour under electric fields. I also have projects in the areas of medical and biological systems. Current projects also include investigations of active fluids, such as bacterium or micro-organism organisation within fluid flows, and biological flow systems. 

In a wider context I am a member of the British Liquid Crystal Society, the Edinburgh Mathematical Society, and a Fellow of the Institute for Mathematics and its Applications, as well as an active participant in the European Consortium for Mathematics in Industry and the UK Fluids Network. 

I am interested in mathematics applied to real-world problems in a general sense and I welcome enquiries from anyone interested to understand more about mathematical modelling.

Continuum theory of anisotropic materials

• Anisotropy in the natural environment: swimming/self-organised organisms, tissue growth, mixing 
• Order parameter changes in nematic liquid crystals: defects, field induced changes, Q tensor theory.
• Theories of biaxial nematic liquid crytals
• Surface effects: induced order, bistabilty in anisotropic fluids.
• Disclination line motion: annihilation, formation, effects of electric field and surface interactions.
• Thin films: flow in thin films of anisotropic fluids, painting and spin-coating.
• Use of fractional calculus to represent memory in dynamical systems.
• Physiologically-based Pharmacokinetics and dynamics
• Blood flow: non-newtonian models of blood flow in microfluidic devices.
• Oxygen transfer: novel medical device modelling for artificial livers.

Collaborations

• I collaborate with scientists from many different disciplines and many countries around the world.
• My industrial collaborations currently include GSK, Merck and Kirkstall and past collaborators include HP, Sharp, Dow Corning. 

• 1989-1992: BA in Mathematics at the University of Oxford (Keble College).
• 1992-1996: PhD in the Department of Engineering Mathematics at the University of Bristol. Boundary effects in nematic liquid crystal cells, supervised by Prof. S. J. Hogan (external link)
• 1995-1997: Post Doctoral Research Assistant in the Department of Engineering Mathematics at the University of Bristol. Working on nematic liquid crystal theory with Prof. Hogan.
• 1997-1999: Post Doctoral Research Assistant in the Department of Engineering Science at the University of Oxford. Working on smectic liquid crystal theory with Dr S. J. Elston (external link).
• 1999-2004: Lecturer in the Department of Mathematics at the University of Strathclyde.
• 2001-2006: EPSRC Advanced Research Fellow
• 2004-2007: Reader in the Department of Mathematics at the University of Strathclyde.
• 2007-present: Professor in the Department of Mathematics and Statistics at the University of Strathclyde.

Research areas of expertise

• Mathematical modelling of real-world systems
• Fluid dynamics
• Liquid crystal theory
• Optical devices
• Multiphyscics models
• Numerical simulation of fluids, electrostatics, ions.