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Industrial mathematics: in particular fluid dynamics, liquid crystal theory

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Personal profile

Personal Statement

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.

Research Interests

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, 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.


  • 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. 

Academic / Professional qualifications

  • 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.

Expertise & Capabilities

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.



  • liquid crystals
  • anisotropic material science
  • mathematical modelling
  • self-organisation
  • environmental modelling
  • active fluids


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