Professor John MacKenzie

Mathematics and Statistics

Personal statement

What makes Professor Mackenzie’s recent research stand out is his ability to work on a wide range of interdisciplinary and industrial problems.   Below are just a few of the current projects he is involved with indicating his breadth of research activities. 

For the last ten years Professor Mackenzie has been collaborating with Professor Robert Insall from the Beatson Institute for Cancer Research,  on developing computational models of eukaryotic cell migration and chemotaxis.  This subject area has implications in the understanding of important biological processes such as wound healing, embryonic development and cancer metastasis. Key to the success of this collaboration is Professor Mackenzie's assimilation of the biological issues and his innovative use of state of the art numerical modelling techniques. His work in this area has been recognised by the award of a Leverhulme Research Fellowship (£44,000 Oct 2014-2016) to work on "The Mechanisms Behind Cell Migration and Chemotaxis: Disection using Computational Modelling"  He is also currently  supervising an EPSRC funded industrial CASE PhD student (£98,294) which is partially funded by the CRUK. Dr Mackenzie is also a member of the Research in Cancer at Strathclyde (RICAS) group which is a component of the Health Technologies theme of the University’s Technology and Innovation Centre. 

Professor Mackenzie has also recently applied his knowledge of the adaptive solution of partial differential equations to the solution of mathematical models of liquid crystals. This work is funded by an EPSRC Maths CASE award with Hewlett-Packard (£90,298). These devices have the potential for significant reductions in energy consumption and in the production of reflective colour e-inks systems.  

Professor Mackenzie is also working with Professor Andrew Mills at Queens University, Belfast. This work is funded through an EPSRC DTA studentship (£67,000),  investigating the kinetics of photocatalytic activated intelligent ink systems.  These inks have been used to detect rapidly the photocatalytic activity of self-cleaning glass and in the detection of oxygen in modified atmosphere packaging used in the food industry.  These systems are not well understood, being a complex combination of diffusion through thin polymer films and photocatalytic activation control.  His current research is focussed on the use of a combination of mathematical and computational models which is leading to a greater understanding of the key limiting factors – in terms of kinetics- of such systems and this information will be used to produce faster acting indicators with the potential for greater commercial impact.  

Recently Professor Mackenzie was involved with a KTN industrial internship funded by Proctor and Gamble investigating the mathematical modelling of spray drying towers. This process is used to produce detergents and other comsumer products and their design and operation are poorly understood. The successful outcome from the internship led to Proctor and Gamble funding an EPSRC Industrial CASE studentship (£91,296).  Dr Mackenzie’s team are constructing a validated computational model for the complex processes of droplet transport, evaporation and allomeration in spray drying towers. 



Local modulation of chemoattractant concentrations by single cells : dissection using a bulk-surface computational model
Mackenzie JA, Nolan M, Insall RH
Interface Focus Vol 6 (2016)
Kinetics of reduction of a Resazurin-based photocatalytic activity ink
MacKenzie John, MacDonald Grant, Mills Andrew, Wells Nathan
Catalysis Today (2016)
A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds : application to a model of cell migration and chemotaxis
MacDonald G, MacKenzie JA, Nolan M, Insall RH
Journal of Computational Physics Vol 309, pp. 207–226 (2016)
Efficient moving mesh methods for Q-tensor models of nematic liquid crystals
MacDonald Craig S, MacKenzie John A, Ramage Alison, Newton Christopher J P
SIAM Journal on Scientific Computing Vol 37, pp. B215-B238 (2015)
Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals
MacDonald Craig, MacKenzie John, Ramage Alison, Newton Chris
Computers and Mathematics with Applications Vol 64, pp. 3627-3640 (2012)
An unconditionally stable second-order accurate ALE–FEM scheme for two-dimensional convection–diffusion problems
Mackenzie John, Mekwi WR
IMA Journal of Numerical Analysis Vol 32, pp. 888-905 (2012)

more publications

Professional activities

28th Biennial Conference on Numerical Analysis
Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, non-local and discrete structures
Invited speaker
UKIE SIAM Annual Meeting
BIRS Workshop on Adaptive Numerical Methods for Partial Differential Equations with Applications
Invited speaker
British Applied Mathematics Colloquium (BAMC) 2018
Scottish Numerical Methods Workshop 2018
Invited speaker

more professional activities


Understanding Cancer Metastasis by Combining Models, Numbers and Molecules
MacKenzie, John (Principal Investigator)
01-Jan-2015 - 30-Jan-2020
The Mechanisims Behind Cell Migration and Chemotaxis: Dissection using Computational Modelling
MacKenzie, John (Principal Investigator)
01-Jan-2014 - 30-Jan-2016
EPSRC Science and Innovation - Numerical Analysis | Gonzalez Aguayo, Cheherazada
Barrenechea, Gabriel (Principal Investigator) MacKenzie, John (Co-investigator) Gonzalez Aguayo, Cheherazada (Research Co-investigator)
01-Jan-2012 - 24-Jan-2017
Industrial Case Account | Wells, Jonathan
MacKenzie, John (Principal Investigator) Lamb, Wilson (Co-investigator) Wells, Jonathan (Research Co-investigator)
01-Jan-2011 - 26-Jan-2018
Industrial Case Account / RS4730
MacKenzie, John (Principal Investigator)
01-Jan-2011 - 30-Jan-2016
A Computational Model for Cell Migration in 3D
MacKenzie, John (Co-investigator) Webb, Steven (Co-investigator) Nolan, Michael (Post Grad Student) Insall, Robert (Co-investigator)
This project is funded by an EPSRC Industrial CASE studentship.
01-Jan-2011 - 28-Jan-2014

more projects


Mathematics and Statistics
Livingstone Tower

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