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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

Image of graphene

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.

People, projects, publications and PhDs

People

Professor Christopher Howls

Professor of Mathematics

Research interests

  • Asymptotic Analysis
  • Semiclassical Analysis
  • Applied Mathematics

Accepting applications from PhD students

Connect with Christopher

Email: [email protected]

Tel: +44 23 8059 5145

ORCID

Dr David Turton

Principal Research Fellow

Research interests

  • String theory
  • Black holes
  • Holography

Accepting applications from PhD students

Connect with David

Email: [email protected]

Tel: +44 23 8059 5142

Google Scholar
ORCID

Miss Elisa Marieni

Research interests

  • Quantum Field Theory
  • Gauge Theories
  • Topological Field Theory
Connect with Elisa

Email: [email protected]

ORCID
LinkedIn

Dr Felix Haehl

UKRI/ERC Frontier Principal Res Fellow

Research interests

  • AdS/CFT duality
  • Black holes in quantum gravity
  • Conformal field theory

Accepting applications from PhD students

Connect with Felix

Email: [email protected]

Tel: +44 2380597493

Google Scholar
ORCID

Emeritus Professor Giampaolo D'Alessandro

Research interests

  • Liquid crystals
  • Optics
  • Mathematical modelling
Connect with Giampaolo

Email: [email protected]

Tel: +44 23 8059 3650

ORCID

Professor Giles Richardson

Professor

Research interests

  • Modelling renewable energy storage and generation
  • Modelling in biomedicine

Accepting applications from PhD students

Connect with Giles

Email: [email protected]

Tel: +44 23 8059 3659

Google Scholar
ORCID

Professor Ian Hawke

Professor

Research interests

  • Numerical relativity
  • Neutron Stars
  • Gravitational waves

Accepting applications from PhD students

Connect with Ian

Email: [email protected]

Tel: +44 23 8059 8993

ORCID

Professor Ian Jones

Professor of Mathematical Physics

Research interests

  • Gravitational wave astronomy
  • Neutron stars
  • Radio pulsars

Accepting applications from PhD students

Connect with Ian

Email: [email protected]

Tel: +44 23 8059 4829

ORCID

Dr Ines Aniceto

Principal Research Fellow

Research interests

  • 1. Perturbation theory and asymptotic analysis of N=non-perturbative phenomena in AdS/CFT
  • 2. Exponential Asymptotics and resurgence in non-linear ODEs and discrete equations
  • 3.  Exact quantisation methods for field theoretic observables

Accepting applications from PhD students

Connect with Ines

Email: [email protected]

Tel: +44 23 8059 3685

ORCID

Dr Ioannis Matthaiakakis

STFC Research Fellow

Research interests

  • Holography and AdS/CMT correspondence
  • Hydrodynamics
  • Gravity
Connect with Ioannis

Email: [email protected]

Google Scholar
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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