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Applied and Computational Mathematics Research Group

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.

Our national and international collaborators include research groups at Imperial, Oxford, Cambridge, Warwick, Swansea, Canberra, Curtin (Perth), Perth, Delft, Northwestern, Ljubljana and Montréal.

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.

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, boundary layer flow control, viscoelastic flows, bubble dynamics, constitutive modelling of polymeric liquids.

Mathematics and mechanics of solids

Nonlinear elasticity, contact problems, limit states analysis, constitutive modelling in materials science.

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.

Numerical analysis and scientific computing

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

Head of Group

Professor Tim Phillips

Professor Tim Phillips

Head of School, Mathematics

Email:
phillipstn@cardiff.ac.uk
Telephone:
+44 (0)29 2087 4194

Academic staff

Dr Mikhail Cherdantsev

Dr Mikhail Cherdantsev

Lecturer

Email:
cherdantsevm@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5549
Dr Chris Davies

Dr Chris Davies

Reader

Email:
daviesc9@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5531
Professor Russell Davies

Professor Russell Davies

Honorary Distinguished Professor

Email:
daviesr@cardiff.ac.uk
Telephone:
+44 (0)29 2087 4827
Dr Usama Kadri

Dr Usama Kadri

Lecturer in Applied Mathematics

Email:
kadriu@cardiff.ac.uk
Telephone:
029 208 75863
Dr Katerina Kaouri

Dr Katerina Kaouri

Lecturer in Applied Mathematics

Email:
kaourik@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5259
Dr Angela Mihai

Dr Angela Mihai

Reader in Applied Mathematics

Email:
mihaila@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5570
Professor John Pryce

Professor John Pryce

Emeritus Professor

Email:
prycejd1@cardiff.ac.uk
Telephone:
+44 (0)29 2087 4207
Dr Nikos Savva

Dr Nikos Savva

Lecturer in Applied Mathematics

Email:
savvan@cardiff.ac.uk
Telephone:
+44 (0)29 2087 5116
Dr Thomas Woolley

Dr Thomas Woolley

Lecturer in Applied Mathematics

Email:
woolleyt1@cardiff.ac.uk
Telephone:
02920 870618

Seminars

All seminars are held on Tuesday 14:10-15:00 in Room M/0.34, Mathematics Institute, Senghennydd Road, Cardiff, unless stated otherwise.

Programme organiser and contact:  Dr Angela Mihai

DateSpeakerSeminar
3 March 2020Dr Zahir Hussain,
Manchester Metropolitan University

To be confirmed

11 February 2020Dr Paul Ledger,
Swansea University

To be confirmed

4 February 2020Dr Hermes Gadelha,
University of Bristol

To be confirmed

28 January 2020

Dr Pierre Ricco, University of Sheffield

To be confirmed

26 November 2019

Dr Eugeny Buldakov, UCL

To be confirmed

19 November 2019

Professor Alison Raby, University of Plymouth

To be confirmed

12 November 2019

Professor Peter Schmid, Imperial College

Koopman analysis and dynamic modes

Koopman analysis is a mathematical technique that embeds nonlinear dynamical systems into a linear framework based on a sequence of observables of the state vector. Computing the proper embeddings that result in a closed linear system requires the extraction of the eigenfunctions of the Koopman operator from data. Dynamic modes approximate these eigenfunctions via a tailored data-matrix decomposition. The associated spectrum of this decomposition is given by a convex optimization problem that balances data-conformity with sparsity of the spectrum. The Koopman-dynamic mode process will be discussed and illustrated on physical examples.

5 November 2019

Professor Derek Moulton, University of Oxford

Morphorods: the mechanics of growing elastic rods

Filamentary structures display a wide range of patterns and behaviours, such as in polymers, vines, axons, trachea, and elephant trunks, to name a few. Mechanically, a key feature prevalent in biological filaments is growth. Growth is the critical element underlying biological pattern formation and may also be utilised in other ways, for instance to generate movement or provide mechanical support against external loads. Due to their inherent slenderness, the mechanical behaviour of growing filaments is well-characterised by a one-dimensional continuum representation. We have in recent years developed a framework for modelling such structures by including growth in classical elastic rod equations; we  term these morphoelastic rods or simply morphorods.

In this talk I will first briefly outline our framework and demonstrate the variety of applications and patterns that can be generated. I will then turn to our current efforts to confront the significant challenge of incorporating tissue level properties in the morphorod setting. A motivating example is in gravitropic growth, in which a branch or stem develops curvature in response to an external field (gravity). To model such a multiscale process we have developed a robust system of mapping from growth in a 3D finite elasticity setting to a 1D morphorod.

22 October 2019

Professor Catherine Powell, University of Manchester

Adaptive stochastic Galerkin approximation for parameter-dependent linear elasticity problems

In this talk, we give an overview of some recent work on the use of stochastic Galerkin mixed finite element methods (SG-MFEMs) for performing forward uncertainty quantification in parameter-dependent linear elasticity equations. Starting from a three-field PDE model in which the Young's modulus is represented as an affine function of a set of parameters, we discuss how to implement SG-MFEM approximation and introduce a novel a posteriori error estimation scheme. We examine the error in the natural weighted norm with respect to which the weak formulation is stable. Exploiting the connection between this norm and the underlying PDE operator also leads to an efficient preconditioning strategy.

Unlike standard residual-based error estimation schemes, the proposed strategy requires the solution of auxiliary problems on carefully constructed detail spaces on both the spatial and parameter domains. We establish upper and lower bounds for the SG-MFEM approximation error in terms of the proposed estimator. The constants in the bounds are independent of the Poisson ratio as well as the SG-MFEM discretisation parameters, meaning that the estimator is robust in the incompressible limit.

Finally, we briefly discuss proxies for the error reduction associated with potential enrichments of the SG-MFEM spaces and use these to develop an adaptive algorithm that terminates when the estimated error falls below a user-prescribed tolerance.

15 October 2019

Dr Ian Griffiths, University of Oxford

iPhones, Dysons and Cheerios: using fluid dynamics to aid technology

As technology continues to advance, new strategies involving a range of scientific disciplines are required. Mathematicians can provide frameworks to predict operating regimes and manufacture techniques. In this talk we show how mathematics can be used to help in the fabrication of precision glass, for smartphones and new flexible devices; the development of superior filters for vacuum cleaners; and the manufacture of unusual cereal shapes (like Nestlé Alphabet cereals).

8 October 2019

Professor Jonathan Healey, Keel University

Fractal neutral curves in the linear stability of shear flows

Rayleigh showed that the linear stability properties of inviscid shear
layers are described by a second order linear ODE, and the effects of
buoyancy due to fluid density variations were included by Taylor and
Goldstein in 1931, resulting in one additional linear term in
Rayleigh's equation (for weakly varying density). Rayleigh's inflexion
point theorem no longer applies and Taylor gave an example where
stable stratification (density increasing with depth) destabilizes an
inflexionless flow. The Taylor-Goldstein equation is widely used in
many geophysical and astrophysical flow applications. In this talk we
show that this linear ODE can produce neutral curves (separating
stable from unstable regimes) with fractal properties, and discuss
possible implications for nonlinear dynamics.

2019/20 events will be advertised here when the schedule is confirmed.

Past events

Applied and Computational Mathematics Seminars 2018-19

Applied and Computational Mathematics Seminars 2017-18

Applied and Computational Mathematics Seminars 2016-17

Applied and Computational Mathematics Seminars 2015-16