Applied and Computational Mathematics Research Group

Our research in applied and computational mathematics includes: theoretical and applied fluid mechanics, mathematics and mechanics of solids, mathematical biology, applied analysis, and numerical analysis and scientific computing.

Our research in the area of applied and computational mathematics is informed by problems at the interface with physical sciences, biological sciences and engineering and there are many productive interdisciplinary collaborations within Cardiff University and further afield. Interdisciplinary collaborators at Cardiff University include colleagues in Biosciences, Earth and Environmental Sciences, and Engineering.

Our national and international collaborators include research groups at Barcelona, Oxford, Cambridge, MIT, Manchester, Edinburgh, Cyprus, Duke, Mexico City

Our research has applications in the early detection of tsunamis, deep water transportation, granular flows such as debris avalanches, subsea landslides and pharmaceutical powder processing, biomechanics, materials science, process engineering, calcium signalling in fertilization and embryogenesis, magnetic targeting for bio applications and other biofluids challenges, morphogenesis, cellular motion, Stochastic dynamics, neurobiology, oncology.

The group hosts the Cardiff University Student Chapter of the Society for Industrial and Applied Mathematics and the Institute of Mathematics and its Applications (SIAM-IMA Student Chapter) which encompasses postgraduate students and faculty members from across the University who are interested in mathematics or scientific computing and their real-world applications.

Research

The main areas of research within the current group are:

Theoretical and applied fluid mechanics

Free-surface flows, dynamics of liquid films and jets, hydrodynamic stability theory, laminar-turbulent transition mechanisms, boundary-layer and wake flow instabilities, acoustic-gravity waves, viscoelastic flows, bubble dynamics, constitutive modelling of polymeric liquids, granular flow, geophysical flow modelling, non-Brownian suspensions.

Mathematics and mechanics of solids

Nonlinear elasticity, nonlinear viscoelasticity, contact problems, limit states analysis, constitutive modelling in materials science, strain-limiting theory of material response.

Mathematical biology

The development of mathematical, computational and statistical methods to address biological and medical problems.

Applied analysis

Inverse problems in materials modelling, homogenisation and the mechanics of composites. Calculus of variations.

Numerical analysis and scientific computing

The development and analysis of algorithms for the numerical solution of partial differential applications.

We are keen to supervise students in these areas. To give a more specific flavour of our work to date, recent examples of PhD topics supervised by our group include:

Stochastic finite strain analysis of inhomogeneous hyperelastic solids
Underwater earthquake characterization by acoustic radiation analysis
Stochastic modelling and analysis of homogeneous hyperelastic solids
Debonding and stretching of biogenic cellular structures
Linear stability and transient behaviour of viscoelastic fluids in boundary layers
Efficient spectral element methods for partial differential equations
Droplet dynamics on heterogeneous surfaces
Theoretical and computational modelling of compressible and non-isothermal viscoelastic fluids.