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Research group

Mathematical Modelling

Textures in a mesoscopic system made of a nematic liquid crystal doped with nanoparticles.

The modelling group focuses on mathematical modelling across science and engineering, including physics (from the physics of quanta and strings to that of liquid crystals), chemistry (modelling lithium-ion batteries and solar cells), engineering (controlling sound direction), biology, medicine and healthcare (from stem cell population dynamics to medical imaging and healthcare models).

Part of the Applied Mathematics and Theoretical Physics, Mathematical sciences

About

The underlying theme of the group is the application of rigorous mathematical models to quantitatively analyse and understand in depth problems in science and engineering. We have a wide range of mathematical expertise and techniques in modelling, from partial differential equations, to agent modelling, dynamical systems, or topological methods. Often, the research take place in close interdisciplinary collaborations. As an example, we have developed a very successful model of lithium-ion batteries by combining classical differential equation modelling with asymptotic analysis and state of the art coding to produce a software package that is both fast and comprehensive.  Other examples are the application of asymptotic analysis in controlling aircraft sounds, stochastic methods in modelling gene expression and agent-based techniques in healthcare.  We apply topological data analysis to model phase transitions of mesoscopic physical systems, and to enhance and up-scale optical imaging in medical applications, as precursors to efficient machine learning and data analysis.

Research highlights

Droplets of water falling on water along with their concentric wave patterns

Applicable Resurgent Asymptotics: towards a universal theory. An Isaac Newton Institute Programme

Future societies and communities
AI, big data and analytics
Engineering
An innovative Southampton initiative, that brought together mathematicians and theoretical physicists from around the world, is helping shed light on complex challenges in mathematics and physics.

Disorder is Good – Taming disorder in self-assembled materials with topology

AI, big data and analytics
Environment, sustainability and clean growth
Instead of fighting disorder, we should identify structures that are ordered enough to perform the required function.
We have combined cutting edge experiments with breakthrough methods from topological data analysis to quantify emerging structure in apparently disordered nano-assemblies and classify their response to light. We aim to design a new generation of controllable nanosystems at a fraction of the cost of the current methods.
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People, projects, publications and PhDs

People

Mathematical modelling allows you to see the world as an interconnected whole, with causes and effects, so that we can fulfil knowledgeably our responsibility to sustain it.
Emeritus Professor Giampaolo D'Alessandro

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