Topics in Asymptotic Analysis, Industrial and Applied Mathematical Modelling

• Complex fluids with memory
  
  Asymptotic and numerical solutions of viscoelastic fluids. These are fluids that behave as both liquids and solids. Particular interest in behaviour near singularities arising in re-entrant corner geometries, wedge flows and stick-slip regimes.
  
  Applications in polymer, food, petroleum and minerals industries, inkjet printing, nanotechnology, smart materials and intelligent gels.
  
  Collaborators: Institute of Non-Newtonian Fluid Mechanics including Prof Ken Walters (FRS), Aberystwyth. Dr T. Hagen, Department of Mathematics, Univerity of Memphis, USA.
  
  Right: David Boger illustrating his class of constant viscosity non-Newtonian Boger fluids with fundamental applications to the environment, economy, society (triple bottom line).
  
  Videos showing the bizzare properties of these types of fluids.
  
  
  
• High order nonlinear evolutionary PDEs
  
  Fourth, sixth and tenth order Cahn-Hilliard and thin film type equations (semi-linear and degenerate quasi-linear PDEs). Investigation of self-similar blow-up and spreading solutions.
  
  Collaborators: Prof Victor Galaktionov, Bath. Dr Pablo Alvarez-Caudevilla, Carlos III University, Madrid.



• Free boundary problems
  
  Engineering applications: heat and mass transfer, semiconductor fabrication (silicon oxidation and device isolation techniques), concrete carbonation.
  
  Collaborators academic: Prof J.R. King, School of Mathematics, University of Nottingham. Dr A. Muntean, TU Eindhoven, Netherlands.
  Collaborators industrial: Dr A. Nejim, Silvaco, Cambridge. (Past contacts include Prof C. Hill and Dr S. Jones, GEC-Marconi Materials Technology, Caswell, Northampton.)
  
  Finance: Pricing of American style options/derivatives. Fractal identification in pricing data.
  
  Collaborators: Prof R.A. Kuske, Department of Mathematics, University of British Columbia, Canada. Prof J.B. Keller, Department of Mathematics, University of Stanford, USA. Prof D Hobson, Warwick.

• Nerve cell Modelling - Passive cable modeling for neurones.
  
  Past Collaborators: Prof J.J.B. Jack (FRS) and his group (including Dr Guy Major) at the Department of Physiology, Oxford University. Dr Guy Kember, Department of Applied Mathematics, Dalhousie University, Canada.
  
  
• Geodesy - Geoid computation and modified kernel analysis.
  
  Past Collaborators: Prof W. Featherstone, Faculty of Engineering, Curtin University, Perth, Western Australia. Dr J. Oliver, Department of Earth Sciences, Oxford University. Prof Petr Vanicek, Department of Geodesy, University of New Brunswick, Canada.

• Full Publication List
  
  

• Ben Boyle (Oct. 2012 - present). Topic: "Instabilities in Cahn-Hilliard and thin film flows". Ben is currently investigating free boundary problems for sixth-order Cahn-Hilliard type equations.
  
  
• Andrea Fernandez (Oct. 2009 - June 2013). Topic: "Sharp interface models from homogeneous reaction systems". Andrea focused on the application of concrete carbonation and the derivation of general free boundary problems from reaction-diffusion systems.
  
  
• David Sibley (Oct. 2006 - Oct. 2009). Topic: "Viscoelastic flows of PTT fluids". David looked at the re-entrant corner singularity for Phan-Thien--Tanner fluids and subsequently did a post-doc at Imperial.
  
  
• Aidan O'Byrne (Oct. 2006 - Dec. 2010). Topic: "Re-entrant corner flows of Oldroyd-B fluids". Aidan considered the re-entrant corner singularity for Oldroyd-B fluids. He then considered teaching before deciding to be an actuary.
  
  
• Jason Cook (April 2005 - June 2009). Topic: "Asymptotic Analysis of American-Style Options". Jason looked at the pricing of American options. He then worked for British Energy and Gazprom earning a six figure salary pricing energy derivatives!
  
  
• Damien Harwin (Oct. 2002 - May 2007). Topic: "Flows in porous channels". Damien studied the effect of temperature varying viscosity and power law fluids on the Classic porous channel Berman problem.
  
  

• Please get in touch (email me) if you are interested in pursuing a PhD in any of the areas mentioned above.
  
  
• Nuffield Bursaries are available to undergraduates to experience research for normally an 8 week period.
  Tom Begly obtained one in the summer of his second year to study "The elastic limit of interpolated Maxwell models for fluids with memory" (2010).
  
  

• INNFM (Institute of Non-Newtonian Fluid Mechanics), Kavli Meeting at the Royal Society, Chicheley Hall (March 2013). Presentation on “Corner flows of some common viscoelastic fluids”. Invited speaker at the session on Theoretical Rheology, celebrating the retirement of Prof. A.R. Davies.
• ICNAAM, Kos, Greece (Sept. 2012). Presentation on “Sharp-interface models for concrete carbonation” with A.Fernandez. In minisymposium on “Multiscale methods and their application to the problems arising in complex system’s modeling”.
• International Centre for Mathematical Sciences (ICMS): £25,000 grant for a workshop in June 4-8 2012 on “Scale transitions in Biology and Chemistry”. Co-organisers JR King (Nottingham), M Peletier and A Muntean (Eindhoven). The workshop included a 1 day postgraduate conference June 6 2012 on “Techniques for Multiscale Analysis”, supported by the ICMS and London Mathematical Society (LMS Postgraduate Conference grant £3000).
• BAMC (British Applied Mathematics Colloquium), UCL (March 2012). Presentation on “Single- and two-scale sharp-interface models for concrete” with A. Fernandez.
• ITN FIRST (Initial Training Network for Fronts and Interfaces in Science and Technology), Bath (2011). Presentation on “2mth-order thin film equation”.
• ICNAAM, Rhodes, Greece (Sept. 2010). Presentation on “Re-entrant corner singularity of the Phan-Thien-Tanner fluid”. In minisymposium sessions 45 & 80 on “Modeling and Simulation in Food Processing & Non-Newtonian Fluid Flows”.
• ICNAAM, Rhodes, Greece (Sept. 2010). Presentation on “The asymptotic behaviour at a re-entrant corner for a PTT fluid in the limit of small k”. In minisymposium sessions 45 & 80 on “Modeling and Simulation in Food Processing & Non-Newtonian Fluid Flows”.
• ICNAAM, Crete, Greece (Sept. 2009). Presentation on “Re-entrant corner singularity of the Giesekus fluid” and Session Chair for “Modelling of Materials and Simulation of Flows in Polymer Process Engineering”.
• Annual European Rheology Conference, Cardiff (April 2009). Presentation on “Re-entrant corner behaviour of the Giesekus fluid with a solvent viscosity”.
• Department of Mathematics, Birmingham University (Feb. 2009). Seminar speaker on “Re-entrant corner singularity of viscoelastic fluids”.
• Department of Mathematics, Cardiff University (Dec. 2008). Seminar speaker on “Re-entrant corner behaviour of some common viscoelastic fluids”.
• Lorentz Center Workshop on PDE Approximations in Fast Reaction – Slow Diffusion Scenarios, Leiden University, Holland (Nov. 2008). “On the derivation of heterogeneous reaction kinetics from a homogeneous reaction model”.