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.
The development of mathematical, computational and statistical methods to address biological and medical problems.
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
Honorary Distinguished Professor
- +44 (0)29 2087 4827
Lecturer in Applied Mathematics
- 029 208 75863
Lecturer in Applied Mathematics
- +44 (0)29 2087 5259
Lecturer in Applied Mathematics
- +44 (0)29 2087 5570
Lecturer in Applied Mathematics
- +44 (0)29 2087 5116
All seminars are held at 14:10 in Room M/2.06, Senghennydd Road, Cardiff unless stated otherwise.
Programme organiser and contact: Dr Thomas Woolley
4 December 2018
Some spatiotemporal phenomena in biological and physical media
I will present some recent work on problems in complex spatiotemporal environments. I will first discuss diffusion-driven (Turing) instabilities in realistic flow regimes whereby interacting chemical species are advected by Stokes flow in different geometries. Such advection results in changing the regime wherein patterns emerge, as well as modulating their structure in nontrivial ways. I will spend a few minutes discussing systems of Ginzburg-Landau equations, and the role of different kinds of nonlinearities, before moving on to recent results on amplitude death due to cross-phase modulation. Finally I will discuss spatiotemporal fluctuations of infection in metapopulation models of epidemics. The stochasticity in such models will be shown to be essentially negligible for small noise, leading to small fluctuations about the deterministic limit. Nevertheless, control strategies such as vaccination and treatment can be much more difficult even for such small fluctuations, and the form of the equations can lead to an effective additive noise structure which can lead to negative values of the infected proportion of the population, and hence unphysical results. Truncated noise processes can be used to recover essentially all of the qualitative features of these models while preserving non-negative populations, and non-local control strategies can ameliorate some difficulties due to the fluctuating populations. Throughout, the overall theme is on where simple canonical (e.g. linear) thinking can lead to useful understanding of the phenomena, and where such thinking can lead one astray.
27 November 2018
The application of mathematics to the understanding of sporting techniques and tactics: examples and future opportunities
This seminar will discuss how sports science, in particular the sub-disciplines of sports biomechanics and performance analysis, have applied mathematics to aid the technical and tactical understanding of sport. Examples from recent research will be presented, mathematical challenges facing sports scientists in ongoing work will be discussed, and future opportunities for mathematicians to apply their knowledge to the sporting world will be considered. Neil Bezodis is a Senior Lecturer in Biomechanics & Technology in the Applied Sports, Technology, Exercise and Medicine (A-STEM) Research Centre at Swansea University, and has worked on a range of applied biomechanics and performance analysis projects with collaborators including British Athletics and the Rugby Football Union.
20 November 2018
Modelling Allee effects in a transgenic mosquito population during range expansion
Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. I present a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations.
13 November 2018
From a steady plume to periodic puffs during confined carbon dioxide dissolution
It is now widely accepted that the continuous global warming of the atmosphere observed in the last 150 years is partially due to an increase in the atmospheric concentrations of greenhouse gases, and that the storage of carbon dioxide in deep geological formations is a feasible medium term solution to the problem. The storage procedure mainly consists in injecting carbon dioxide into a brine saturated porous formation (aquifer) that is confined by an impermeable formation (cap rock). Because CO2 is partially soluble in water, partial mixing occurs at the brine/CO2 interface, resulting in a mixture that happens to be denser than the resident fluid. Specifically, the dissolution of the supercritical CO2 into the brine at the CO2/brine interface creates a heavy layer of CO2-enriched brine, which destabilises when its thickness becomes sufficiently large. Such a gravitational instability generates convective rolls, which evolve into fingers (plumes) of CO2-brine mixture that sink down to the bottom of the brine layer.
We present here an extensive study of the stability of a single laminar plume due to gravity-induced. A topless vertical tube containing water is put in a pressure cell filled with carbon dioxide. The diffusion of CO2 at the free surface creates a thin layer of heavy fluid underneath the surface. This unstable density gradient generates a steady laminar plume which goes downward through the entire tube. A quasi-steady flow settles in the tube, filling gradually the bottom of the tube with heavy fluid. During this laminar regime, the velocity of the plume slowly decreases due to the build-up of the background density gradient. Surprisingly, despite the decrease of the Reynolds number, the laminar plume suddenly destabilises via a varicose mode into periodic pulsed puffs after an onset time which depends on the height of the tube and on the solutal Rayleigh number. This periodic regime is followed by an aperiodic regime, which lasts until the complete saturation of the solution. The observed destabilisation is explained as a result of the interplay between the feedback of the global recirculating flow and the progressive density stratification of the background fluid.
6 November 2018
Towards a morphoelastic model of a buckling intestinal crypt
The intestinal epithelium exhibits remarkable rates of self-renewal to protect the small intestine and colon during digestion and injury. This monolayer is maintained by the crypts of Liehberkühn, test-tube-shaped glands that are robust in morphology and structure. While the molecular processes governing crypt morphogenesis are relatively well understood, there is a lack of understanding on the relevant biomechanical factors, especially in the context of colorectal cancer progression and injury response. In this talk, we will present our work on understanding the mechanics of crypt morphogenesis, using the framework of morphoelastic rods, which extends Kirchhoff rod theory to account for local growth. The crypt and its underlying stroma are modelled as a growing, planar rod attached to a foundation. We first discuss our analysis on the effect of spatial heterogeneity within different material properties on a simplified version of the model. We then show how insights from this analysis have informed further biological specialisations, which has constituted the majority of current work.
30 October 2018
Quantitative approaches to investigating epithelial morphogenesis
Recent years have seen a rise in quantitative data for many biological applications. These new data can lead to challenges at each stage of the scientific method. We need to design quantitative hypotheses through mathematical models, make quantitative experimental predictions, devise methods for quantitative data analysis, and design methods for quantitative inference using models and data. My work aims to enable this quantitative transition for the integrative analysis of morphogenesis in epithelia, one of the major tissue types in animals. In this talk, I will show how I used mathematical approaches to design and analyse cell-based models of embryonic epithelia, how I use these models to make explicit experimental predictions, and how I use Bayesian techniques to compare cell-based computational models with live-imaging microscopy data.
23 October 2018
The Myriad Hues of Liquid Crystals Across Mathematics, Physics and Applications
Liquid crystals are classical examples of partially ordered materials intermediate between conventional solids and liquids. The concept of partial order is ubiquitous in nature and in this talk, we focus on nematic liquid crystals. Nematics are anisotropic liquids with no translational order and long-range orientational order, featured by the existence of special distinguished directions. We review the main continuum theories for nematic liquid crystals, the essential mathematical frameworks and how they are used to describe pattern formation in confined geometries. The pattern formation and the observable singularities arise from a complex interplay of geometry, topology, boundary effects and material properties. New analytical advances and computational techniques allow us to beautifully model pattern formation in exotic geometries, structural transitions and equally importantly, how to control structural transitions by experimental parameters to get desired properties. I will present some illustrative examples of pattern formation for nematic liquid crystals in square wells and shells emphasizing the mathematical intricacies, the underpinning physics and the plethora of novel applications in materials research in the near future.
16 October 2018
Noemi Picco (St John’s College, Mathematical Institute, University of Oxford)
Modelling Transient Traits of Cortex Evolution: the Importance of Evolving Cell Division Strategies
The brain is the most complicated organ of any animal, formed and sculpted over 500 million years of evolution. The cerebral cortex is the folded grey matter that forms the outside of the brain, and is the seat of higher cognitive function.
Many factors influence how neurogenesis in the cortex differs between species, including the types of neurons and neural progenitor cells, the different ways in which they proliferate and differentiate, and the length of the process. Critically, to fully understand the development of the cortex we are faced with the challenge of understanding the temporal changes in cell division strategy. Combining mathematical modelling and experimental observations we incorporate these different factors to model development and evolution of the mammalian cortex.
A key determinant of the neuronal production is the modulation of proliferative (self-amplifying) and differentiative (neurogenic) divisions, as well as programmed cell death. In this talk I will present models at different scales that can help us understanding how temporal changes in cell division and death events result in the final cortical size.
Joint work with Thomas Woolley (Cardiff University), Fernando García-Moreno (Achucarro Basque Center for Neuroscience), Zoltán Molnár (University of Oxford) and Philip Maini (University of Oxford). Funding: St John’s College, Oxford.
9 October 2018
Louise Dyson (University of Warwick)
From ants to epidemiology: applications of mathematical modelling in biology and epidemiology
From discovering the secrets of ant colony decisions to the modelling of treatment campaigns for eliminating endemic diseases, I am interested in the application of mathematical modelling to many different systems. In this talk I will show examples where modelling has helped to interpret and shape experimental work and data collection. I will present two case studies: understanding noise-induced bistable states in a simple model of the distribution of worker ants between two food sources; and determining if household-level contact tracing can lead to the elimination of yaws.
2 October 2018
Dr Mokarram Hossain (Zienkiewicz Centre for Computational Engineering, Swansea University)
Modelling curing process in polymers: From a single field to multiple fields
In this talk, the modelling of curing process from a single field to multiple fields will be discussed. The curing of polymers is a very complex process involving a series of chemical reactions which result in the conversion of liquid low molecular weight monomer mixtures into highly cross-linked solid macromolecular structures. This phase transition from a viscous fluid to a viscoelastic solid can be modelled by a constitutive relation which is based on a temporal evolution of shear modulus and relaxation time. Some numerical examples demonstrate the capability of the model to correctly represent the evolution of elastic and inelastic material properties as well as the volume shrinkage taking place during the curing process . Furthermore, in dielectric elastomers, a large actuation voltage is required to produce a desired mechanical deformation. To reduce the amount of the actuation voltage, several mechanisms can be applied and the inclusion of high dielectric permittivity fillers in the matrix material in the uncured stage is one of them . Moreover, to obtain a maximum advantage from the high dielectric permittivity fillers, an electric field is applied during the curing process, which helps the particles to align in a preferred direction. In this contribution, we will show how to extend a phenomenologically-inspired large strain framework for simulating the curing process of polymers in a single field can be extended to work under the use of an electro-mechanically coupled load. The application of the proposed approach is demonstrated via some numerical examples. These illustrate that the model can predict common features in particle-filled electro-active polymers undergoing curing processes in the presence of an electro-mechanically coupled load [3,4].
 Hossain et al. (2009), A small-strain model to simulate the curing of thermosets, Comput., Mech., 43, 2009
 Romasanta et al. Increasing the performance of dielectric elastomer actuators : A review from the materials perspective, Progess in Polymer Science, 51, 188-211, 2015
 Hossain, M; Steinmann, P; Modelling electro-active polymers with a dispersion-type anisotropy, Smart Materials and Structures, 27(2), 2018
 Hossain M, Modelling the curing process with a dispersion-type anisotropy in particle-filled electro-active polymers, In review (2018)
11 September 2018
Associate Professor Amin Chabchoub (The University of Sydney)
Hydrodynamic Shock and Rogue Waves