Mathematical modelling has played a key role in our scientific understanding of the world. However the technological environmental and societal challenges we face are evolving rapidly, posing novel interdisciplinary research challenges that demand a wide range of modelling skills.
There are many applications in which discrete, continuous, deterministic and stochastic aspects all come into play. The Southampton Initiative in Mathematical Modelling brings together internationally leading groups of researchers into multidisciplinary teams offering a diverse set of sophisticated and flexible modelling skills.
The breadth of mathematical expertise and first hand experience in applying these skills to real world problems will allow SIMM to tackle cutting–edge research problems of direct relevance to industry, academics and other end-users.
Examples of recent collaborations
Food resources are under pressure because of ever expanding human population and climate change. To continue to improve agricultural efficiency we need a detailed understanding of the factors controlling crop growth. Modelling provides invaluable information on how to translate experimental work from the lab to the field/crop scale. We model the processes controlling crop growth using multiscale analysis of partial differential equations. Collaborations include : SBS, SES, NSRI, IRRI, BOKU, Bangor, INRA.
Flight Paths of Spacecraft
Flight trajectories for satellites and other spacecraft need to be carefully chosen in order to optimise the performance of the vehicle. Such optimisation takes place throughout the full range of the mission, from initial ascent to orbit transfers, deep space manoeuvring, re-entry, and emergency scenarios. In conjunction with the European Space Agency, we model and optimise such flight paths using novel approaches from nonlinear multiobjective optimisation.
Airport Modelling & Optimisation
Air traffic control in busy airports will be one of the most challenging airport management problems in the coming decade. In collaboration with EUROCONTROL and further partners, we develop generic models for airport runway scheduling and other problems in logistics and transport and design efficient and robust algorithms that are suffi ciently fast to be used in practice.
Development of tissue for repairing cartilage requires understanding the complex interaction of cell movement, nutrient transport, extracellular development and tissue growth. Continuum models of these processes have been developed and then analysed using asymptotic methods, homogenisation and numerical solution. Insight into how to design scaffolds to alter growth have been gained in collaboration with Bio-engineering and the School of Medicine.
Spatiotemporal Data Modelling
Often, in analysing large space-time data it is challenging to make valid inference about the true underlying spatiotemporal processes in the presence of many complications in the observations such as missing data, bias error and measurement error. Statistical inference methods meeting such challenges have been developed and applied to the assessment and understanding of trends in ozone levels in the US in collaboration with the US Environmental Protection Agency and Duke University.
Modelling Wide area Blackouts
With increasing use of distributed power generation wide area blackouts are a growing problem with potential disruption on a trans-national scale. The Pure Mathematics Group are working with engineers from Edinburgh and Durham to develop strategies for protecting the grid by proactively separating it into sustainable units during a crisis. This strategy will use tools from analytic graph theory, similar to those used to design robust communications networks, requiring sophisticated tools from analysis and algebra.