Computational Modelling Group


Diffusion is a wide-spread phenomenon with prime examples being the diffusive behaviour of, say, salt or some chemical substance, in a liquid, or the spread of heat through a sample.

Diffusion of heat animation

(Animation has been taken from

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Centre for Doctoral Training in Next Generation Computational Modelling

Hans Fangohr, Ian Hawke, Peter Horak (Investigators), Susanne Ufermann Fangohr, Ryan Pepper, Hossam Ragheb, Emanuele Zappia, Ashley Setter, David Lusher, Alvaro Perez-Diaz, Kieran Selvon, Thorsten Wittemeier, Mihails Milehins, Stephen Gow, Ioannis Begleris, Jonathon Waters, James Harrison, Joshua Greenhalgh, Rory Brown, Robert Entwistle, Paul Chambers, Jan Kamenik, Craig Rafter

The £10million Centre for Doctoral Training was launched in November 2013 and is jointly funded by EPSRC, the University of Southampton, and its partners.

The NGCM brings together world-class simulation modelling research activities from across the University of Southampton and hosts a 4-year doctoral training programme that is the first of its kind in the UK.

Diffusion at solute/solvent interfaces

Anatoliy Vorobev (Investigator), Ruilin Xie

We aim to develop the theoretical model that would provide an accurate description for the mixing process of two miscible liquids, and, in particular, would reproduce our experimental optical observations. The model based on the phase-field (Cahn-Hilliard) approach is adopted for the mixture of two miscible liquids. The model takes into account the surface tension effects, the non-Fickian diffusion across the liquid/liquid interface, and hydrodynamic flows that might be generated near the interface by the concentration gradients.

Investigation into the Interfacial Physics of Field Effect Biosensors

Nicolas Green, Chris-Kriton Skylaris (Investigators), Benjamin Lowe

This interdisciplinary research aims to improve understanding of Field Effect Transistor Biosensors (Bio-FETs) and to work towards a multiscale model which can be used to better understand and predict device response.

Multiscale Modelling of Cellular Calcium Signalling

Hans Fangohr, Jonathan Essex (Investigators), Dan Mason

Calcium ions play a vitally important role in signal transduction and are key to many cellular processes including muscle contraction and cell apoptosis (cell death). This importance has made calcium an active area in biomedical science and mathematical modelling.

Porous Media and Hydrothermal Circulation in Weakened Ocean Crust

Formation of oceanic crust is an interplay between magma and the cooling hydrothermal system above that its own heat drives. To understand this system we must understand where and how water circulates through the crust.

Ocean crust is riddled with faults and other permeable pathways along which water preferentially flows. We seek to use basic numerical models of circulation in porous media to understand how much of an influence on crust formation these anomalous features have, compared to the bulk, unfractured crust.

Simulation of biological systems at long length and distance scales

Jonathan Essex (Investigator), Kieran Selvon

This project aims to shed light on cell membrane mechanisms which are difficult to probe experimentally, in particular drug permiation across the cell membrane. If one had a full understanding of the mechanism, drugs could be designed to target particular embedded proteins to improve their efficacy, the viability of nano based medicines and materials could also be assessed, testing for toxicity etc.

The Ca-geospeedometer - A tool for investigating the processes that generate oceanic crust

We quantify the errors inherent in the current methods of geospeedometry, which lets one obtain the cooling rate of a rock, using mineral trace element chemistry. Calcium-in-Olivine geospeedometry is useful for deep ocean crust.

We want to use this proxy to figure out how ocean crust actually accretes, it provides key evidence as to how magma chambers and hydrothermal systems interact to produce new lithosphere. But to do so we first have to determine how reliable the method is and therefore how much can be inferred from results.

The Maximum Entropy Production Principle and Natural Convection

Seth Bullock, James Dyke (Investigators), Stuart Bartlett

In this project I wanted to perform some tests of the so-called Maximum Entropy Production Principle (MEPP) in the context of buoyancy-driven convection in a system with negative feedback boundary conditions.

Using MEP to determine parameter values of ocean and atmosphere diffusivity

Kevin Oliver, James Dyke (Investigators), Maike Sonnewald

Entropy budgets can potentially offer new and valuable insights into the dissipation of energy in the ocean system. Specifically, if one assumes the Earth system maximises the dissipation of energy, one can use this as a guiding principle maximising the internal entropy production. In this study, resultant temperature distributions from a four box ocean-atmosphere-ice model are used to assess to what extent such considerations could ameliorate the need for tuning parameter values associated with oceanic and atmospheric diffusivity. Results from a standard implementation with fixed, empirically determined, parameters were compared to one where the maximum entropy production principle is applied to determine the value of oceanic and atmospheric diffusivity parameters. These methods have been successfully applied to cloud fraction and convection in the atmosphere.

The MEP principle suggested using diffusivity values of 3.3×1014 W K −1 and 3.2×1014 W K −1
for the ocean and atmosphere respectively, where the empirical values were 2.0 × 1014 W K −1
and 1.0 × 1014 W K −1 . The oceanic temperatures of the MEP implementation were 3 and -1oC
away the high and low latitude observed ocean temperatures respectively, while the empirical
implementation was -5 and 3oC away, largely within the observational standard deviation of
8 and 2◦ C respectively. For the atmospheric values, MEP implementation was 3W m−2 away
from the high latitude observed value, while the empirical implementation was 6W m−2 away,
both within the standard deviation of 13.2W m−2 . However, in the low latitudes this reverses,
with the empirical implementation being only -16W m−2 off while the MEP implementation
is -21W m−2 off. However, both figures are outside the range of the standard deviation of
4.2W m−2 . Overall, both methods were found to be very close to oceanic observations. This
confirms that in the model used, the assumption of maximal dissipation of energy is reasonable.

Furthermore, the nature of the landscape of internal entropy production created by the
oceanic and atmospheric diffusivity was found to be fairly smooth, with non-linearities mainly
coming from ice albedo. Assuming the Earth system is in a state of maximal energy dissipa-
tion, applying the MEP principle successfully may depend on such a smooth, easily optimisable
landscape. Thus, the successful application of the MEP principle could be much more difficult
if attempting to aid parametrisation in more detailed ocean models, as these are likely to have
internal entropy production landscapes with local maxima. Nevertheless, results presented
are very promising, and encourage further exploration of to what extent this principle could
be applied to ameliorate the need for tuning parameters in light of lacking information.


Seth Bullock
Professor, Electronics and Computer Science (FPAS)
Jonathan Essex
Professor, Chemistry (FNES)
Hans Fangohr
Professor, Engineering Sciences (FEE)
Nicolas Green
Reader, Electronics and Computer Science (FPAS)
Peter Horak
Reader, Optoelectronics Research Centre
James Dyke
Lecturer, Electronics and Computer Science (FPAS)
Ian Hawke
Lecturer, Mathematics (FSHS)
Kevin Oliver
Lecturer, National Oceanography Centre (FNES)
Chris-Kriton Skylaris
Lecturer, Chemistry (FNES)
Anatoliy Vorobev
Lecturer, Engineering Sciences (FEE)
Stuart Bartlett
Postgraduate Research Student, Electronics and Computer Science (FPAS)
Ioannis Begleris
Postgraduate Research Student, Engineering Sciences (FEE)
Rory Brown
Postgraduate Research Student, Civil Engineering & the Environment (FEE)
Jamie Caldwell
Postgraduate Research Student, Engineering Sciences (FEE)
Paul Chambers
Postgraduate Research Student, Engineering Sciences (FEE)
Robert Entwistle
Postgraduate Research Student, Engineering Sciences (FEE)
Stephen Gow
Postgraduate Research Student, Engineering Sciences (FEE)
Joshua Greenhalgh
Postgraduate Research Student, Engineering Sciences (FEE)
James Harrison
Postgraduate Research Student, Engineering Sciences (FEE)
Nicholas Hill
Postgraduate Research Student, Electronics and Computer Science (FPAS)
Jan Kamenik
Postgraduate Research Student, Engineering Sciences (FEE)
Benjamin Lowe
Postgraduate Research Student, Electronics and Computer Science (FPAS)
David Lusher
Postgraduate Research Student, Engineering Sciences (FEE)
Juraj Mihalik
Postgraduate Research Student, Engineering Sciences (FEE)
Alvaro Perez-Diaz
Postgraduate Research Student, Engineering Sciences (FEE)
Craig Rafter
Postgraduate Research Student, Engineering Sciences (FEE)
Hossam Ragheb
Postgraduate Research Student, Engineering Sciences (FEE)
Sabin Roman
Postgraduate Research Student, University of Southampton
Kieran Selvon
Postgraduate Research Student, Engineering Sciences (FEE)
Ashley Setter
Postgraduate Research Student, Engineering Sciences (FEE)
Maike Sonnewald
Postgraduate Research Student, National Oceanography Centre (FNES)
Jonathon Waters
Postgraduate Research Student, Engineering Sciences (FEE)
Thorsten Wittemeier
Postgraduate Research Student, Engineering Sciences (FEE)
Martin Wood
Postgraduate Research Student, Ocean & Earth Science (FNES)
Ruilin Xie
Postgraduate Research Student, Engineering Sciences (FEE)
Emanuele Zappia
Postgraduate Research Student, Engineering Sciences (FEE)
Susanne Ufermann Fangohr
Administrative Staff, Civil Engineering & the Environment (FEE)
Dan Mason
Alumnus, University of Southampton
Mihails Milehins
Alumnus, University of Southampton