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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.

People, projects, publications and PhDs

People

Professor Benjamin Macarthur

Personal Chair

Research interests

  • Mathematical modeling
  • Machine learning 
  • Networks

Accepting applications from PhD students

Email: bdm@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

ORCID

Professor Carlos Lobo

Professor

Research interests

  • Superfluidity (rotational aspects, microscopics)
  • Superconductivity (multicomponent pairing theory, FFLO states)
  • Condensed Matter aspects of ultracold atoms (topological states in lattices)

Accepting applications from PhD students

Email: c.lobo@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

ORCID
Twitter

Professor Christopher Howls

Professor of Mathematics

Research interests

  • Asymptotic Analysis
  • Semiclassical Analysis
  • Applied Mathematics

Accepting applications from PhD students

Email: c.j.howls@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

ORCID

Dr Gaurav Singh

Research Fellow

Research interests

  • Lithium-Ion Battery
  • Mathematical Modelling
  • Computational mechanics

Email: gaurav.singh@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

Google Scholar
ORCID
LinkedIn

Professor Giampaolo D'Alessandro

Professor

Research interests

  • Liquid crystals
  • Optics
  • Mathematical modelling

Email: dales@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

ORCID

Professor Giles Richardson

Professor

Research interests

  • Modelling renewable energy storage and generation
  • Modelling in biomedicine

Accepting applications from PhD students

Email: g.richardson@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

Google Scholar
ORCID

Dr Ines Aniceto

Senior Research Fellow

Accepting applications from PhD students

Email: i.aniceto@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

ORCID

Dr Ivan Korotkin

Senior Research Fellow

Research interests

  • Lithium-ion batteries
  • Numerical methods
  • High-performance computing

Email: i.korotkin@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

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ORCID
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Ms Mozhdeh Shiranirad

Research Fellow in Machine Learning

Email: m.shiranirad@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

ORCID

Dr Philip Greulich

Associate Professor

Research interests

  • Mathematical modelling of stem cell fate choices
  • Universal features of cell lineages
  • Cell population dynamics

Accepting applications from PhD students

Email: p.s.greulich@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ (View in Google Maps)

ORCID
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.
Professor Giampaolo D'Alessandro
Professor

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