School of Mathematical Sciences

Industrial and Applied Mathematics

Industrial and Applied Mathematics covers a wide range of mathematical topics and application, e.g. in engineering, industry, physics, chemistry or biology.

Mathematical modelling of these systems involves appropriate formulation of equations describing the behaviour of, for example, particles, solids, fluids or electromagnetic fields.

Orange and blue fractal


These equations are generally nonlinear and cannot be solved exactly, so various mathematical techniques are used to obtain approximate solutions.  These approaches may include asymptotic methods - when one parameter in the problem is very small, similarity methods - to find a limited class of solutions, bifurcation theory - to give a qualitative description of the solution, or numerical methods - to find approximate solutions with the help of a computer. 


Research Areas

  • Bifurcation theory
  • Elasticity
  • Exponential asymptotics
  • Fluid Mechanics
  • Industrial Mathematics
  • Nonlinear and Statistical optics
  • Nonlinear waves and solitons
  • Nucleation/Coagulation-fragmentation processes
  • Pattern formation
  • Reaction-diffusion equations
  • Uncertainty quantification


In particular, members of the group also coordinate the Wave Modelling Research Group, together with colleagues in Engineering and Physics. 


Group Members


Core members of the group are:

John Billingham

Professor Billingham undertakes a wide range of industrial modelling projects, e.g. on travelling waves in reaction-diffusion systems, thermal barrier coatings, laser ablation and waterjet etching. He collaborates regularly with colleagues in the Faculty of Engineering.


Donald Brown



Stephen Cox

Dr Cox works on projects for modelling switching technologies (class-D amplifiers and power converters), chaotic mixing, thermal convection and pattern formation.


Stephen Creagh

Dr Creagh works on approximation and simulation of high-frequency wave problems, including quantum systems, electromagnetics and sound and vibration, with emphasis on the use of methods originating from the field of "quantum chaos" to understand wave propagation phenomena in classical wave problems, especially in cases where the geometry and/or driving is complex or uncertain. Applications of complex ray tracing to phenomena related to tunnelling and evanescent propagation. He works with the Wave Modelling Research Group.


Gabriele Gradoni



Richard Graham

Dr Graham has a background in rheology, and works in areas including:

  • Equations of state for carbon capture and storage
  • Flow-induced crystallisation of polymer melts
  • Electrophoresis of DNA molecules
  • Dynamics of entangled polymers
  • Neutron scattering from polymers under strong flow
He collaborates regularly with colleagues in the Faculty of Engineering and with industry.
Keith Hopcraft

Dr Hopcraft has interests in both continuum mechanics and in statistical physics with his regular collaborator Eric Jakeman. His work has applications to industry in the energy and manufacturing sectors.


Matteo Icardi



Paul Matthews

Dr Matthews has interests in the areas of fluid mechanics, nonlinear systems, pattern formation, bifurcations with symmetry, magnetohydrodynamics, numerical methods and mathematical biology.


Gareth Parry

Dr Parry carries out research in the mechanics of crystals, in particular into the continuum theory of defective crystals. Recent research has shown how mechanisms of plastic flow emerge naturally from geometrical ideas to do with the microscopic structure of the crystals. He is interested in exploring the recently discovered connection between the structure of crystals with constant dislocation density and the theory of Lie groups.


Matt Scase

Dr Scase works on problems of industrial relevance in fluid mechanics, in particular on turbulence in fluid plumes and jets.


Kostas Soldatos

Dr Soldatos has research interests in solid mechanics, and has made contributions in the area of three- and two-dimensional modelling and analysis of homogeneous and laminated anisotropic composite structures and structural components (elastic beams, etc.).


Gregor Tanner



Richard Tew

Dr Tew works on acoustic, elastic and electromagnetic wave propagation as well as real and complex ray theory, diffraction and scattering of high-frequency waves, exponential asymptotics, fluid-structure interactions and more generally industrial mathematics.




Other members of staff working on problems of industrial relevance include:


  • Daniele Avitabile
  • Steve Coombes
  • Ian Dryden
  • Etienne Farcot
  • Sven Gnutzmann
  • David Hodge



  • Paul Houston
  • Matthew Hubbard
  • Marco Iglesias
  • John King
  • Markus Owen
  • Simon Preston



  • Michael Tretyakov
  • Kris van der Zee
  • Jonathan Wattis
  • Andy Wood
  • Kewei Zhang




Thinking of joining us?

We are keen to create an environment which supports all staff members by providing:





Professor John Billingham

School of Mathematical Sciences

University of Nottingham
University Park

t: +44 (0) 115 95 13846

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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